Bitcoin Definition

Technical: Taproot: Why Activate?

This is a follow-up on https://old.reddit.com/Bitcoin/comments/hqzp14/technical_the_path_to_taproot_activation/
Taproot! Everybody wants it!! But... you might ask yourself: sure, everybody else wants it, but why would I, sovereign Bitcoin HODLer, want it? Surely I can be better than everybody else because I swapped XXX fiat for Bitcoin unlike all those nocoiners?
And it is important for you to know the reasons why you, o sovereign Bitcoiner, would want Taproot activated. After all, your nodes (or the nodes your wallets use, which if you are SPV, you hopefully can pester to your wallet vendoimplementor about) need to be upgraded in order for Taproot activation to actually succeed instead of becoming a hot sticky mess.
First, let's consider some principles of Bitcoin.
I'm sure most of us here would agree that the above are very important principles of Bitcoin and that these are principles we would not be willing to remove. If anything, we would want those principles strengthened (especially the last one, financial privacy, which current Bitcoin is only sporadically strong with: you can get privacy, it just requires effort to do so).
So, how does Taproot affect those principles?

Taproot and Your /Coins

Most HODLers probably HODL their coins in singlesig addresses. Sadly, switching to Taproot would do very little for you (it gives a mild discount at spend time, at the cost of a mild increase in fee at receive time (paid by whoever sends to you, so if it's a self-send from a P2PKH or bech32 address, you pay for this); mostly a wash).
(technical details: a Taproot output is 1 version byte + 32 byte public key, while a P2WPKH (bech32 singlesig) output is 1 version byte + 20 byte public key hash, so the Taproot output spends 12 bytes more; spending from a P2WPKH requires revealing a 32-byte public key later, which is not needed with Taproot, and Taproot signatures are about 9 bytes smaller than P2WPKH signatures, but the 32 bytes plus 9 bytes is divided by 4 because of the witness discount, so it saves about 11 bytes; mostly a wash, it increases blockweight by about 1 virtual byte, 4 weight for each Taproot-output-input, compared to P2WPKH-output-input).
However, as your HODLings grow in value, you might start wondering if multisignature k-of-n setups might be better for the security of your savings. And it is in multisignature that Taproot starts to give benefits!
Taproot switches to using Schnorr signing scheme. Schnorr makes key aggregation -- constructing a single public key from multiple public keys -- almost as trivial as adding numbers together. "Almost" because it involves some fairly advanced math instead of simple boring number adding, but hey when was the last time you added up your grocery list prices by hand huh?
With current P2SH and P2WSH multisignature schemes, if you have a 2-of-3 setup, then to spend, you need to provide two different signatures from two different public keys. With Taproot, you can create, using special moon math, a single public key that represents your 2-of-3 setup. Then you just put two of your devices together, have them communicate to each other (this can be done airgapped, in theory, by sending QR codes: the software to do this is not even being built yet, but that's because Taproot hasn't activated yet!), and they will make a single signature to authorize any spend from your 2-of-3 address. That's 73 witness bytes -- 18.25 virtual bytes -- of signatures you save!
And if you decide that your current setup with 1-of-1 P2PKH / P2WPKH addresses is just fine as-is: well, that's the whole point of a softfork: backwards-compatibility; you can receive from Taproot users just fine, and once your wallet is updated for Taproot-sending support, you can send to Taproot users just fine as well!
(P2WPKH and P2WSH -- SegWit v0 -- addresses start with bc1q; Taproot -- SegWit v1 --- addresses start with bc1p, in case you wanted to know the difference; in bech32 q is 0, p is 1)
Now how about HODLers who keep all, or some, of their coins on custodial services? Well, any custodial service worth its salt would be doing at least 2-of-3, or probably something even bigger, like 11-of-15. So your custodial service, if it switched to using Taproot internally, could save a lot more (imagine an 11-of-15 getting reduced from 11 signatures to just 1!), which --- we can only hope! --- should translate to lower fees and better customer service from your custodial service!
So I think we can say, very accurately, that the Bitcoin principle --- that YOU are in control of your money --- can only be helped by Taproot (if you are doing multisignature), and, because P2PKH and P2WPKH remain validly-usable addresses in a Taproot future, will not be harmed by Taproot. Its benefit to this principle might be small (it mostly only benefits multisignature users) but since it has no drawbacks with this (i.e. singlesig users can continue to use P2WPKH and P2PKH still) this is still a nice, tidy win!
(even singlesig users get a minor benefit, in that multisig users will now reduce their blockchain space footprint, so that fees can be kept low for everybody; so for example even if you have your single set of private keys engraved on titanium plates sealed in an airtight box stored in a safe buried in a desert protected by angry nomads riding giant sandworms because you're the frickin' Kwisatz Haderach, you still gain some benefit from Taproot)
And here's the important part: if P2PKH/P2WPKH is working perfectly fine with you and you decide to never use Taproot yourself, Taproot will not affect you detrimentally. First do no harm!

Taproot and Your Contracts

No one is an island, no one lives alone. Give and you shall receive. You know: by trading with other people, you can gain expertise in some obscure little necessity of the world (and greatly increase your productivity in that little field), and then trade the products of your expertise for necessities other people have created, all of you thereby gaining gains from trade.
So, contracts, which are basically enforceable agreements that facilitate trading with people who you do not personally know and therefore might not trust.
Let's start with a simple example. You want to buy some gewgaws from somebody. But you don't know them personally. The seller wants the money, you want their gewgaws, but because of the lack of trust (you don't know them!! what if they're scammers??) neither of you can benefit from gains from trade.
However, suppose both of you know of some entity that both of you trust. That entity can act as a trusted escrow. The entity provides you security: this enables the trade, allowing both of you to get gains from trade.
In Bitcoin-land, this can be implemented as a 2-of-3 multisignature. The three signatories in the multisgnature would be you, the gewgaw seller, and the escrow. You put the payment for the gewgaws into this 2-of-3 multisignature address.
Now, suppose it turns out neither of you are scammers (whaaaat!). You receive the gewgaws just fine and you're willing to pay up for them. Then you and the gewgaw seller just sign a transaction --- you and the gewgaw seller are 2, sufficient to trigger the 2-of-3 --- that spends from the 2-of-3 address to a singlesig the gewgaw seller wants (or whatever address the gewgaw seller wants).
But suppose some problem arises. The seller gave you gawgews instead of gewgaws. Or you decided to keep the gewgaws but not sign the transaction to release the funds to the seller. In either case, the escrow is notified, and if it can sign with you to refund the funds back to you (if the seller was a scammer) or it can sign with the seller to forward the funds to the seller (if you were a scammer).
Taproot helps with this: like mentioned above, it allows multisignature setups to produce only one signature, reducing blockchain space usage, and thus making contracts --- which require multiple people, by definition, you don't make contracts with yourself --- is made cheaper (which we hope enables more of these setups to happen for more gains from trade for everyone, also, moon and lambos).
(technology-wise, it's easier to make an n-of-n than a k-of-n, making a k-of-n would require a complex setup involving a long ritual with many communication rounds between the n participants, but an n-of-n can be done trivially with some moon math. You can, however, make what is effectively a 2-of-3 by using a three-branch SCRIPT: either 2-of-2 of you and seller, OR 2-of-2 of you and escrow, OR 2-of-2 of escrow and seller. Fortunately, Taproot adds a facility to embed a SCRIPT inside a public key, so you can have a 2-of-2 Taprooted address (between you and seller) with a SCRIPT branch that can instead be spent with 2-of-2 (you + escrow) OR 2-of-2 (seller + escrow), which implements the three-branched SCRIPT above. If neither of you are scammers (hopefully the common case) then you both sign using your keys and never have to contact the escrow, since you are just using the escrow public key without coordinating with them (because n-of-n is trivial but k-of-n requires setup with communication rounds), so in the "best case" where both of you are honest traders, you also get a privacy boost, in that the escrow never learns you have been trading on gewgaws, I mean ewww, gawgews are much better than gewgaws and therefore I now judge you for being a gewgaw enthusiast, you filthy gewgawer).

Taproot and Your Contracts, Part 2: Cryptographic Boogaloo

Now suppose you want to buy some data instead of things. For example, maybe you have some closed-source software in trial mode installed, and want to pay the developer for the full version. You want to pay for an activation code.
This can be done, today, by using an HTLC. The developer tells you the hash of the activation code. You pay to an HTLC, paying out to the developer if it reveals the preimage (the activation code), or refunding the money back to you after a pre-agreed timeout. If the developer claims the funds, it has to reveal the preimage, which is the activation code, and you can now activate your software. If the developer does not claim the funds by the timeout, you get refunded.
And you can do that, with HTLCs, today.
Of course, HTLCs do have problems:
Fortunately, with Schnorr (which is enabled by Taproot), we can now use the Scriptless Script constuction by Andrew Poelstra. This Scriptless Script allows a new construction, the PTLC or Pointlocked Timelocked Contract. Instead of hashes and preimages, just replace "hash" with "point" and "preimage" with "scalar".
Or as you might know them: "point" is really "public key" and "scalar" is really a "private key". What a PTLC does is that, given a particular public key, the pointlocked branch can be spent only if the spender reveals the private key of the given public key to you.
Another nice thing with PTLCs is that they are deniable. What appears onchain is just a single 2-of-2 signature between you and the developemanufacturer. It's like a magic trick. This signature has no special watermarks, it's a perfectly normal signature (the pledge). However, from this signature, plus some datta given to you by the developemanufacturer (known as the adaptor signature) you can derive the private key of a particular public key you both agree on (the turn). Anyone scraping the blockchain will just see signatures that look just like every other signature, and as long as nobody manages to hack you and get a copy of the adaptor signature or the private key, they cannot get the private key behind the public key (point) that the pointlocked branch needs (the prestige).
(Just to be clear, the public key you are getting the private key from, is distinct from the public key that the developemanufacturer will use for its funds. The activation key is different from the developer's onchain Bitcoin key, and it is the activation key whose private key you will be learning, not the developer's/manufacturer's onchain Bitcoin key).
So:
Taproot lets PTLCs exist onchain because they enable Schnorr, which is a requirement of PTLCs / Scriptless Script.
(technology-wise, take note that Scriptless Script works only for the "pointlocked" branch of the contract; you need normal Script, or a pre-signed nLockTimed transaction, for the "timelocked" branch. Since Taproot can embed a script, you can have the Taproot pubkey be a 2-of-2 to implement the Scriptless Script "pointlocked" branch, then have a hidden script that lets you recover the funds with an OP_CHECKLOCKTIMEVERIFY after the timeout if the seller does not claim the funds.)

Quantum Quibbles!

Now if you were really paying attention, you might have noticed this parenthetical:
(technical details: a Taproot output is 1 version byte + 32 byte public key, while a P2WPKH (bech32 singlesig) output is 1 version byte + 20 byte public key hash...)
So wait, Taproot uses raw 32-byte public keys, and not public key hashes? Isn't that more quantum-vulnerable??
Well, in theory yes. In practice, they probably are not.
It's not that hashes can be broken by quantum computes --- they're still not. Instead, you have to look at how you spend from a P2WPKH/P2PKH pay-to-public-key-hash.
When you spend from a P2PKH / P2WPKH, you have to reveal the public key. Then Bitcoin hashes it and checks if this matches with the public-key-hash, and only then actually validates the signature for that public key.
So an unconfirmed transaction, floating in the mempools of nodes globally, will show, in plain sight for everyone to see, your public key.
(public keys should be public, that's why they're called public keys, LOL)
And if quantum computers are fast enough to be of concern, then they are probably fast enough that, in the several minutes to several hours from broadcast to confirmation, they have already cracked the public key that is openly broadcast with your transaction. The owner of the quantum computer can now replace your unconfirmed transaction with one that pays the funds to itself. Even if you did not opt-in RBF, miners are still incentivized to support RBF on RBF-disabled transactions.
So the extra hash is not as significant a protection against quantum computers as you might think. Instead, the extra hash-and-compare needed is just extra validation effort.
Further, if you have ever, in the past, spent from the address, then there exists already a transaction indelibly stored on the blockchain, openly displaying the public key from which quantum computers can derive the private key. So those are still vulnerable to quantum computers.
For the most part, the cryptographers behind Taproot (and Bitcoin Core) are of the opinion that quantum computers capable of cracking Bitcoin pubkeys are unlikely to appear within a decade or two.
So:
For now, the homomorphic and linear properties of elliptic curve cryptography provide a lot of benefits --- particularly the linearity property is what enables Scriptless Script and simple multisignature (i.e. multisignatures that are just 1 signature onchain). So it might be a good idea to take advantage of them now while we are still fairly safe against quantum computers. It seems likely that quantum-safe signature schemes are nonlinear (thus losing these advantages).

Summary

I Wanna Be The Taprooter!

So, do you want to help activate Taproot? Here's what you, mister sovereign Bitcoin HODLer, can do!

But I Hate Taproot!!

That's fine!

Discussions About Taproot Activation

submitted by almkglor to Bitcoin [link] [comments]

Atomic swaps between Bitcoin and cryptocurrencies without scripts (e.g. Nano, Monero, & Meros)

Some of y'all might find this interesting. From PlasmaPower on Discord:
I've been collaborating with @Kayaba | MR, the developer of Meros, to make https://github.com/MerosCrypto/asmr which allows for atomic swaps between Bitcoin and cryptocurrencies without scripts, like Nano, Monero, and Meros. Right now it only supports Meros, but we've built it to be extensible, and I'll be making a PR to add Nano support soon
This is based off of h4sh3d's work https://raw.githubusercontent.com/h4sh3d/xmr-btc-atomic-swap/mastewhitepapexmr-btc.pdf which is in turn based off of Lloyd Fournier's work https://raw.githubusercontent.com/LLFourn/one-time-VES/mastemain.pdf . Thanks @sev for linking me this in nanotrade a while back! It's always fun to implement some new cryptography
This is still just a proof of concept for now though, I definitely wouldn't use it with any serious funds. In theory, it should be atomic (Kayaba has implemented the refund paths), but in practice we might've missed something, and it doesn't save the state to disk so if e.g. you lose power you'll lose funds.
Imagine being able to swap Nano directly for BTC or XMR without an exchange. That would be pretty awesome 😮
submitted by Qwahzi to nanocurrency [link] [comments]

[ Bitcoin ] Technical: Taproot: Why Activate?

Topic originally posted in Bitcoin by almkglor [link]
This is a follow-up on https://old.reddit.com/Bitcoin/comments/hqzp14/technical_the_path_to_taproot_activation/
Taproot! Everybody wants it!! But... you might ask yourself: sure, everybody else wants it, but why would I, sovereign Bitcoin HODLer, want it? Surely I can be better than everybody else because I swapped XXX fiat for Bitcoin unlike all those nocoiners?
And it is important for you to know the reasons why you, o sovereign Bitcoiner, would want Taproot activated. After all, your nodes (or the nodes your wallets use, which if you are SPV, you hopefully can pester to your wallet vendoimplementor about) need to be upgraded in order for Taproot activation to actually succeed instead of becoming a hot sticky mess.
First, let's consider some principles of Bitcoin.
I'm sure most of us here would agree that the above are very important principles of Bitcoin and that these are principles we would not be willing to remove. If anything, we would want those principles strengthened (especially the last one, financial privacy, which current Bitcoin is only sporadically strong with: you can get privacy, it just requires effort to do so).
So, how does Taproot affect those principles?

Taproot and Your /Coins

Most HODLers probably HODL their coins in singlesig addresses. Sadly, switching to Taproot would do very little for you (it gives a mild discount at spend time, at the cost of a mild increase in fee at receive time (paid by whoever sends to you, so if it's a self-send from a P2PKH or bech32 address, you pay for this); mostly a wash).
(technical details: a Taproot output is 1 version byte + 32 byte public key, while a P2WPKH (bech32 singlesig) output is 1 version byte + 20 byte public key hash, so the Taproot output spends 12 bytes more; spending from a P2WPKH requires revealing a 32-byte public key later, which is not needed with Taproot, and Taproot signatures are about 9 bytes smaller than P2WPKH signatures, but the 32 bytes plus 9 bytes is divided by 4 because of the witness discount, so it saves about 11 bytes; mostly a wash, it increases blockweight by about 1 virtual byte, 4 weight for each Taproot-output-input, compared to P2WPKH-output-input).
However, as your HODLings grow in value, you might start wondering if multisignature k-of-n setups might be better for the security of your savings. And it is in multisignature that Taproot starts to give benefits!
Taproot switches to using Schnorr signing scheme. Schnorr makes key aggregation -- constructing a single public key from multiple public keys -- almost as trivial as adding numbers together. "Almost" because it involves some fairly advanced math instead of simple boring number adding, but hey when was the last time you added up your grocery list prices by hand huh?
With current P2SH and P2WSH multisignature schemes, if you have a 2-of-3 setup, then to spend, you need to provide two different signatures from two different public keys. With Taproot, you can create, using special moon math, a single public key that represents your 2-of-3 setup. Then you just put two of your devices together, have them communicate to each other (this can be done airgapped, in theory, by sending QR codes: the software to do this is not even being built yet, but that's because Taproot hasn't activated yet!), and they will make a single signature to authorize any spend from your 2-of-3 address. That's 73 witness bytes -- 18.25 virtual bytes -- of signatures you save!
And if you decide that your current setup with 1-of-1 P2PKH / P2WPKH addresses is just fine as-is: well, that's the whole point of a softfork: backwards-compatibility; you can receive from Taproot users just fine, and once your wallet is updated for Taproot-sending support, you can send to Taproot users just fine as well!
(P2WPKH and P2WSH -- SegWit v0 -- addresses start with bc1q; Taproot -- SegWit v1 --- addresses start with bc1p, in case you wanted to know the difference; in bech32 q is 0, p is 1)
Now how about HODLers who keep all, or some, of their coins on custodial services? Well, any custodial service worth its salt would be doing at least 2-of-3, or probably something even bigger, like 11-of-15. So your custodial service, if it switched to using Taproot internally, could save a lot more (imagine an 11-of-15 getting reduced from 11 signatures to just 1!), which --- we can only hope! --- should translate to lower fees and better customer service from your custodial service!
So I think we can say, very accurately, that the Bitcoin principle --- that YOU are in control of your money --- can only be helped by Taproot (if you are doing multisignature), and, because P2PKH and P2WPKH remain validly-usable addresses in a Taproot future, will not be harmed by Taproot. Its benefit to this principle might be small (it mostly only benefits multisignature users) but since it has no drawbacks with this (i.e. singlesig users can continue to use P2WPKH and P2PKH still) this is still a nice, tidy win!
(even singlesig users get a minor benefit, in that multisig users will now reduce their blockchain space footprint, so that fees can be kept low for everybody; so for example even if you have your single set of private keys engraved on titanium plates sealed in an airtight box stored in a safe buried in a desert protected by angry nomads riding giant sandworms because you're the frickin' Kwisatz Haderach, you still gain some benefit from Taproot)
And here's the important part: if P2PKH/P2WPKH is working perfectly fine with you and you decide to never use Taproot yourself, Taproot will not affect you detrimentally. First do no harm!

Taproot and Your Contracts

No one is an island, no one lives alone. Give and you shall receive. You know: by trading with other people, you can gain expertise in some obscure little necessity of the world (and greatly increase your productivity in that little field), and then trade the products of your expertise for necessities other people have created, all of you thereby gaining gains from trade.
So, contracts, which are basically enforceable agreements that facilitate trading with people who you do not personally know and therefore might not trust.
Let's start with a simple example. You want to buy some gewgaws from somebody. But you don't know them personally. The seller wants the money, you want their gewgaws, but because of the lack of trust (you don't know them!! what if they're scammers??) neither of you can benefit from gains from trade.
However, suppose both of you know of some entity that both of you trust. That entity can act as a trusted escrow. The entity provides you security: this enables the trade, allowing both of you to get gains from trade.
In Bitcoin-land, this can be implemented as a 2-of-3 multisignature. The three signatories in the multisgnature would be you, the gewgaw seller, and the escrow. You put the payment for the gewgaws into this 2-of-3 multisignature address.
Now, suppose it turns out neither of you are scammers (whaaaat!). You receive the gewgaws just fine and you're willing to pay up for them. Then you and the gewgaw seller just sign a transaction --- you and the gewgaw seller are 2, sufficient to trigger the 2-of-3 --- that spends from the 2-of-3 address to a singlesig the gewgaw seller wants (or whatever address the gewgaw seller wants).
But suppose some problem arises. The seller gave you gawgews instead of gewgaws. Or you decided to keep the gewgaws but not sign the transaction to release the funds to the seller. In either case, the escrow is notified, and if it can sign with you to refund the funds back to you (if the seller was a scammer) or it can sign with the seller to forward the funds to the seller (if you were a scammer).
Taproot helps with this: like mentioned above, it allows multisignature setups to produce only one signature, reducing blockchain space usage, and thus making contracts --- which require multiple people, by definition, you don't make contracts with yourself --- is made cheaper (which we hope enables more of these setups to happen for more gains from trade for everyone, also, moon and lambos).
(technology-wise, it's easier to make an n-of-n than a k-of-n, making a k-of-n would require a complex setup involving a long ritual with many communication rounds between the n participants, but an n-of-n can be done trivially with some moon math. You can, however, make what is effectively a 2-of-3 by using a three-branch SCRIPT: either 2-of-2 of you and seller, OR 2-of-2 of you and escrow, OR 2-of-2 of escrow and seller. Fortunately, Taproot adds a facility to embed a SCRIPT inside a public key, so you can have a 2-of-2 Taprooted address (between you and seller) with a SCRIPT branch that can instead be spent with 2-of-2 (you + escrow) OR 2-of-2 (seller + escrow), which implements the three-branched SCRIPT above. If neither of you are scammers (hopefully the common case) then you both sign using your keys and never have to contact the escrow, since you are just using the escrow public key without coordinating with them (because n-of-n is trivial but k-of-n requires setup with communication rounds), so in the "best case" where both of you are honest traders, you also get a privacy boost, in that the escrow never learns you have been trading on gewgaws, I mean ewww, gawgews are much better than gewgaws and therefore I now judge you for being a gewgaw enthusiast, you filthy gewgawer).

Taproot and Your Contracts, Part 2: Cryptographic Boogaloo

Now suppose you want to buy some data instead of things. For example, maybe you have some closed-source software in trial mode installed, and want to pay the developer for the full version. You want to pay for an activation code.
This can be done, today, by using an HTLC. The developer tells you the hash of the activation code. You pay to an HTLC, paying out to the developer if it reveals the preimage (the activation code), or refunding the money back to you after a pre-agreed timeout. If the developer claims the funds, it has to reveal the preimage, which is the activation code, and you can now activate your software. If the developer does not claim the funds by the timeout, you get refunded.
And you can do that, with HTLCs, today.
Of course, HTLCs do have problems:
Fortunately, with Schnorr (which is enabled by Taproot), we can now use the Scriptless Script constuction by Andrew Poelstra. This Scriptless Script allows a new construction, the PTLC or Pointlocked Timelocked Contract. Instead of hashes and preimages, just replace "hash" with "point" and "preimage" with "scalar".
Or as you might know them: "point" is really "public key" and "scalar" is really a "private key". What a PTLC does is that, given a particular public key, the pointlocked branch can be spent only if the spender reveals the private key of the given private key to you.
Another nice thing with PTLCs is that they are deniable. What appears onchain is just a single 2-of-2 signature between you and the developemanufacturer. It's like a magic trick. This signature has no special watermarks, it's a perfectly normal signature (the pledge). However, from this signature, plus some datta given to you by the developemanufacturer (known as the adaptor signature) you can derive the private key of a particular public key you both agree on (the turn). Anyone scraping the blockchain will just see signatures that look just like every other signature, and as long as nobody manages to hack you and get a copy of the adaptor signature or the private key, they cannot get the private key behind the public key (point) that the pointlocked branch needs (the prestige).
(Just to be clear, the public key you are getting the private key from, is distinct from the public key that the developemanufacturer will use for its funds. The activation key is different from the developer's onchain Bitcoin key, and it is the activation key whose private key you will be learning, not the developer's/manufacturer's onchain Bitcoin key).
So:
Taproot lets PTLCs exist onchain because they enable Schnorr, which is a requirement of PTLCs / Scriptless Script.
(technology-wise, take note that Scriptless Script works only for the "pointlocked" branch of the contract; you need normal Script, or a pre-signed nLockTimed transaction, for the "timelocked" branch. Since Taproot can embed a script, you can have the Taproot pubkey be a 2-of-2 to implement the Scriptless Script "pointlocked" branch, then have a hidden script that lets you recover the funds with an OP_CHECKLOCKTIMEVERIFY after the timeout if the seller does not claim the funds.)

Quantum Quibbles!

Now if you were really paying attention, you might have noticed this parenthetical:
(technical details: a Taproot output is 1 version byte + 32 byte public key, while a P2WPKH (bech32 singlesig) output is 1 version byte + 20 byte public key hash...)
So wait, Taproot uses raw 32-byte public keys, and not public key hashes? Isn't that more quantum-vulnerable??
Well, in theory yes. In practice, they probably are not.
It's not that hashes can be broken by quantum computes --- they're still not. Instead, you have to look at how you spend from a P2WPKH/P2PKH pay-to-public-key-hash.
When you spend from a P2PKH / P2WPKH, you have to reveal the public key. Then Bitcoin hashes it and checks if this matches with the public-key-hash, and only then actually validates the signature for that public key.
So an unconfirmed transaction, floating in the mempools of nodes globally, will show, in plain sight for everyone to see, your public key.
(public keys should be public, that's why they're called public keys, LOL)
And if quantum computers are fast enough to be of concern, then they are probably fast enough that, in the several minutes to several hours from broadcast to confirmation, they have already cracked the public key that is openly broadcast with your transaction. The owner of the quantum computer can now replace your unconfirmed transaction with one that pays the funds to itself. Even if you did not opt-in RBF, miners are still incentivized to support RBF on RBF-disabled transactions.
So the extra hash is not as significant a protection against quantum computers as you might think. Instead, the extra hash-and-compare needed is just extra validation effort.
Further, if you have ever, in the past, spent from the address, then there exists already a transaction indelibly stored on the blockchain, openly displaying the public key from which quantum computers can derive the private key. So those are still vulnerable to quantum computers.
For the most part, the cryptographers behind Taproot (and Bitcoin Core) are of the opinion that quantum computers capable of cracking Bitcoin pubkeys are unlikely to appear within a decade or two.
So:
For now, the homomorphic and linear properties of elliptic curve cryptography provide a lot of benefits --- particularly the linearity property is what enables Scriptless Script and simple multisignature (i.e. multisignatures that are just 1 signature onchain). So it might be a good idea to take advantage of them now while we are still fairly safe against quantum computers. It seems likely that quantum-safe signature schemes are nonlinear (thus losing these advantages).

Summary

I Wanna Be The Taprooter!

So, do you want to help activate Taproot? Here's what you, mister sovereign Bitcoin HODLer, can do!

But I Hate Taproot!!

That's fine!

Discussions About Taproot Activation

almkglor your post has been copied because one or more comments in this topic have been removed. This copy will preserve unmoderated topic. If you would like to opt-out, please send a message using [this link].
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submitted by anticensor_bot to u/anticensor_bot [link] [comments]

Quantum Resistance

Before jumping to conclusions about this post, know that I am not looking to spread any FUD but rather am trying to understand a forthcoming risk and potential solutions from an unbiased standpoint. My research has not yielded any definitive answer so I am turning here to seek direction from those more knowledgable than me.
--
When it comes to predicting quantum computing's ability to break Bitcoin cryptographically, I've seen estimates as small as two years and as large as 25 years. Either way, it is easily conceivable that quantum processors will improve to the point of threatening Bitcoin as a reliable form of currency and store of value.
One way to prevent vulnerability to quantum threats is by storing Bitcoin in an address that has only ever received Bitcoin and never sent it. Although, this is an unrealistic mitigant for an asset/currency that is intended to be bought and sold, for all trust will be lost in the network once quantum computing becomes powerful enough to hack Bitcoin. Nobody will place any value in a currency that can be hacked by sending a transaction.
Another argument I've seen is that once quantum computing is strong enough to hack Bitcoin's cryptography, Bitcoin will be a non-factor compared to the other digital security breakdowns that will have transpired. For example, nuclear codes, bank accounts, digital privacy, etc. However, those centralized networks will have the ability to preemptively update their internal security to the standard required in a quantum computing world. In a similar manner, cryptocurrency and blockchain as a whole will survive such transition via improved cryptography.
But when it comes to Bitcoin specifically, will it be possible to generate consensus among the miners to switch to a quantum resistant protocol? My research has found conflicting perspectives - one side being that in order to upgrade Bitcoin's security, it would require manual movement of coins to a new address by all users, and a burning of the coins that did not move after a "sufficient" amount of time. Burning one's assets would undoubtedly not hold in a court of law. Even if we are still several years away, an unsolvable existential threat on the horizon would be priced into the value of Bitcoin and drive it down to zero.
With that being said, are there any feasible solutions to bring Bitcoin to quantum resistance? How can Bitcoin survive this threat in the long run? What is being done currently to resolve such problem?
submitted by fuegoblue to Bitcoin [link] [comments]

Mega eTextbooks release thread (part-28)! Find your textbooks here between $5-$25 :)

Please find the list below:
  1. Disease Gene Identification: Methods and Protocols, 2nd Edition: Johanna K. DiStefano
  2. Statistical Aspects of the Microbiological Examination of Foods, 3rd Edition: Basil Jarvis
  3. Revel for Social Problems, 14th Edition: Stanley Eitzen & Maxine Baca Zinn & Kelly Ei Smith
  4. Fundamentals of Human Resource Management: Pearson New International Edition, 3rd Edition: Gary Dessler
  5. Economics Today: The Micro View, 18th Edition: Roger LeRoy Miller
  6. Employment Law for Business, 8th Edition: Dawn Bennett-Alexander & Laura Hartman
  7. Surgical Exposures in Orthopaedics: The Anatomic Approach, 5th Edition: Stanley Hoppenfeld & Piet de Boer & Richard Buckley
  8. Project Management in Construction, 7th Edition: Sidney Levy
  9. Financial and Managerial Accounting, 7th Edition: John Wild & Ken Shaw & Barbara Chiappetta
  10. Handbook of Plant Disease Identification and Management, 1st Edition: Balaji Aglave
  11. Ubuntu Unleashed 2019 Edition: Covering 18.04, 18.10, 19.04, 13th Edition: Matthew Helmke
  12. Handbook of Insulin Therapies, 1st Edition: Winston Crasto & Janet Jarvis & Melanie J. Davies
  13. Python for Programmers: with Big Data and Artificial Intelligence Case Studies, 1st Edition: Paul J. Deitel & Harvey Deitel
  14. Medical Ethics: Accounts of Ground-Breaking Cases, 7th Edition: Gregory Pence
  15. Human Resource Management, 13th Edition: Gary Dessler
  16. The Biology and Therapeutic Application of Mesenchymal Cells, 2 Volume Set, 1st Edition: Kerry Atkinson
  17. Computer Security Fundamentals, 3rd Edition: William Chuck Easttom
  18. Hendee's Radiation Therapy Physics, 4th Edition: Todd Pawlicki & Daniel J. Scanderbeg & George Starkschall
  19. Nutrient Delivery, 1st Edition: Alexandru Grumezescu
  20. Technology Entrepreneurship: Taking Innovation to the Marketplace, 2nd Edition: Thomas N. Duening & Robert A. Hisrich & Michael A. Lechter
  21. Chemistry of Metalloproteins: Problems and Solutions in Bioinorganic Chemistry, 1st Edition: Joseph J. Stephanos & Anthony W. Addison
  22. Mathematical Statistics with Applications in R, 2nd Edition: Kandethody M. Ramachandran & Chris P. Tsokos
  23. Diagnostic Imaging: Genitourinary, 3rd Edition: Mitchell E. Tublin
  24. Comprehensive Management of Arteriovenous Malformations of the Brain and Spine, 1st Edition: Robert F. Spetzler & Douglas S. Kondziolka & Randall T. Higashida & M. Yashar S. Kalani
  25. Digital Design: With an Introduction to the Verilog HDL, 5th Edition: M. Morris R. Mano & Michael D. Ciletti
  26. Plasmids: Biology and Impact in Biotechnology and Discovery, 1st Edition: Marcelo E. Tolmasky & Juan C. Alonso
  27. Consumer Behavior: Buying, Having, and Being, Global Edition, 12th Edition: Michael R. Solomon
  28. Project Management Case Studies, 5th Edition: Harold Kerzner
  29. Medical Phisiology: Principles for Clinical Medicine, 4th Edition: Rodney A. Rhoades & David R. Bell
  30. Essentials of Contemporary Management, 7th Edition: Gareth Jones & Jennifer George
  31. Harmony and Voice Leading, 4th Edition: Thomas E. Benjamin & Michael Horvit & Robert S. Nelson
  32. Principles of Economics, 2nd Edition: Lee Coppock & Dirk Mateer
  33. Oral Microbiology and Immunology, 2nd Edition: Richard J. Lamont & George N. Hajishengallis & Howard F. Jenkinson
  34. Magnetic Resonance Imaging of the Brain and Spine, 5th Edition: Scott W. Atlas
  35. Accounting Information Systems: Controls and Processes, 3rd Edition: Leslie Turner & Andrea B. Weickgenannt & Mary Kay Copeland
  36. Strategic Corporate Social Responsibility: Sustainable Value Creation, 5th Edition: David Chandler
  37. Julien's Primer of Drug Action: A Comprehensive Guide to the Actions, Uses, and Side Effects of Psychoactive Drugs, 14th Edition: Claire D. Advokat & Joseph Comaty & Robert Julien
  38. The Grand Chessboard: American Primacy And Its Geostrategic Imperatives, 1st Edition: Zbigniew Brzezinski
  39. The Cosmic Perspective: The Solar System, 8th Edition: Jeffrey O. Bennett & Megan O. Donahue & Nicholas Schneider & Mark Voit
  40. Ultrastructure Atlas of Human Tissues, 1st Edition: Fred Hossler
  41. Advances in the Biology and Management of Modern Bed Bugs, 1st Edition: Stephen L. Doggett & Dini M. Miller & Chow-Yang Lee
  42. Patterns of World History: Volume One: To 1600, 1st Edition: Peter von Sivers & Charles A. Desnoyers & George B. Stow
  43. Genitourinary Imaging: A Core Review, 1st Edition: Matthew Davenport
  44. Evidence-based Obstetrics and Gynecology, 1st Edition: Errol R. Norwitz & Carolyn M. Zelop & David A. Miller & David L. Keefe
  45. Zoology, 10th Edition: Stephen Miller & John Harley
  46. Radical and Reconstructive Gynecologic Cancer Surgery, 1st Edition: Robert Bristow & Dennis Chi
  47. Davis's Diseases & Disorders A Nursing Therapeutics Manual, 6th Edition: Marilyn Sawyer Sommers
  48. Management & Cost Accounting, 6th Edition: Alnoor Bhimani
  49. Elements of Modern Algebra, 8th Edition: Linda Gilbert
  50. Psychiatric & Mental Health Nursing, 4th Edition: Katie Evans & Debra Nizette & Anthony O'Brien
  51. Molecular Biology: Different Facets, 1st Edition: Anjali Priyadarshini & Prerna Pandey
  52. Elementary Number Theory, 7th Edition: David Burton
  53. Accounting Information Systems, 14th Edition: Marshall B. Romney & Paul J. Steinbart
  54. Microeconomics, Global Edition, 9th Edition: Robert Pindyck & Daniel Rubinfeld
  55. Psychiatric and Mental Health Nursing Demystified, 1st Edition: Jim Keogh
  56. Entrepreneurship, 10th Edition: Robert Hisrich & Michael Peters & Dean Shepherd
  57. Ganong's Review of Medical Physiology, 26th Edition: Kim E. Barrett & Susan M. Barman & Jason Yuan & Heddwen L. Brooks
  58. Textbook of Obstetrics and Gynaecology: A life course approach, 1st Edition: Eric A.P. Steegers & Bart C.J.M. Fauser & Carina G.J.M. Hilders
  59. Engineering Mechanics: Statics, 8th Edition: James L. Meriam & L. G. Kraige & J. N. Bolton
  60. Basic Concepts of Psychiatric-Mental Health Nursing, 8th Edition: Louise Rebraca Shives
  61. Beckmann and Ling's Obstetrics and Gynecology, 8th Edition: Robert Casanova
  62. Biology: Concepts and Applications, 10th Edition: Cecie Starr & Christine Evers & Lisa Starr
  63. Estimating in Building Construction, 9th Edition: Steven J. Peterson & Frank R. Dagostino
  64. The Big Back Book: Tips & Tricks for Therapists, 1st Edition: Jane Johnson
  65. University Physics with Modern Physics, 14th Edition: Hugh D. Young & Roger A. Freedman
  66. Poisoning and Drug Overdose, 7th Edition: Kent Olson & Ilene Anderson & Neal Benowitz & Paul Blanc
  67. Koneman's Color Atlas and Textbook of Diagnostic Microbiology, 7th Edition: Gary W. Procop
  68. Experimental Psychology, 7th Edition: Anne Myers & Christine H. Hansen
  69. Marketing: An Introduction, 13th Edition: Gary Armstrong & Philip Kotler
  70. Gray's Anatomy for Students: With Student Consult, 3rd Edition: Richard Drake & A. Wayne Vogl & Adam W. M. Mitchell
  71. Chestnut's Obstetric Anesthesia: Principles and Practice, 5th Edition: David H. Chestnut & Cynthia A Wong & Lawrence C Tsen & Warwick D Ngan Kee & Yaakov Beilin & Jill Mhyre
  72. Chemistry: The Molecular Science, 5th Edition: John W. Moore & Conrad L. Stanitski
  73. Head, Neck and Dental Emergencies, 2nd Edition: Mike Perry
  74. Wong's Nursing Care of Infants and Children, 10th Edition: Marilyn J. Hockenberry & David Wilson
  75. Sports Emergency Care: A Team Approach, 3rd Edition: Robb Rehberg & Jeff G. Konin
  76. New Venture Creation: Entrepreneurship for the 21st Century, 10th Edition: Stephen Spinelli & Rob Adams
  77. Caring for the Vulnerable: Perspectives in Nursing Theory, Practice, and Research, 5th Edition: Mary de Chesnay & Barbara Anderson
  78. Geometry: The Line and the Circle: Maureen T. Carroll & Elyn Rykken
  79. Histories of Human Engineering: Tact and Technology: Maarten Derksen
  80. Land Restoration: Reclaiming Landscapes for a Sustainable Future, 1st Edition: Ilan Chabay & Martin Frick & Jennifer Helgeson
  81. Yamada's Handbook of Gastroenterology, 3rd Edition: Tadataka Yamada & John M. Inadomi & Renuka Bhattacharya & Jason A. Dominitz & Joo Ha Hwang
  82. Theoretical Physics 9: Fundamentals of Many-body Physics, 2nd Edition: Wolfgang Nolting & William D. Brewer
  83. Introduction to Programming with C++, 3rd Edition: Y. Daniel Liang
  84. Dental Emergencies, 1st Edition: Mark Greenwood & Ian Corbett
  85. Fundamentals of Physics and Chemistry of the Atmosphere, 2nd Edition: Guido Visconti
  86. Calculus: Early Transcendentals, 3rd Edition: William L. Briggs & Lyle Cochran & Bernard Gillett & Eric Schulz
  87. Educating Physical Therapists, 1st Edition: Gail Jensen
  88. Strategic Developments in Eurasia After 11 September, 1st Edition: Shireen Hunter
  89. Contemporary Issues in Healthcare Law and Ethics, 4th Edition: Dean Harris
  90. Transitioning from RN to MSN: Principles of Professional Role Development: Brenda Scott & Mindy Thompson
  91. Principles and Practice of Public Health Surveillance, 3rd Edition: Lisa M. Lee & Steven M. Teutsch & Stephen B. Thacker & Michael E. St. Louis
  92. Elementary Statistics: Picturing the World, 6th Edition: Ron Larson & Betsy Farber
  93. Human Sexuality in a World of Diversity, 6th Canadian Edition: Spencer A. Rathus & Jeffrey S. Nevid & Lois Fichner-Rathus & Alex McKay & Robin Milhausen
  94. Becoming Your Own Banker, 6th Edition: R. Nelson Nash
  95. Murach's MySQL, 3rd Edition: Joel Murach
  96. Intermediate Algebra, 13th Edition: Marvin L. Bittinger & Judith A. Beecher & Barbara L. Johnson
  97. Planning Health Promotion Programs: An Intervention Mapping Approach, 4th Edition: L. Kay Bartholomew Eldredge & Christine M. Markham & Robert A. C. Ruiter & Maria E. Fernández & Gerjo Kok & Guy S. Parcel
  98. Human Factors in Simple and Complex Systems, 3rd Edition: Robert W. Proctor & Trisha Van Zandt
  99. The Irony of Democracy: An Uncommon Introduction to American Politics, 17th Edition: Louis Schubert & Thomas R. Dye & Harmon Zeigler
  100. Understanding Earth, 7th Edition: John Grotzinger
  101. Nursing Research in Canada: Methods, Critical Appraisal, and Utilization, 4th Edition: Geri LoBiondo-Wood & Judith Haber & Cherylyn Cameron & Mina Singh
  102. The Philosophy of Film, 1st Edition: Thomas E. Wartenberg & Angela Curran
  103. Disaster Nursing and Emergency Preparedness, 4th Edition: Tener Goodwin Veenema
  104. Language in Mind: An Introduction to Psycholinguistics, 2nd Edition: Julie Sedivy
  105. Medical Anthropology: A Biocultural Approach, 3rd Edition: Andrea S. Wiley & John S. Allen
  106. Exploring Biology in the Laboratory, 3rd Edition: Murray P. Pendarvis & John L. Crawley
  107. Guide to Networking Essentials, 8th Edition: Greg Tomsho
  108. Social Psychology: A Storytelling Approach, 2nd Edition: Leonard Newman & Ralph Erber
  109. Managing Conflict: An Introspective Journey to Negotiating Skills, 1st Edition: Dorothy Balancio
  110. Environmental Change and Challenge: A Canadian Perspective, 5th Edition: Philip Dearden & Bruce Mitchell
  111. Brain and Behavior: A Cognitive Neuroscience Perspective, 1st Edition: David Eagleman & Jonathan Downar
  112. Cardiac/Vascular Nurse Exam Secrets Study Guide: Cardiac/Vascular Nurse Test Review for the Cardiac/Vascular Nurse Exam: Mometrix Media & Cardiac Vascular Nurse Exam Secrets
  113. Keeping the Republic: Power and Citizenship in American Politics, The Essentials, 9th Edition: Christine Barbour & Gerald Wright
  114. Principles of Environmental Science, 9th Edition: William Cunningham & Mary Cunningham
  115. Thomas' Calculus, 14th Edition: Joel R. Hass & Christopher E. Heil & Maurice D. Weir
  116. Pharmacology for Canadian Pharmacy Technicians, 1st Edition: Leland Norman Holland & Michael P. Adams & Jeanine Lynn Brice & Heather V. LeBlanc
  117. Cellular and Molecular Immunology, 9th Edition: Abul K. Abbas & Andrew H. Lichtman & Shiv Pillai
  118. Operations Management: Processes and Supply Chains, 11th Edition: Lee J. Krajewski & Manoj K. Malhotra & Larry P. Ritzman
  119. Jews, Christians, Muslims: A Comparative Introduction to Monotheistic Religions, 2nd Edition: John Corrigan & Frederick Denny & Martin S Jaffee & Carlos Eire
  120. Professional Nursing: Concepts & Challenges, 9th Edition: Beth Black
  121. Practical Homicide Investigation: Tactics, Procedures, and Forensic Techniques, 4th Edition: Vernon J. Geberth
  122. Fundamentals of Modern Manufacturing: Materials, Processes and Systems, 7th Edition: Mikell P. Groover
  123. Genetics: A Conceptual Approach, 7th Edition: Benjamin A. Pierce
  124. Computer Science Illuminated, 7th Edition: Nell Dale & John Lewis
  125. The Globalization of World Politics: An Introduction to International Relations, 8th Edition: John Baylis & Steve Smith & Patricia Owens
  126. Behavioral Neuroscience, 9th Edition: S. Marc Breedlove & Neil V. Watson
  127. Canadian Human Resource Management: A Strategic Approach, 12th Edition: Hermann Schwind & Krista Uggerslev & Terry Wagar & Neil Fassina
  128. Brief Principles of Macroeconomics, 9th Edition: N. Gregory Mankiw
  129. Living in the Environment, 4th Canadian Edition: G. Miller & Dave Hackett & Carl Wolfe
  130. Principles of Economics, 9th Edition: N. Gregory Mankiw
  131. Principles of Microeconomics, 9th Edition: N. Gregory Mankiw
  132. Child Development, 9th Edition: Laura E. Berk
  133. Home, School, and Community Collaboration: Culturally Responsive Family Engagement, 4th Edition: Kathy Beth Grant & Julie A. Ray
  134. Set Lighting Technician's Handbook, 4th Edition: Harry Box
  135. Clinical Nurse Leader Certification Review, 2nd Edition: Cynthia R. King
  136. Basic Chemistry, 4th Edition: Karen C. Timberlake & William Timberlake
  137. Sparks & Taylor's Nursing Diagnosis Pocket Guide, 3rd Edition: Linda Phelps
  138. Family Theories: Foundations and Applications, 1st Edition: Katherine R. Allen & Angela C. Henderson
  139. The Earth and Its Peoples: A Global History, 7th Edition: Richard Bulliet & Pamela Crossley & Daniel Headrick & Steven Hirsch & Lyman Johnson
  140. Sociology in Action: A Canadian Perspective, 3rd Edition: Tami Bereska & Diane Symbaluk
  141. Operations Management: Processes and Supply Chains, 12th Edition: Lee J. Krajewski & Manoj K. Malhotra & Larry P. Ritzman
  142. Introduction to Food Science and Food Systems, 2nd Edition: Rick Parker & Miriah Pace
  143. Liaisons, Student Edition: An Introduction to French, 3rd Edition: Wynne Wong & Stacey Weber-Fève & Bill VanPatten
  144. Zuckerman Parker Handbook of Developmental and Behavioral Pediatrics for Primary Care, 4th Edition: Marilyn Augustyn & Barry Zuckerman
  145. Teaching in Today's Inclusive Classrooms: A Universal Design for Learning Approach, 3rd Edition: Richard M. Gargiulo & Debbie Metcalf
  146. The Biological Basis of Mental Health, 3rd Edition: William T. Blows
  147. Developing and Managing Electronic Collections: The Essentials: Peggy Johnson
  148. Western Civilization: Volume II: Since 1500, 10th Edition: Jackson J. Spielvogel
  149. Talking to Strangers: What We Should Know about the People We Don't Know, 1st Edition: Malcolm Gladwell
  150. Understanding Pathophysiology, 7th Edition: Sue E. Huether & Kathryn L. McCance
  151. Our Environment: A Canadian Perspective, 5th edition: Dianne Draper & Ann Zimmerman
  152. Criminal Law: Cases and Materials, 8th Edition: John Kaplan & Robert Weisberg & Guyora Binder
  153. A Photographic Atlas of Histology, 2nd Edition: Michael J Leboffe
  154. Dragons and Tigers: A Geography of South, East, and Southeast Asia, 3rd Edition: Barbara A. Weightman
  155. Climate Change Biology, 1st Edition: Jonathan A. Newman & Madhur Anand & Hugh A. L. Henry & Shelley L. Hunt & Ze'ev Gedalof
  156. The Power of Critical Thinking: 5th Canadian Edition: Chris MacDonald and Lewis Vaughn
  157. Principles of Fire Behavior and Combustion, 4th Edition: Richard Gann & Raymond Friedman
  158. Informatics Nurse Exam Secrets Study Guide: Informatics Test Review for the Informatics Nurse Certification Exam: Informatics Exam Secrets Test Prep Team
  159. General Chemistry, 10th Edition: Darrell Ebbing & Steven D. Gammon
  160. A Practical Guide to Computer Forensics Investigations, 1st Edition: Darren R. Hayes
  161. Basic Biomechanics, 8th Edition: Susan Hall
  162. Essay Writing for Canadian Students, 8th Edition: Roger Davis & Laura K. Davis
  163. Biology, 11th Edition: Peter Raven & George Johnson & Kenneth Mason & Jonathan Losos & Susan Singer
  164. Molecular Imaging, 1st Edition: Ralph Weissleder& Brian D. Ross & Alnawaz Rehemtulla & Sanjiv Sam Gambhir
  165. Criminology, 4th Edition: Frank Schmalleger
  166. A Theory of Truthmaking: Metaphysics, Ontology, and Reality: Jamin Asay
  167. The Routledge Handbook of Metaphysical Grounding, 1st Edition: Michael J. Raven
  168. Linear Algebra and Its Applications, 5th Edition: David C. Lay & Steven R. Lay & Judi J. McDonald
  169. Essentials of Human Communication, 9th Edition: Joseph A. DeVito
  170. Economics: Principles, Applications, and Tools, 9th Edition, Global Edition: Arthur O'Sullivan & Steven Sheffrin & Stephen Perez
  171. Global Health 101, 3rd Edition: Richard Skolnik
  172. Mathematical Proofs: A Transition to Advanced Mathematics, 4th Edition: Gary Chartrand & Albert D. Polimeni & Ping Zhang
  173. Concepts in Strategic Management and Business Policy: Globalization, Innovation and Sustainability, 15th Edition, Global Edition: Thomas L. Wheelen & J. David Hunger & Alan N. Hoffman & Charles E. Bamford
  174. Chemistry: The Central Science, 14th Edition, Global Edition: Theodore E. Brown & H. Eugene LeMay & Bruce E. Bursten & Catherine Murphy & Patrick Woodward & Matthew E. Stoltzfus
  175. Biopsychology, 10th Edition, Global Edition: John P. J. Pinel & Steven Barnes
  176. Electric Circuits, 11th Edition: James W. Nilsson & Susan Riedel
  177. Keeping the Republic; Power and Citizenship in American Politics, the Essentials, 8th Edition: Christine Barbour & Gerald C Wright
  178. Applied Behavior Analysis: Pearson New International Edition, 2nd Edition: John O. Cooper & Timothy E. Heron & William L. Heward
  179. Cryptography and Network Security: Principles and Practice, 7th Edition, Global Edition: William Stallings
  180. Operating Systems: Internals and Design Principles, 9th Edition, Global Edition: William Stallings
  181. Options, Futures, and Other Derivatives, 9th Edition, Global Edition: John C. Hull
  182. Invitation to the Psychology of Religion, 3rd Edition: Raymond F. Paloutzian
  183. Valuation: The Art and Science of Corporate Investment Decisions, 3rd Edition: Sheridan Titman
  184. Comprehensive Clinical Nephrology, 5th Edition: Richard J. Johnson & John Feehally & Jurgen Floege
  185. Miller & Freund's Probability and Statistics for Engineers, 9th Edition, Global Edition: Richard Johnson & Irwin Miller & John Freund
  186. Exploring Strategy: Text and Cases, 11th Edition: Gerry Johnson & Richard Whittington & Patrick Regnér & Kevan Scholes & Duncan Angwin
  187. Economics for Business, 7th Edition: John Sloman
  188. Essentials of Economics, 7th Edition: John Sloman & Dean Garratt
  189. Economics, 9th Edition: John Sloman & Dean Garratt & Alison Wride
  190. Essential Economics for Business, 5th Edition: Johnsloman & Jones Elizabeth
  191. Finite Mathematics, 7th Edition: Stefan Waner & Steven Costenoble
  192. The SAGE Encyclopedia of Surveillance, Security, and Privacy, 1st Edition: Bruce A. Arrigo
  193. Evolution, 4th Edition: Douglas J. Futuyma & Mark Kirkpatrick
  194. Adult Development and Aging, 7th Edition: John C. Cavanaugh & Fredda Blanchard-Fields
  195. Foundations of Finance, 9th Edition, Global Edition: Arthur J. Keown & John D Martin & J. William Petty
  196. Learning PHP, MySQL & JavaScript: With jQuery, CSS & HTML5, 4th Edition: Robin Nixon
  197. Head First Learn to Code: A Learner's Guide to Coding and Computational Thinking, 1st Edition: Eric Freeman
  198. Learning Swift: Building Apps for macOS, iOS, and Beyond, 3rd Edition: Jonathon Manning & Paris Buttfield-Addison & Tim Nugent
  199. Database Systems: Design, Implementation, & Management, 12th Edition: Carlos Coronel & Steven Morris
  200. Introduction to Solid Modeling Using SolidWorks, 13th Edition: William Howard & Joseph Musto
  201. Communications Receivers: Principles and Design, 4th Edition: Ulrich Rohde & Jerry Whitaker & Hans Zahnd
  202. Connect Core Concepts in Health, 15th Edition: Paul Insel & Walton Roth
  203. On Course: Strategies for Creating Success in College and in Life, 8th Edition: Skip Downing
  204. Vander's Human Physiology, 15th Edition: Eric Widmaier & Hershel Raff & Kevin Strang
  205. Biology, 4th Edition: Robert Brooker & Eric Widmaier & Linda Graham & Peter Stiling
  206. The Essentials of Statistics: A Tool for Social Research, 4th Edition: Joseph F. Healey
  207. Oracle 12c: SQL, 3rd Edition: Joan Casteel
  208. Global Business Today, 10th Edition: Charles Hill & G. Tomas M. Hult
  209. Project Management: The Managerial Process, 7th Edition: Erik Larson & Clifford Gray
  210. Organizational Behavior: A Practical, Problem-Solving Approach, 2nd Edition: Angelo Kinicki & Mel Fugate
  211. International Management: Culture, Strategy, and Behavior, 10th Edition: Fred Luthans & Jonathan Doh
  212. CorelDRAW X8: The Official Guide, 12th Edition: Gary David Bouton
  213. Physics for Scientists and Engineers: An Interactive Approach, 2nd Edition: Robert Hawkes & Javed Iqbal & Firas Mansour & Marina Milner-Bolotin & Peter Williams
  214. Programmable Logic Controllers, 5th Edition: Frank Petruzella
  215. Foundations in Microbiology, 10th Edition: Kathleen Park Talaro & Barry Chess
  216. Applied Numerical Methods with MATLAB for Engineers and Scientists, 4th Edition: Steven Chapra
  217. Tonal Harmony, 8th Edition: Stefan Kostka & Dorothy Payne & Byron Almén
  218. Discrete Mathematics, 8th Edition: Richard Johnsonbaugh
  219. Bates' Pocket Guide to Physical Examination and History Taking, 8th Edition: Lynn S. Bickley
  220. NANDA International Nursing Diagnoses: Definitions & Classification 2018-2020, 11th Edition: T. Heather Herdman & Shigemi Kamitsuru & Heather T. Herdman
  221. Biology: Concepts and Investigations, 4th Edition: Mariëlle Hoefnagels
  222. Biology: Concepts and Investigations, 3rd Edition: Mariëlle Hoefnagels
  223. Human Biology: Concepts and Current Issues, 8th Edition, Global Edition: Michael D. Johnson
  224. Messages: Building Interpersonal Communication Skills, 5th Canadian Edition: Joseph A. DeVito & Rena Shimoni & Dawne Clark
  225. The Interpersonal Communication Book, 14th Edition, Global Edition: Joseph A. DeVito
  226. Computational Systems Pharmacology and Toxicology, 1st Edition: Rudy J Richardson & Dale E Johnson & Noffisat Oki & David Faulkner
  227. Shelly Cashman Series Microsoft Office 365 & Office 2019 Introductory, 1st Edition: Sandra Cable & Steven M. Freund & Ellen Monk & Susan L. Sebok & Joy L. Starks
  228. The Practice of Emotionally Focused Couple Therapy: Creating Connection, 2nd Edition: Susan M. Johnson
  229. The Marriage Clinic: A Scientifically Based Marital Therapy, 1st Edition: John M. Gottman
  230. Cognitive-Behavioral Therapy with Couples and Families: A Comprehensive Guide for Clinicians, 1st Edition: Frank M. Dattilio & Aaron T. Beck
  231. International Marketing, 17th Edition: Philip R. Cateora & John Graham & Mary C Gilly
  232. Kaplan and Sadock's Concise Textbook of Clinical Psychiatry, 3rd Edition: Benjamin Sadock & Virginia Alcott Sadock
  233. Anthropology, 14th Edition: Carol R. Ember & Melvin Ember & Peter N. Peregrine
  234. The Men They Will Become: The Nature And Nurture Of Male Character: Eli Newberger
  235. Accounting, 27th Edition: Carl S. Warren & James M. Reeve & Jonathan Duchac
  236. ICD-10-CM 2019: The Complete Official Codebook, 1st Edition: American Medical Association
  237. Essentials of Human Anatomy & Physiology, 12th Edition, Global Edition: Elaine N. Marieb & Suzanne M. Keller
  238. Early Childhood Education Today, 14th Edition: George S Morrison
  239. Programming Bitcoin: Learn How to Program Bitcoin from Scratch, 1st Edition: Jimmy Song
  240. The Physiology and Biochemistry of Prokaryotes, 4th Edition: David White & James Drummond & Clay Fuqua
  241. Environmental Microbiology, 3rd Edition: Ian L. Pepper & Charles P. Gerba & Terry J. Gentry
  242. Industrial Microbiology: An Introduction, 1st Edition: Michael J. Waites & Neil L. Morgan & John S. Rockey & Gary Higton
  243. Introduction to Econometrics, Updated 3rd Edition, Global Edition: James H. Stock & Mark W. Watson
  244. Introduction to Econometrics, 3rd Edition: James H. Stock & Mark W. Watson
  245. Expert Oracle Application Express, 2nd Edition: Doug Gault & Dimitri Gielis & Martin DSouza & Roel Hartman
  246. The Art of Reasoning: An Introduction to Logic and Critical Thinking, 4th Edition: David Kelley
  247. Physics, 5th Edition: James S. Walker
  248. Applied Fluid Mechanics, 7th Edition: Robert L. Mott & Joseph A. Untener
  249. Applied Strength of Materials, SI Units Version, 6th Edition: Robert L. Mott & Joseph A. Untener
  250. Social Psychology, 12th Edition: David Myers & Jean Twenge
  251. Applied Strength of Materials, 6th Edition: Robert Mott & Joseph A. Untener
  252. Foundations of Nursing Research, 7th Edition: Rose Marie Nieswiadomy & Catherine Bailey
  253. Molecular Cell Biology, 8th Edition: Harvey Lodish & Arnold Berk & Chris A. Kaiser & Monty Krieger & Anthony Bretscher
  254. Machine Elements in Mechanical Design, 6th Edition: Robert L. Mott & Edward M. Vavrek & Jyhwen Wang
  255. DeVita, Hellman, and Rosenberg's Cancer, 11th Edition: Vincent T. DeVita & Steven A. Rosenberg & Theodore S. Lawrence
  256. Particle Image Velocimetry: A Practical Guide, 3rd Edition: Markus Raffel & Christian E. Willert & Fulvio Scarano & Christian J. Kähler
  257. Smith's Textbook of Endourology, 4th Edition: Arthur D. Smith & Glenn Preminger & Gopal H. Badlani & Louis R. Kavoussi
  258. College Algebra with Modeling & Visualization, 6th Edition: Gary K. Rockswold
  259. Financial Accounting Theory, 7th Edition: William R. Scott
  260. Biology Now, 2nd Edition: Anne Houtman & Megan Scudellari & Cindy Malone
  261. Psychological Science, 5th Edition: Michael Gazzaniga & Diane Halpern
  262. The Handbook of Technical Writing, 11th Edition: Gerald J. Alred & Charles T. Brusaw & Walter E. Oliu
  263. A Graphical Approach to College Algebra, 6th Edition: John Hornsby & Margaret L. Lial & Gary K. Rockswold
  264. Business Analytics, 4th Edition: Jeffrey D. Camm & James J. Cochran & Michael J. Fry & Jeffrey W. Ohlmann
  265. Biological Psychology, 13th Edition: James W. Kalat
  266. Business Communication Today, 14th Edition: Courtland L. Bovee & John V. Thill
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  268. Principles of Information Security, 6th Edition: Michael E. Whitman & Herbert J. Mattord
  269. Financial & Managerial Accounting, 14th Edition: Carl S. Warren & James M. Reeve & Jonathan Duchac
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  279. The Human Brain Book: An Illustrated Guide to its Structure, Function, and Disorders, New Edition: Rita Carter
  280. Introduction to Materials Science for Engineers, 8th Edition: James F. Shackelford
  281. Adobe Dreamweaver CC Classroom in a Book, 1st Edition: Jim Maivald
  282. Trigonometry, 11th Edition: Margaret L. Lial & John Hornsby & David I. Schneider & Callie Daniels
  283. Investment Banks, Hedge Funds, and Private Equity, 3rd Edition: David P. Stowell
  284. Cognitive Neuroscience: The Biology of the Mind, 5th Edition: Michael Gazzaniga & Richard B. Ivry & George R. Mangun
  285. Cognitive Neuroscience: The Biology of the Mind, 5th Edition: Michael Gazzaniga & Richard B. Ivry (Author), George R. Mangun (Author)
  286. Project Management Theory and Practice, 3rd Edition: Gary L. Richardson & Brad M. Jackson
  287. Organic Chemistry: Structure and Function, 8th Edition: K. Peter C. Vollhardt & Neil E. Schore
  288. Read, Reason, Write: An Argument Text and Read, 11th Edition: Dorothy Seyler
  289. Fundamentals of Management: Management Myths Debunked!, Global Edition, 10th Edition: Stephen P Robbins & David A. De Cenzo & Mary Coulter
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  291. An Introduction to Banking: Principles, Strategy and Risk Management, 2nd Edition: Moorad Choudhry
  292. The Immune System, 4th Edition: Peter Parham
  293. Biochemistry: Concepts and Connections, Global Edition, 1st Edition: Dean R. Appling & Spencer J. Anthony-Cahill & Christopher K. Mathews
  294. Writing about Writing, 3rd Edition: Elizabeth Wardle & Douglas Downs
  295. Data Wrangling with JavaScript, 1st Edition: Ashley Davis
  296. Experience Psychology, 4th Edition: Laura King
  297. An Introduction to Mathematical Statistics: Fetsje Bijma & Marianne Jonker & Aad van der Vaart & Reinie Erné
  298. Business Communication: Polishing Your Professional Presence, 3rd Edition: Barbara G. Shwom & Lisa Gueldenzoph Snyder
  299. Earth's Evolving Systems: The History of Planet Earth, 2nd Edition: Ronald E. Martin
  300. Business Ethics: Decision Making for Personal Integrity & Social Responsibility, 4th Edition: Laura Hartman & Joseph DesJardins & Chris MacDonald
  301. College Algebra and Trigonometry, Global Edition, 6th Edition: Margaret L. Lial & John Hornsby & David I. Schneider & Callie Daniels
  302. Essentials of MIS, 12th Edition: Kenneth C. Laudon & Jane P. Laudon
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  304. University Physics, 14th Edition: Hugh D. Young & Roger A. Freedman
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  306. Analytical Mechanics, 2nd Edition: Nivaldo A. Lemos
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  308. Computer Accounting with QuickBooks Online: A Cloud Based Approach, 2nd Edition: Carol Yacht & Susan Crosson
  309. Cost Accounting and Financial Management for Construction Project Managers, 1st Edition: Len Holm
  310. Business Continuity Management in Construction, 1st Edition: Leni Sagita Riantini Supriadi & Low Sui Pheng
  311. Contemporary Logistics, 12th Edition, Global Edition: Paul R. Murphy & A. Michael Knemeyer
  312. Mechanical Engineers' Handbook, Volume 1: Materials and Engineering Mechanics, 4th Edition: Myer Kutz
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  336. English Grammar Workbook For Dummies with Online Practice, 3rd Edition: Geraldine Woods
  337. Naked: The Dark Side of Shame and Moral Life, 1st Edition: Krista K. Thomason
  338. Ashcraft's Pediatric Surgery, 6th Edition: George W. Holcomb III & J. Patrick Murphy & Daniel J Ostlie
  339. Mobile Apps Engineering: Design, Development, Security, and Testing, 1st Edition: Ghita K. Mostefaoui & Faisal Tariq
  340. Lange Clinical Neurology, 10th Edition: Roger Simon & David Greenberg & Michael Aminoff
  341. International Textbook of Diabetes Mellitus, 2 Volume Set, 4th Edition: R. A. DeFronzo & E. Ferrannini & Paul Zimmet & George Alberti
  342. Java Programming, 9th Edition: Joyce Farrell
  343. Discovering Behavioral Neuroscience: An Introduction to Biological Psychology, 4th Edition: Laura Freberg
  344. How the Immune System Works, 5th Edition: Lauren M. Sompayrac
  345. Fundamentals of Electroceramics: Materials, Devices, and Applications, 1st Edition: R. K. Pandey
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  347. Biology of Humans: Concepts, Applications, and Issues, 6th Edition: Judith Goodenough & Betty A. McGuire
  348. Williams Textbook of Endocrinology, 13th Edition: Shlomo Melmed & Kenneth S. Polonsky & P. Reed Larsen & Henry M. Kronenberg
  349. Financial Management: Principles and Applications, Global Edition, 13th Edition: Sheridan Titman & Arthur J. Keown & John D Martin
  350. Case Studies in Immunology: A Clinical Companion, 7th Edition: Raif S. Geha & Luigi Notarangelo
  351. Handbook of MRI Technique, 4th Edition: Catherine Westbrook
  352. MRI: Basic Principles and Applications, 5th Edition: Brian M. Dale & Mark A. Brown & Richard C. Semelka
  353. Robbins Basic Pathology, 10th Edition: Vinay Kumar & Abul K. Abbas & Jon C. Aster & Vinay Kumar & Abul K. Abbas & Jon C. Aster
  354. Rosen's Emergency Medicine: Concepts and Clinical Practice: 2-Volume Set, 9th Edition: Ron Walls & Robert Hockberger & Marianne Gausche-Hill
  355. BNF for Children: 2018-2019, 1st Edition: Paediatric Formulary Committee
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  357. Practical Gastroenterology and Hepatology Board Review Toolkit, 2nd Edition: Kenneth R. DeVault & Michael B. Wallace & Bashar A. Aqel & Keith D. Lindor
  358. Reinforcement Learning: An Introduction, 2nd edition: Richard S. Sutton & Andrew G. Barto
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Scaling Reddit Community Points with Arbitrum Rollup: a piece of cake

Scaling Reddit Community Points with Arbitrum Rollup: a piece of cake
https://preview.redd.it/b80c05tnb9e51.jpg?width=2550&format=pjpg&auto=webp&s=850282c1a3962466ed44f73886dae1c8872d0f31
Submitted for consideration to The Great Reddit Scaling Bake-Off
Baked by the pastry chefs at Offchain Labs
Please send questions or comments to [[email protected] ](mailto:[email protected])
1. Overview
We're excited to submit Arbitrum Rollup for consideration to The Great Reddit Scaling Bake-Off. Arbitrum Rollup is the only Ethereum scaling solution that supports arbitrary smart contracts without compromising on Ethereum's security or adding points of centralization. For Reddit, this means that Arbitrum can not only scale the minting and transfer of Community Points, but it can foster a creative ecosystem built around Reddit Community Points enabling points to be used in a wide variety of third party applications. That's right -- you can have your cake and eat it too!
Arbitrum Rollup isn't just Ethereum-style. Its Layer 2 transactions are byte-for-byte identical to Ethereum, which means Ethereum users can continue to use their existing addresses and wallets, and Ethereum developers can continue to use their favorite toolchains and development environments out-of-the-box with Arbitrum. Coupling Arbitrum’s tooling-compatibility with its trustless asset interoperability, Reddit not only can scale but can onboard the entire Ethereum community at no cost by giving them the same experience they already know and love (well, certainly know).
To benchmark how Arbitrum can scale Reddit Community Points, we launched the Reddit contracts on an Arbitrum Rollup chain. Since Arbitrum provides full Solidity support, we didn't have to rewrite the Reddit contracts or try to mimic their functionality using an unfamiliar paradigm. Nope, none of that. We launched the Reddit contracts unmodified on Arbitrum Rollup complete with support for minting and distributing points. Like every Arbitrum Rollup chain, the chain included a bridge interface in which users can transfer Community Points or any other asset between the L1 and L2 chains. Arbitrum Rollup chains also support dynamic contract loading, which would allow third-party developers to launch custom ecosystem apps that integrate with Community Points on the very same chain that runs the Reddit contracts.
1.1 Why Ethereum
Perhaps the most exciting benefit of distributing Community Points using a blockchain is the ability to seamlessly port points to other applications and use them in a wide variety of contexts. Applications may include simple transfers such as a restaurant that allows Redditors to spend points on drinks. Or it may include complex smart contracts -- such as placing Community Points as a wager for a multiparty game or as collateral in a financial contract.
The common denominator between all of the fun uses of Reddit points is that it needs a thriving ecosystem of both users and developers, and the Ethereum blockchain is perhaps the only smart contract platform with significant adoption today. While many Layer 1 blockchains boast lower cost or higher throughput than the Ethereum blockchain, more often than not, these attributes mask the reality of little usage, weaker security, or both.
Perhaps another platform with significant usage will rise in the future. But today, Ethereum captures the mindshare of the blockchain community, and for Community Points to provide the most utility, the Ethereum blockchain is the natural choice.
1.2 Why Arbitrum
While Ethereum's ecosystem is unmatched, the reality is that fees are high and capacity is too low to support the scale of Reddit Community Points. Enter Arbitrum. Arbitrum Rollup provides all of the ecosystem benefits of Ethereum, but with orders of magnitude more capacity and at a fraction of the cost of native Ethereum smart contracts. And most of all, we don't change the experience from users. They continue to use the same wallets, addresses, languages, and tools.
Arbitrum Rollup is not the only solution that can scale payments, but it is the only developed solution that can scale both payments and arbitrary smart contracts trustlessly, which means that third party users can build highly scalable add-on apps that can be used without withdrawing money from the Rollup chain. If you believe that Reddit users will want to use their Community Points in smart contracts--and we believe they will--then it makes the most sense to choose a single scaling solution that can support the entire ecosystem, eliminating friction for users.
We view being able to run smart contracts in the same scaling solution as fundamentally critical since if there's significant demand in running smart contracts from Reddit's ecosystem, this would be a load on Ethereum and would itself require a scaling solution. Moreover, having different scaling solutions for the minting/distribution/spending of points and for third party apps would be burdensome for users as they'd have to constantly shuffle their Points back and forth.
2. Arbitrum at a glance
Arbitrum Rollup has a unique value proposition as it offers a combination of features that no other scaling solution achieves. Here we highlight its core attributes.
Decentralized. Arbitrum Rollup is as decentralized as Ethereum. Unlike some other Layer 2 scaling projects, Arbitrum Rollup doesn't have any centralized components or centralized operators who can censor users or delay transactions. Even in non-custodial systems, centralized components provide a risk as the operators are generally incentivized to increase their profit by extracting rent from users often in ways that severely degrade user experience. Even if centralized operators are altruistic, centralized components are subject to hacking, coercion, and potential liability.
Massive Scaling. Arbitrum achieves order of magnitude scaling over Ethereum's L1 smart contracts. Our software currently supports 453 transactions-per-second for basic transactions (at 1616 Ethereum gas per tx). We have a lot of room left to optimize (e.g. aggregating signatures), and over the next several months capacity will increase significantly. As described in detail below, Arbitrum can easily support and surpass Reddit's anticipated initial load, and its capacity will continue to improve as Reddit's capacity needs grow.
Low cost. The cost of running Arbitrum Rollup is quite low compared to L1 Ethereum and other scaling solutions such as those based on zero-knowledge proofs. Layer 2 fees are low, fixed, and predictable and should not be overly burdensome for Reddit to cover. Nobody needs to use special equipment or high-end machines. Arbitrum requires validators, which is a permissionless role that can be run on any reasonable on-line machine. Although anybody can act as a validator, in order to protect against a “tragedy of the commons” and make sure reputable validators are participating, we support a notion of “invited validators” that are compensated for their costs. In general, users pay (low) fees to cover the invited validators’ costs, but we imagine that Reddit may cover this cost for its users. See more on the costs and validator options below.
Ethereum Developer Experience. Not only does Arbitrum support EVM smart contracts, but the developer experience is identical to that of L1 Ethereum contracts and fully compatible with Ethereum tooling. Developers can port existing Solidity apps or write new ones using their favorite and familiar toolchains (e.g. Truffle, Buidler). There are no new languages or coding paradigms to learn.
Ethereum wallet compatibility. Just as in Ethereum, Arbitrum users need only hold keys, but do not have to store any coin history or additional data to protect or access their funds. Since Arbitrum transactions are semantically identical to Ethereum L1 transactions, existing Ethereum users can use their existing Ethereum keys with their existing wallet software such as Metamask.
Token interoperability. Users can easily transfer their ETH, ERC-20 and ERC-721 tokens between Ethereum and the Arbitrum Rollup chain. As we explain in detail below, it is possible to mint tokens in L2 that can subsequently be withdrawn and recognized by the L1 token contract.
Fast finality. Transactions complete with the same finality time as Ethereum L1 (and it's possible to get faster finality guarantees by trading away trust assumptions; see the Arbitrum Rollup whitepaper for details).
Non-custodial. Arbitrum Rollup is a non-custodial scaling solution, so users control their funds/points and neither Reddit nor anyone else can ever access or revoke points held by users.
Censorship Resistant. Since it's completely decentralized, and the Arbitrum protocol guarantees progress trustlessly, Arbitrum Rollup is just as censorship-proof as Ethereum.
Block explorer. The Arbitrum Rollup block explorer allows users to view and analyze transactions on the Rollup chain.
Limitations
Although this is a bake-off, we're not going to sugar coat anything. Arbitrum Rollup, like any Optimistic Rollup protocol, does have one limitation, and that's the delay on withdrawals.
As for the concrete length of the delay, we've done a good deal of internal modeling and have blogged about this as well. Our current modeling suggests a 3-hour delay is sufficient (but as discussed in the linked post there is a tradeoff space between the length of the challenge period and the size of the validators’ deposit).
Note that this doesn't mean that the chain is delayed for three hours. Arbitrum Rollup supports pipelining of execution, which means that validators can keep building new states even while previous ones are “in the pipeline” for confirmation. As the challenge delays expire for each update, a new state will be confirmed (read more about this here).
So activity and progress on the chain are not delayed by the challenge period. The only thing that's delayed is the consummation of withdrawals. Recall though that any single honest validator knows immediately (at the speed of L1 finality) which state updates are correct and can guarantee that they will eventually be confirmed, so once a valid withdrawal has been requested on-chain, every honest party knows that the withdrawal will definitely happen. There's a natural place here for a liquidity market in which a validator (or someone who trusts a validator) can provide withdrawal loans for a small interest fee. This is a no-risk business for them as they know which withdrawals will be confirmed (and can force their confirmation trustlessly no matter what anyone else does) but are just waiting for on-chain finality.
3. The recipe: How Arbitrum Rollup works
For a description of the technical components of Arbitrum Rollup and how they interact to create a highly scalable protocol with a developer experience that is identical to Ethereum, please refer to the following documents:
Arbitrum Rollup Whitepaper
Arbitrum academic paper (describes a previous version of Arbitrum)
4. Developer docs and APIs
For full details about how to set up and interact with an Arbitrum Rollup chain or validator, please refer to our developer docs, which can be found at https://developer.offchainlabs.com/.
Note that the Arbitrum version described on that site is older and will soon be replaced by the version we are entering in Reddit Bake-Off, which is still undergoing internal testing before public release.
5. Who are the validators?
As with any Layer 2 protocol, advancing the protocol correctly requires at least one validator (sometimes called block producers) that is honest and available. A natural question is: who are the validators?
Recall that the validator set for an Arbitrum chain is open and permissionless; anyone can start or stop validating at will. (A useful analogy is to full nodes on an L1 chain.) But we understand that even though anyone can participate, Reddit may want to guarantee that highly reputable nodes are validating their chain. Reddit may choose to validate the chain themselves and/or hire third-party validators.To this end, we have begun building a marketplace for validator-for-hire services so that dapp developers can outsource validation services to reputable nodes with high up-time. We've announced a partnership in which Chainlink nodes will provide Arbitrum validation services, and we expect to announce more partnerships shortly with other blockchain infrastructure providers.
Although there is no requirement that validators are paid, Arbitrum’s economic model tracks validators’ costs (e.g. amount of computation and storage) and can charge small fees on user transactions, using a gas-type system, to cover those costs. Alternatively, a single party such as Reddit can agree to cover the costs of invited validators.
6. Reddit Contract Support
Since Arbitrum contracts and transactions are byte-for-byte compatible with Ethereum, supporting the Reddit contracts is as simple as launching them on an Arbitrum chain.
Minting. Arbitrum Rollup supports hybrid L1/L2 tokens which can be minted in L2 and then withdrawn onto the L1. An L1 contract at address A can make a special call to the EthBridge which deploys a "buddy contract" to the same address A on an Arbitrum chain. Since it's deployed at the same address, users can know that the L2 contract is the authorized "buddy" of the L1 contract on the Arbitrum chain.
For minting, the L1 contract is a standard ERC-20 contract which mints and burns tokens when requested by the L2 contract. It is paired with an ERC-20 contract in L2 which mints tokens based on whatever programmer provided minting facility is desired and burns tokens when they are withdrawn from the rollup chain. Given this base infrastructure, Arbitrum can support any smart contract based method for minting tokens in L2, and indeed we directly support Reddit's signature/claim based minting in L2.
Batch minting. What's better than a mint cookie? A whole batch! In addition to supporting Reddit’s current minting/claiming scheme, we built a second minting design, which we believe outperforms the signature/claim system in many scenarios.
In the current system, Reddit periodically issues signed statements to users, who then take those statements to the blockchain to claim their tokens. An alternative approach would have Reddit directly submit the list of users/amounts to the blockchain and distribute the tokens to the users without the signature/claim process.
To optimize the cost efficiency of this approach, we designed an application-specific compression scheme to minimize the size of the batch distribution list. We analyzed the data from Reddit's previous distributions and found that the data is highly compressible since token amounts are small and repeated, and addresses appear multiple times. Our function groups transactions by size, and replaces previously-seen addresses with a shorter index value. We wrote client code to compress the data, wrote a Solidity decompressing function, and integrated that function into Reddit’s contract running on Arbitrum.
When we ran the compression function on the previous Reddit distribution data, we found that we could compress batched minting data down to to 11.8 bytes per minting event (averaged over a 6-month trace of Reddit’s historical token grants)compared with roughly 174 bytes of on-chain data needed for the signature claim approach to minting (roughly 43 for an RLP-encoded null transaction + 65 for Reddit's signature + 65 for the user's signature + roughly 8 for the number of Points) .
The relative benefit of the two approaches with respect to on-chain call data cost depends on the percentage of users that will actually claim their tokens on chain. With the above figures, batch minting will be cheaper if roughly 5% of users redeem their claims. We stress that our compression scheme is not Arbitrum-specific and would be beneficial in any general-purpose smart contract platform.
8. Benchmarks and costs
In this section, we give the full costs of operating the Reddit contracts on an Arbitrum Rollup chain including the L1 gas costs for the Rollup chain, the costs of computation and storage for the L2 validators as well as the capital lockup requirements for staking.
Arbitrum Rollup is still on testnet, so we did not run mainnet benchmarks. Instead, we measured the L1 gas cost and L2 workload for Reddit operations on Arbitrum and calculated the total cost assuming current Ethereum gas prices. As noted below in detail, our measurements do not assume that Arbitrum is consuming the entire capacity of Ethereum. We will present the details of our model now, but for full transparency you can also play around with it yourself and adjust the parameters, by copying the spreadsheet found here.
Our cost model is based on measurements of Reddit’s contracts, running unmodified (except for the addition of a batch minting function) on Arbitrum Rollup on top of Ethereum.
On the distribution of transactions and frequency of assertions. Reddit's instructions specify the following minimum parameters that submissions should support:
Over a 5 day period, your scaling PoC should be able to handle:
  • 100,000 point claims (minting & distributing points)
  • 25,000 subscriptions
  • 75,000 one-off points burning
  • 100,000 transfers
We provide the full costs of operating an Arbitrum Rollup chain with this usage under the assumption that tokens are minted or granted to users in batches, but other transactions are uniformly distributed over the 5 day period. Unlike some other submissions, we do not make unrealistic assumptions that all operations can be submitted in enormous batches. We assume that batch minting is done in batches that use only a few percent on an L1 block’s gas, and that other operations come in evenly over time and are submitted in batches, with one batch every five minutes to keep latency reasonable. (Users are probably already waiting for L1 finality, which takes at least that long to achieve.)
We note that assuming that there are only 300,000 transactions that arrive uniformly over the 5 day period will make our benchmark numbers lower, but we believe that this will reflect the true cost of running the system. To see why, say that batches are submitted every five minutes (20 L1 blocks) and there's a fixed overhead of c bytes of calldata per batch, the cost of which will get amortized over all transactions executed in that batch. Assume that each individual transaction adds a marginal cost of t. Lastly assume the capacity of the scaling system is high enough that it can support all of Reddit's 300,000 transactions within a single 20-block batch (i.e. that there is more than c + 300,000*t byes of calldata available in 20 blocks).
Consider what happens if c, the per-batch overhead, is large (which it is in some systems, but not in Arbitrum). In the scenario that transactions actually arrive at the system's capacity and each batch is full, then c gets amortized over 300,000 transactions. But if we assume that the system is not running at capacity--and only receives 300,000 transactions arriving uniformly over 5 days-- then each 20-block assertion will contain about 200 transactions, and thus each transaction will pay a nontrivial cost due to c.
We are aware that other proposals presented scaling numbers assuming that 300,000 transactions arrived at maximum capacity and was executed in a single mega-transaction, but according to our estimates, for at least one such report, this led to a reported gas price that was 2-3 orders of magnitude lower than it would have been assuming uniform arrival. We make more realistic batching assumptions, and we believe Arbitrum compares well when batch sizes are realistic.
Our model. Our cost model includes several sources of cost:
  • L1 gas costs: This is the cost of posting transactions as calldata on the L1 chain, as well as the overhead associated with each batch of transactions, and the L1 cost of settling transactions in the Arbitrum protocol.
  • Validator’s staking costs: In normal operation, one validator will need to be staked. The stake is assumed to be 0.2% of the total value of the chain (which is assumed to be $1 per user who is eligible to claim points). The cost of staking is the interest that could be earned on the money if it were not staked.
  • Validator computation and storage: Every validator must do computation to track the chain’s processing of transactions, and must maintain storage to keep track of the contracts’ EVM storage. The cost of computation and storage are estimated based on measurements, with the dollar cost of resources based on Amazon Web Services pricing.
It’s clear from our modeling that the predominant cost is for L1 calldata. This will probably be true for any plausible rollup-based system.
Our model also shows that Arbitrum can scale to workloads much larger than Reddit’s nominal workload, without exhausting L1 or L2 resources. The scaling bottleneck will ultimately be calldata on the L1 chain. We believe that cost could be reduced substantially if necessary by clever encoding of data. (In our design any compression / decompression of L2 transaction calldata would be done by client software and L2 programs, never by an L1 contract.)
9. Status of Arbitrum Rollup
Arbitrum Rollup is live on Ethereum testnet. All of the code written to date including everything included in the Reddit demo is open source and permissively licensed under the Apache V2 license. The first testnet version of Arbitrum Rollup was released on testnet in February. Our current internal version, which we used to benchmark the Reddit contracts, will be released soon and will be a major upgrade.
Both the Arbitrum design as well as the implementation are heavily audited by independent third parties. The Arbitrum academic paper was published at USENIX Security, a top-tier peer-reviewed academic venue. For the Arbitrum software, we have engaged Trail of Bits for a security audit, which is currently ongoing, and we are committed to have a clean report before launching on Ethereum mainnet.
10. Reddit Universe Arbitrum Rollup Chain
The benchmarks described in this document were all measured using the latest internal build of our software. When we release the new software upgrade publicly we will launch a Reddit Universe Arbitrum Rollup chain as a public demo, which will contain the Reddit contracts as well as a Uniswap instance and a Connext Hub, demonstrating how Community Points can be integrated into third party apps. We will also allow members of the public to dynamically launch ecosystem contracts. We at Offchain Labs will cover the validating costs for the Reddit Universe public demo.
If the folks at Reddit would like to evaluate our software prior to our public demo, please email us at [email protected] and we'd be more than happy to provide early access.
11. Even more scaling: Arbitrum Sidechains
Rollups are an excellent approach to scaling, and we are excited about Arbitrum Rollup which far surpasses Reddit's scaling needs. But looking forward to Reddit's eventual goal of supporting hundreds of millions of users, there will likely come a time when Reddit needs more scaling than any Rollup protocol can provide.
While Rollups greatly reduce costs, they don't break the linear barrier. That is, all transactions have an on-chain footprint (because all calldata must be posted on-chain), albeit a far smaller one than on native Ethereum, and the L1 limitations end up being the bottleneck for capacity and cost. Since Ethereum has limited capacity, this linear use of on-chain resources means that costs will eventually increase superlinearly with traffic.
The good news is that we at Offchain Labs have a solution in our roadmap that can satisfy this extreme-scaling setting as well: Arbitrum AnyTrust Sidechains. Arbitrum Sidechains are similar to Arbitrum Rollup, but deviate in that they name a permissioned set of validators. When a chain’s validators agree off-chain, they can greatly reduce the on-chain footprint of the protocol and require almost no data to be put on-chain. When validators can't reach unanimous agreement off-chain, the protocol reverts to Arbitrum Rollup. Technically, Arbitrum Sidechains can be viewed as a hybrid between state channels and Rollup, switching back and forth as necessary, and combining the performance and cost that state channels can achieve in the optimistic case, with the robustness of Rollup in other cases. The core technical challenge is how to switch seamlessly between modes and how to guarantee that security is maintained throughout.
Arbitrum Sidechains break through this linear barrier, while still maintaining a high level of security and decentralization. Arbitrum Sidechains provide the AnyTrust guarantee, which says that as long as any one validator is honest and available (even if you don't know which one will be), the L2 chain is guaranteed to execute correctly according to its code and guaranteed to make progress. Unlike in a state channel, offchain progress does not require unanimous consent, and liveness is preserved as long as there is a single honest validator.
Note that the trust model for Arbitrum Sidechains is much stronger than for typical BFT-style chains which introduce a consensus "voting" protocols among a small permissioned group of validators. BFT-based protocols require a supermajority (more than 2/3) of validators to agree. In Arbitrum Sidechains, by contrast, all you need is a single honest validator to achieve guaranteed correctness and progress. Notice that in Arbitrum adding validators strictly increases security since the AnyTrust guarantee provides correctness as long as any one validator is honest and available. By contrast, in BFT-style protocols, adding nodes can be dangerous as a coalition of dishonest nodes can break the protocol.
Like Arbitrum Rollup, the developer and user experiences for Arbitrum Sidechains will be identical to that of Ethereum. Reddit would be able to choose a large and diverse set of validators, and all that they would need to guarantee to break through the scaling barrier is that a single one of them will remain honest.
We hope to have Arbitrum Sidechains in production in early 2021, and thus when Reddit reaches the scale that surpasses the capacity of Rollups, Arbitrum Sidechains will be waiting and ready to help.
While the idea to switch between channels and Rollup to get the best of both worlds is conceptually simple, getting the details right and making sure that the switch does not introduce any attack vectors is highly non-trivial and has been the subject of years of our research (indeed, we were working on this design for years before the term Rollup was even coined).
12. How Arbitrum compares
We include a comparison to several other categories as well as specific projects when appropriate. and explain why we believe that Arbitrum is best suited for Reddit's purposes. We focus our attention on other Ethereum projects.
Payment only Rollups. Compared to Arbitrum Rollup, ZK-Rollups and other Rollups that only support token transfers have several disadvantages:
  • As outlined throughout the proposal, we believe that the entire draw of Ethereum is in its rich smart contracts support which is simply not achievable with today's zero-knowledge proof technology. Indeed, scaling with a ZK-Rollup will add friction to the deployment of smart contracts that interact with Community Points as users will have to withdraw their coins from the ZK-Rollup and transfer them to a smart contract system (like Arbitrum). The community will be best served if Reddit builds on a platform that has built-in, frictionless smart-contract support.
  • All other Rollup protocols of which we are aware employ a centralized operator. While it's true that users retain custody of their coins, the centralized operator can often profit from censoring, reordering, or delaying transactions. A common misconception is that since they're non-custodial protocols, a centralized sequencer does not pose a risk but this is incorrect as the sequencer can wreak havoc or shake down users for side payments without directly stealing funds.
  • Sidechain type protocols can eliminate some of these issues, but they are not trustless. Instead, they require trust in some quorum of a committee, often requiring two-third of the committee to be honest, compared to rollup protocols like Arbitrum that require only a single honest party. In addition, not all sidechain type protocols have committees that are diverse, or even non-centralized, in practice.
  • Plasma-style protocols have a centralized operator and do not support general smart contracts.
13. Concluding Remarks
While it's ultimately up to the judges’ palate, we believe that Arbitrum Rollup is the bakeoff choice that Reddit kneads. We far surpass Reddit's specified workload requirement at present, have much room to optimize Arbitrum Rollup in the near term, and have a clear path to get Reddit to hundreds of millions of users. Furthermore, we are the only project that gives developers and users the identical interface as the Ethereum blockchain and is fully interoperable and tooling-compatible, and we do this all without any new trust assumptions or centralized components.
But no matter how the cookie crumbles, we're glad to have participated in this bake-off and we thank you for your consideration.
About Offchain Labs
Offchain Labs, Inc. is a venture-funded New York company that spun out of Princeton University research, and is building the Arbitrum platform to usher in the next generation of scalable, interoperable, and compatible smart contracts. Offchain Labs is backed by Pantera Capital, Compound VC, Coinbase Ventures, and others.
Leadership Team
Ed Felten
Ed Felten is Co-founder and Chief Scientist at Offchain Labs. He is on leave from Princeton University, where he is the Robert E. Kahn Professor of Computer Science and Public Affairs. From 2015 to 2017 he served at the White House as Deputy United States Chief Technology Officer and senior advisor to the President. He is an ACM Fellow and member of the National Academy of Engineering. Outside of work, he is an avid runner, cook, and L.A. Dodgers fan.
Steven Goldfeder
Steven Goldfeder is Co-founder and Chief Executive Officer at Offchain Labs. He holds a PhD from Princeton University, where he worked at the intersection of cryptography and cryptocurrencies including threshold cryptography, zero-knowledge proof systems, and post-quantum signatures. He is a co-author of Bitcoin and Cryptocurrency Technologies, the leading textbook on cryptocurrencies, and he has previously worked at Google and Microsoft Research, where he co-invented the Picnic signature algorithm. When not working, you can find Steven spending time with his family, taking a nature walk, or twisting balloons.
Harry Kalodner
Harry Kalodner is Co-founder and Chief Technology Officer at Offchain Labs where he leads the engineering team. Before the company he attended Princeton as a Ph.D candidate where his research explored economics, anonymity, and incentive compatibility of cryptocurrencies, and he also has worked at Apple. When not up at 3:00am writing code, Harry occasionally sleeps.
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Mega eTextbooks release thread (part-28)! Find your textbooks here between $5-$25 :)

Please find the list below:
  1. Disease Gene Identification: Methods and Protocols, 2nd Edition: Johanna K. DiStefano
  2. Statistical Aspects of the Microbiological Examination of Foods, 3rd Edition: Basil Jarvis
  3. Revel for Social Problems, 14th Edition: Stanley Eitzen & Maxine Baca Zinn & Kelly Ei Smith
  4. Fundamentals of Human Resource Management: Pearson New International Edition, 3rd Edition: Gary Dessler
  5. Economics Today: The Micro View, 18th Edition: Roger LeRoy Miller
  6. Employment Law for Business, 8th Edition: Dawn Bennett-Alexander & Laura Hartman
  7. Surgical Exposures in Orthopaedics: The Anatomic Approach, 5th Edition: Stanley Hoppenfeld & Piet de Boer & Richard Buckley
  8. Project Management in Construction, 7th Edition: Sidney Levy
  9. Financial and Managerial Accounting, 7th Edition: John Wild & Ken Shaw & Barbara Chiappetta
  10. Handbook of Plant Disease Identification and Management, 1st Edition: Balaji Aglave
  11. Ubuntu Unleashed 2019 Edition: Covering 18.04, 18.10, 19.04, 13th Edition: Matthew Helmke
  12. Handbook of Insulin Therapies, 1st Edition: Winston Crasto & Janet Jarvis & Melanie J. Davies
  13. Python for Programmers: with Big Data and Artificial Intelligence Case Studies, 1st Edition: Paul J. Deitel & Harvey Deitel
  14. Medical Ethics: Accounts of Ground-Breaking Cases, 7th Edition: Gregory Pence
  15. Human Resource Management, 13th Edition: Gary Dessler
  16. The Biology and Therapeutic Application of Mesenchymal Cells, 2 Volume Set, 1st Edition: Kerry Atkinson
  17. Computer Security Fundamentals, 3rd Edition: William Chuck Easttom
  18. Hendee's Radiation Therapy Physics, 4th Edition: Todd Pawlicki & Daniel J. Scanderbeg & George Starkschall
  19. Nutrient Delivery, 1st Edition: Alexandru Grumezescu
  20. Technology Entrepreneurship: Taking Innovation to the Marketplace, 2nd Edition: Thomas N. Duening & Robert A. Hisrich & Michael A. Lechter
  21. Chemistry of Metalloproteins: Problems and Solutions in Bioinorganic Chemistry, 1st Edition: Joseph J. Stephanos & Anthony W. Addison
  22. Mathematical Statistics with Applications in R, 2nd Edition: Kandethody M. Ramachandran & Chris P. Tsokos
  23. Diagnostic Imaging: Genitourinary, 3rd Edition: Mitchell E. Tublin
  24. Comprehensive Management of Arteriovenous Malformations of the Brain and Spine, 1st Edition: Robert F. Spetzler & Douglas S. Kondziolka & Randall T. Higashida & M. Yashar S. Kalani
  25. Digital Design: With an Introduction to the Verilog HDL, 5th Edition: M. Morris R. Mano & Michael D. Ciletti
  26. Plasmids: Biology and Impact in Biotechnology and Discovery, 1st Edition: Marcelo E. Tolmasky & Juan C. Alonso
  27. Consumer Behavior: Buying, Having, and Being, Global Edition, 12th Edition: Michael R. Solomon
  28. Project Management Case Studies, 5th Edition: Harold Kerzner
  29. Medical Phisiology: Principles for Clinical Medicine, 4th Edition: Rodney A. Rhoades & David R. Bell
  30. Essentials of Contemporary Management, 7th Edition: Gareth Jones & Jennifer George
  31. Harmony and Voice Leading, 4th Edition: Thomas E. Benjamin & Michael Horvit & Robert S. Nelson
  32. Principles of Economics, 2nd Edition: Lee Coppock & Dirk Mateer
  33. Oral Microbiology and Immunology, 2nd Edition: Richard J. Lamont & George N. Hajishengallis & Howard F. Jenkinson
  34. Magnetic Resonance Imaging of the Brain and Spine, 5th Edition: Scott W. Atlas
  35. Accounting Information Systems: Controls and Processes, 3rd Edition: Leslie Turner & Andrea B. Weickgenannt & Mary Kay Copeland
  36. Strategic Corporate Social Responsibility: Sustainable Value Creation, 5th Edition: David Chandler
  37. Julien's Primer of Drug Action: A Comprehensive Guide to the Actions, Uses, and Side Effects of Psychoactive Drugs, 14th Edition: Claire D. Advokat & Joseph Comaty & Robert Julien
  38. The Grand Chessboard: American Primacy And Its Geostrategic Imperatives, 1st Edition: Zbigniew Brzezinski
  39. The Cosmic Perspective: The Solar System, 8th Edition: Jeffrey O. Bennett & Megan O. Donahue & Nicholas Schneider & Mark Voit
  40. Ultrastructure Atlas of Human Tissues, 1st Edition: Fred Hossler
  41. Advances in the Biology and Management of Modern Bed Bugs, 1st Edition: Stephen L. Doggett & Dini M. Miller & Chow-Yang Lee
  42. Patterns of World History: Volume One: To 1600, 1st Edition: Peter von Sivers & Charles A. Desnoyers & George B. Stow
  43. Genitourinary Imaging: A Core Review, 1st Edition: Matthew Davenport
  44. Evidence-based Obstetrics and Gynecology, 1st Edition: Errol R. Norwitz & Carolyn M. Zelop & David A. Miller & David L. Keefe
  45. Zoology, 10th Edition: Stephen Miller & John Harley
  46. Radical and Reconstructive Gynecologic Cancer Surgery, 1st Edition: Robert Bristow & Dennis Chi
  47. Davis's Diseases & Disorders A Nursing Therapeutics Manual, 6th Edition: Marilyn Sawyer Sommers
  48. Management & Cost Accounting, 6th Edition: Alnoor Bhimani
  49. Elements of Modern Algebra, 8th Edition: Linda Gilbert
  50. Psychiatric & Mental Health Nursing, 4th Edition: Katie Evans & Debra Nizette & Anthony O'Brien
  51. Molecular Biology: Different Facets, 1st Edition: Anjali Priyadarshini & Prerna Pandey
  52. Elementary Number Theory, 7th Edition: David Burton
  53. Accounting Information Systems, 14th Edition: Marshall B. Romney & Paul J. Steinbart
  54. Microeconomics, Global Edition, 9th Edition: Robert Pindyck & Daniel Rubinfeld
  55. Psychiatric and Mental Health Nursing Demystified, 1st Edition: Jim Keogh
  56. Entrepreneurship, 10th Edition: Robert Hisrich & Michael Peters & Dean Shepherd
  57. Ganong's Review of Medical Physiology, 26th Edition: Kim E. Barrett & Susan M. Barman & Jason Yuan & Heddwen L. Brooks
  58. Textbook of Obstetrics and Gynaecology: A life course approach, 1st Edition: Eric A.P. Steegers & Bart C.J.M. Fauser & Carina G.J.M. Hilders
  59. Engineering Mechanics: Statics, 8th Edition: James L. Meriam & L. G. Kraige & J. N. Bolton
  60. Basic Concepts of Psychiatric-Mental Health Nursing, 8th Edition: Louise Rebraca Shives
  61. Beckmann and Ling's Obstetrics and Gynecology, 8th Edition: Robert Casanova
  62. Biology: Concepts and Applications, 10th Edition: Cecie Starr & Christine Evers & Lisa Starr
  63. Estimating in Building Construction, 9th Edition: Steven J. Peterson & Frank R. Dagostino
  64. The Big Back Book: Tips & Tricks for Therapists, 1st Edition: Jane Johnson
  65. University Physics with Modern Physics, 14th Edition: Hugh D. Young & Roger A. Freedman
  66. Poisoning and Drug Overdose, 7th Edition: Kent Olson & Ilene Anderson & Neal Benowitz & Paul Blanc
  67. Koneman's Color Atlas and Textbook of Diagnostic Microbiology, 7th Edition: Gary W. Procop
  68. Experimental Psychology, 7th Edition: Anne Myers & Christine H. Hansen
  69. Marketing: An Introduction, 13th Edition: Gary Armstrong & Philip Kotler
  70. Gray's Anatomy for Students: With Student Consult, 3rd Edition: Richard Drake & A. Wayne Vogl & Adam W. M. Mitchell
  71. Chestnut's Obstetric Anesthesia: Principles and Practice, 5th Edition: David H. Chestnut & Cynthia A Wong & Lawrence C Tsen & Warwick D Ngan Kee & Yaakov Beilin & Jill Mhyre
  72. Chemistry: The Molecular Science, 5th Edition: John W. Moore & Conrad L. Stanitski
  73. Head, Neck and Dental Emergencies, 2nd Edition: Mike Perry
  74. Wong's Nursing Care of Infants and Children, 10th Edition: Marilyn J. Hockenberry & David Wilson
  75. Sports Emergency Care: A Team Approach, 3rd Edition: Robb Rehberg & Jeff G. Konin
  76. New Venture Creation: Entrepreneurship for the 21st Century, 10th Edition: Stephen Spinelli & Rob Adams
  77. Caring for the Vulnerable: Perspectives in Nursing Theory, Practice, and Research, 5th Edition: Mary de Chesnay & Barbara Anderson
  78. Geometry: The Line and the Circle: Maureen T. Carroll & Elyn Rykken
  79. Histories of Human Engineering: Tact and Technology: Maarten Derksen
  80. Land Restoration: Reclaiming Landscapes for a Sustainable Future, 1st Edition: Ilan Chabay & Martin Frick & Jennifer Helgeson
  81. Yamada's Handbook of Gastroenterology, 3rd Edition: Tadataka Yamada & John M. Inadomi & Renuka Bhattacharya & Jason A. Dominitz & Joo Ha Hwang
  82. Theoretical Physics 9: Fundamentals of Many-body Physics, 2nd Edition: Wolfgang Nolting & William D. Brewer
  83. Introduction to Programming with C++, 3rd Edition: Y. Daniel Liang
  84. Dental Emergencies, 1st Edition: Mark Greenwood & Ian Corbett
  85. Fundamentals of Physics and Chemistry of the Atmosphere, 2nd Edition: Guido Visconti
  86. Calculus: Early Transcendentals, 3rd Edition: William L. Briggs & Lyle Cochran & Bernard Gillett & Eric Schulz
  87. Educating Physical Therapists, 1st Edition: Gail Jensen
  88. Strategic Developments in Eurasia After 11 September, 1st Edition: Shireen Hunter
  89. Contemporary Issues in Healthcare Law and Ethics, 4th Edition: Dean Harris
  90. Transitioning from RN to MSN: Principles of Professional Role Development: Brenda Scott & Mindy Thompson
  91. Principles and Practice of Public Health Surveillance, 3rd Edition: Lisa M. Lee & Steven M. Teutsch & Stephen B. Thacker & Michael E. St. Louis
  92. Elementary Statistics: Picturing the World, 6th Edition: Ron Larson & Betsy Farber
  93. Human Sexuality in a World of Diversity, 6th Canadian Edition: Spencer A. Rathus & Jeffrey S. Nevid & Lois Fichner-Rathus & Alex McKay & Robin Milhausen
  94. Becoming Your Own Banker, 6th Edition: R. Nelson Nash
  95. Murach's MySQL, 3rd Edition: Joel Murach
  96. Intermediate Algebra, 13th Edition: Marvin L. Bittinger & Judith A. Beecher & Barbara L. Johnson
  97. Planning Health Promotion Programs: An Intervention Mapping Approach, 4th Edition: L. Kay Bartholomew Eldredge & Christine M. Markham & Robert A. C. Ruiter & Maria E. Fernández & Gerjo Kok & Guy S. Parcel
  98. Human Factors in Simple and Complex Systems, 3rd Edition: Robert W. Proctor & Trisha Van Zandt
  99. The Irony of Democracy: An Uncommon Introduction to American Politics, 17th Edition: Louis Schubert & Thomas R. Dye & Harmon Zeigler
  100. Understanding Earth, 7th Edition: John Grotzinger
  101. Nursing Research in Canada: Methods, Critical Appraisal, and Utilization, 4th Edition: Geri LoBiondo-Wood & Judith Haber & Cherylyn Cameron & Mina Singh
  102. The Philosophy of Film, 1st Edition: Thomas E. Wartenberg & Angela Curran
  103. Disaster Nursing and Emergency Preparedness, 4th Edition: Tener Goodwin Veenema
  104. Language in Mind: An Introduction to Psycholinguistics, 2nd Edition: Julie Sedivy
  105. Medical Anthropology: A Biocultural Approach, 3rd Edition: Andrea S. Wiley & John S. Allen
  106. Exploring Biology in the Laboratory, 3rd Edition: Murray P. Pendarvis & John L. Crawley
  107. Guide to Networking Essentials, 8th Edition: Greg Tomsho
  108. Social Psychology: A Storytelling Approach, 2nd Edition: Leonard Newman & Ralph Erber
  109. Managing Conflict: An Introspective Journey to Negotiating Skills, 1st Edition: Dorothy Balancio
  110. Environmental Change and Challenge: A Canadian Perspective, 5th Edition: Philip Dearden & Bruce Mitchell
  111. Brain and Behavior: A Cognitive Neuroscience Perspective, 1st Edition: David Eagleman & Jonathan Downar
  112. Cardiac/Vascular Nurse Exam Secrets Study Guide: Cardiac/Vascular Nurse Test Review for the Cardiac/Vascular Nurse Exam: Mometrix Media & Cardiac Vascular Nurse Exam Secrets
  113. Keeping the Republic: Power and Citizenship in American Politics, The Essentials, 9th Edition: Christine Barbour & Gerald Wright
  114. Principles of Environmental Science, 9th Edition: William Cunningham & Mary Cunningham
  115. Thomas' Calculus, 14th Edition: Joel R. Hass & Christopher E. Heil & Maurice D. Weir
  116. Pharmacology for Canadian Pharmacy Technicians, 1st Edition: Leland Norman Holland & Michael P. Adams & Jeanine Lynn Brice & Heather V. LeBlanc
  117. Cellular and Molecular Immunology, 9th Edition: Abul K. Abbas & Andrew H. Lichtman & Shiv Pillai
  118. Operations Management: Processes and Supply Chains, 11th Edition: Lee J. Krajewski & Manoj K. Malhotra & Larry P. Ritzman
  119. Jews, Christians, Muslims: A Comparative Introduction to Monotheistic Religions, 2nd Edition: John Corrigan & Frederick Denny & Martin S Jaffee & Carlos Eire
  120. Professional Nursing: Concepts & Challenges, 9th Edition: Beth Black
  121. Practical Homicide Investigation: Tactics, Procedures, and Forensic Techniques, 4th Edition: Vernon J. Geberth
  122. Fundamentals of Modern Manufacturing: Materials, Processes and Systems, 7th Edition: Mikell P. Groover
  123. Genetics: A Conceptual Approach, 7th Edition: Benjamin A. Pierce
  124. Computer Science Illuminated, 7th Edition: Nell Dale & John Lewis
  125. The Globalization of World Politics: An Introduction to International Relations, 8th Edition: John Baylis & Steve Smith & Patricia Owens
  126. Behavioral Neuroscience, 9th Edition: S. Marc Breedlove & Neil V. Watson
  127. Canadian Human Resource Management: A Strategic Approach, 12th Edition: Hermann Schwind & Krista Uggerslev & Terry Wagar & Neil Fassina
  128. Brief Principles of Macroeconomics, 9th Edition: N. Gregory Mankiw
  129. Living in the Environment, 4th Canadian Edition: G. Miller & Dave Hackett & Carl Wolfe
  130. Principles of Economics, 9th Edition: N. Gregory Mankiw
  131. Principles of Microeconomics, 9th Edition: N. Gregory Mankiw
  132. Child Development, 9th Edition: Laura E. Berk
  133. Home, School, and Community Collaboration: Culturally Responsive Family Engagement, 4th Edition: Kathy Beth Grant & Julie A. Ray
  134. Set Lighting Technician's Handbook, 4th Edition: Harry Box
  135. Clinical Nurse Leader Certification Review, 2nd Edition: Cynthia R. King
  136. Basic Chemistry, 4th Edition: Karen C. Timberlake & William Timberlake
  137. Sparks & Taylor's Nursing Diagnosis Pocket Guide, 3rd Edition: Linda Phelps
  138. Family Theories: Foundations and Applications, 1st Edition: Katherine R. Allen & Angela C. Henderson
  139. The Earth and Its Peoples: A Global History, 7th Edition: Richard Bulliet & Pamela Crossley & Daniel Headrick & Steven Hirsch & Lyman Johnson
  140. Sociology in Action: A Canadian Perspective, 3rd Edition: Tami Bereska & Diane Symbaluk
  141. Operations Management: Processes and Supply Chains, 12th Edition: Lee J. Krajewski & Manoj K. Malhotra & Larry P. Ritzman
  142. Introduction to Food Science and Food Systems, 2nd Edition: Rick Parker & Miriah Pace
  143. Liaisons, Student Edition: An Introduction to French, 3rd Edition: Wynne Wong & Stacey Weber-Fève & Bill VanPatten
  144. Zuckerman Parker Handbook of Developmental and Behavioral Pediatrics for Primary Care, 4th Edition: Marilyn Augustyn & Barry Zuckerman
  145. Teaching in Today's Inclusive Classrooms: A Universal Design for Learning Approach, 3rd Edition: Richard M. Gargiulo & Debbie Metcalf
  146. The Biological Basis of Mental Health, 3rd Edition: William T. Blows
  147. Developing and Managing Electronic Collections: The Essentials: Peggy Johnson
  148. Western Civilization: Volume II: Since 1500, 10th Edition: Jackson J. Spielvogel
  149. Talking to Strangers: What We Should Know about the People We Don't Know, 1st Edition: Malcolm Gladwell
  150. Understanding Pathophysiology, 7th Edition: Sue E. Huether & Kathryn L. McCance
  151. Our Environment: A Canadian Perspective, 5th edition: Dianne Draper & Ann Zimmerman
  152. Criminal Law: Cases and Materials, 8th Edition: John Kaplan & Robert Weisberg & Guyora Binder
  153. A Photographic Atlas of Histology, 2nd Edition: Michael J Leboffe
  154. Dragons and Tigers: A Geography of South, East, and Southeast Asia, 3rd Edition: Barbara A. Weightman
  155. Climate Change Biology, 1st Edition: Jonathan A. Newman & Madhur Anand & Hugh A. L. Henry & Shelley L. Hunt & Ze'ev Gedalof
  156. The Power of Critical Thinking: 5th Canadian Edition: Chris MacDonald and Lewis Vaughn
  157. Principles of Fire Behavior and Combustion, 4th Edition: Richard Gann & Raymond Friedman
  158. Informatics Nurse Exam Secrets Study Guide: Informatics Test Review for the Informatics Nurse Certification Exam: Informatics Exam Secrets Test Prep Team
  159. General Chemistry, 10th Edition: Darrell Ebbing & Steven D. Gammon
  160. A Practical Guide to Computer Forensics Investigations, 1st Edition: Darren R. Hayes
  161. Basic Biomechanics, 8th Edition: Susan Hall
  162. Essay Writing for Canadian Students, 8th Edition: Roger Davis & Laura K. Davis
  163. Biology, 11th Edition: Peter Raven & George Johnson & Kenneth Mason & Jonathan Losos & Susan Singer
  164. Molecular Imaging, 1st Edition: Ralph Weissleder& Brian D. Ross & Alnawaz Rehemtulla & Sanjiv Sam Gambhir
  165. Criminology, 4th Edition: Frank Schmalleger
  166. A Theory of Truthmaking: Metaphysics, Ontology, and Reality: Jamin Asay
  167. The Routledge Handbook of Metaphysical Grounding, 1st Edition: Michael J. Raven
  168. Linear Algebra and Its Applications, 5th Edition: David C. Lay & Steven R. Lay & Judi J. McDonald
  169. Essentials of Human Communication, 9th Edition: Joseph A. DeVito
  170. Economics: Principles, Applications, and Tools, 9th Edition, Global Edition: Arthur O'Sullivan & Steven Sheffrin & Stephen Perez
  171. Global Health 101, 3rd Edition: Richard Skolnik
  172. Mathematical Proofs: A Transition to Advanced Mathematics, 4th Edition: Gary Chartrand & Albert D. Polimeni & Ping Zhang
  173. Concepts in Strategic Management and Business Policy: Globalization, Innovation and Sustainability, 15th Edition, Global Edition: Thomas L. Wheelen & J. David Hunger & Alan N. Hoffman & Charles E. Bamford
  174. Chemistry: The Central Science, 14th Edition, Global Edition: Theodore E. Brown & H. Eugene LeMay & Bruce E. Bursten & Catherine Murphy & Patrick Woodward & Matthew E. Stoltzfus
  175. Biopsychology, 10th Edition, Global Edition: John P. J. Pinel & Steven Barnes
  176. Electric Circuits, 11th Edition: James W. Nilsson & Susan Riedel
  177. Keeping the Republic; Power and Citizenship in American Politics, the Essentials, 8th Edition: Christine Barbour & Gerald C Wright
  178. Applied Behavior Analysis: Pearson New International Edition, 2nd Edition: John O. Cooper & Timothy E. Heron & William L. Heward
  179. Cryptography and Network Security: Principles and Practice, 7th Edition, Global Edition: William Stallings
  180. Operating Systems: Internals and Design Principles, 9th Edition, Global Edition: William Stallings
  181. Options, Futures, and Other Derivatives, 9th Edition, Global Edition: John C. Hull
  182. Invitation to the Psychology of Religion, 3rd Edition: Raymond F. Paloutzian
  183. Valuation: The Art and Science of Corporate Investment Decisions, 3rd Edition: Sheridan Titman
  184. Comprehensive Clinical Nephrology, 5th Edition: Richard J. Johnson & John Feehally & Jurgen Floege
  185. Miller & Freund's Probability and Statistics for Engineers, 9th Edition, Global Edition: Richard Johnson & Irwin Miller & John Freund
  186. Exploring Strategy: Text and Cases, 11th Edition: Gerry Johnson & Richard Whittington & Patrick Regnér & Kevan Scholes & Duncan Angwin
  187. Economics for Business, 7th Edition: John Sloman
  188. Essentials of Economics, 7th Edition: John Sloman & Dean Garratt
  189. Economics, 9th Edition: John Sloman & Dean Garratt & Alison Wride
  190. Essential Economics for Business, 5th Edition: Johnsloman & Jones Elizabeth
  191. Finite Mathematics, 7th Edition: Stefan Waner & Steven Costenoble
  192. The SAGE Encyclopedia of Surveillance, Security, and Privacy, 1st Edition: Bruce A. Arrigo
  193. Evolution, 4th Edition: Douglas J. Futuyma & Mark Kirkpatrick
  194. Adult Development and Aging, 7th Edition: John C. Cavanaugh & Fredda Blanchard-Fields
  195. Foundations of Finance, 9th Edition, Global Edition: Arthur J. Keown & John D Martin & J. William Petty
  196. Learning PHP, MySQL & JavaScript: With jQuery, CSS & HTML5, 4th Edition: Robin Nixon
  197. Head First Learn to Code: A Learner's Guide to Coding and Computational Thinking, 1st Edition: Eric Freeman
  198. Learning Swift: Building Apps for macOS, iOS, and Beyond, 3rd Edition: Jonathon Manning & Paris Buttfield-Addison & Tim Nugent
  199. Database Systems: Design, Implementation, & Management, 12th Edition: Carlos Coronel & Steven Morris
  200. Introduction to Solid Modeling Using SolidWorks, 13th Edition: William Howard & Joseph Musto
  201. Communications Receivers: Principles and Design, 4th Edition: Ulrich Rohde & Jerry Whitaker & Hans Zahnd
  202. Connect Core Concepts in Health, 15th Edition: Paul Insel & Walton Roth
  203. On Course: Strategies for Creating Success in College and in Life, 8th Edition: Skip Downing
  204. Vander's Human Physiology, 15th Edition: Eric Widmaier & Hershel Raff & Kevin Strang
  205. Biology, 4th Edition: Robert Brooker & Eric Widmaier & Linda Graham & Peter Stiling
  206. The Essentials of Statistics: A Tool for Social Research, 4th Edition: Joseph F. Healey
  207. Oracle 12c: SQL, 3rd Edition: Joan Casteel
  208. Global Business Today, 10th Edition: Charles Hill & G. Tomas M. Hult
  209. Project Management: The Managerial Process, 7th Edition: Erik Larson & Clifford Gray
  210. Organizational Behavior: A Practical, Problem-Solving Approach, 2nd Edition: Angelo Kinicki & Mel Fugate
  211. International Management: Culture, Strategy, and Behavior, 10th Edition: Fred Luthans & Jonathan Doh
  212. CorelDRAW X8: The Official Guide, 12th Edition: Gary David Bouton
  213. Physics for Scientists and Engineers: An Interactive Approach, 2nd Edition: Robert Hawkes & Javed Iqbal & Firas Mansour & Marina Milner-Bolotin & Peter Williams
  214. Programmable Logic Controllers, 5th Edition: Frank Petruzella
  215. Foundations in Microbiology, 10th Edition: Kathleen Park Talaro & Barry Chess
  216. Applied Numerical Methods with MATLAB for Engineers and Scientists, 4th Edition: Steven Chapra
  217. Tonal Harmony, 8th Edition: Stefan Kostka & Dorothy Payne & Byron Almén
  218. Discrete Mathematics, 8th Edition: Richard Johnsonbaugh
  219. Bates' Pocket Guide to Physical Examination and History Taking, 8th Edition: Lynn S. Bickley
  220. NANDA International Nursing Diagnoses: Definitions & Classification 2018-2020, 11th Edition: T. Heather Herdman & Shigemi Kamitsuru & Heather T. Herdman
  221. Biology: Concepts and Investigations, 4th Edition: Mariëlle Hoefnagels
  222. Biology: Concepts and Investigations, 3rd Edition: Mariëlle Hoefnagels
  223. Human Biology: Concepts and Current Issues, 8th Edition, Global Edition: Michael D. Johnson
  224. Messages: Building Interpersonal Communication Skills, 5th Canadian Edition: Joseph A. DeVito & Rena Shimoni & Dawne Clark
  225. The Interpersonal Communication Book, 14th Edition, Global Edition: Joseph A. DeVito
  226. Computational Systems Pharmacology and Toxicology, 1st Edition: Rudy J Richardson & Dale E Johnson & Noffisat Oki & David Faulkner
  227. Shelly Cashman Series Microsoft Office 365 & Office 2019 Introductory, 1st Edition: Sandra Cable & Steven M. Freund & Ellen Monk & Susan L. Sebok & Joy L. Starks
  228. The Practice of Emotionally Focused Couple Therapy: Creating Connection, 2nd Edition: Susan M. Johnson
  229. The Marriage Clinic: A Scientifically Based Marital Therapy, 1st Edition: John M. Gottman
  230. Cognitive-Behavioral Therapy with Couples and Families: A Comprehensive Guide for Clinicians, 1st Edition: Frank M. Dattilio & Aaron T. Beck
  231. International Marketing, 17th Edition: Philip R. Cateora & John Graham & Mary C Gilly
  232. Kaplan and Sadock's Concise Textbook of Clinical Psychiatry, 3rd Edition: Benjamin Sadock & Virginia Alcott Sadock
  233. Anthropology, 14th Edition: Carol R. Ember & Melvin Ember & Peter N. Peregrine
  234. The Men They Will Become: The Nature And Nurture Of Male Character: Eli Newberger
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Cryptography Intro What is Cryptocurrency? - YouTube Cryptography: Crash Course Computer Science #33 - YouTube Bitcoin: How Cryptocurrencies Work - YouTube Bitcoin explained: How do cryptocurrencies work? - BBC ...

A Definition of Cryptography in the Cloud Cryptography in the cloud employs encryption techniques to secure data that will be used or stored in the cloud. It allows users to conveniently and securely access shared cloud services, as any data that is hosted by cloud providers is protected with encryption. Bitcoin relies on public-key cryptography, in which users have a public key that is available for everyone to see and a private key known only to their computers. In a Bitcoin transaction, users receiving Bitcoins send their public keys to users transferring the Bitcoins. Users transferring the coins sign with their private keys, and the ... Bitcoin is the first and currently the largest decentralized cryptocurrency in the world. Bitcoin uses a peer-to-peer distributed network that uses a proof-of-work chain to overcome Byzantine failures and reach a coherent global blockchain. Bitcoin uses the Public-key cryptography protocol to ensure secure transactions and ownership of bitcoins. Learn about the cryptography of Bitcoin and its algorithm. Cryptography is the study of codes - writing codes, solving codes, and manipulating codes. See the work and methodology of how Bitcoin encryption works today! Bitcoin is a type of cryptocurrency.Balances of Bitcoin tokens are kept using public and private "keys," which are long strings of numbers and letters linked through the mathematical encryption ...

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Cryptography Intro

Today we’re going to talk about how to keep information secret, and this isn’t a new goal. From as early as Julius Caesar’s Caesar cipher to Mary, Queen of S... An estimated £3-4 billion is being laundered via cryptocurrencies in Europe every year, the director of Europol has told the BBC. It comes as the Shadow Trea... Cryptography, the science of writing codes and ciphers for secure communication, is one of the most important elements that goes into making modern cryptocur... Learn about Bitcoin with the most watched Bitcoin video. More information: Start Guide - https://www.weusecoins.com Mining Guide - https://www.bitcoinmining.... I'll explain concepts in cryptography useful to understand to grasp crypto currencies such as Bitcoin and Ripple. This is a simple explanation with no math.

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