Zero knowledge proofs and SNARKs and libsnark

Madars Virza

I am going to tell you about zerocash and our approach of addressing Bitcoin's privacy problem. All of this is joint work with Techion, ETCH Zurich, and MIT, and Matt Green, .. and .. and..

So first to get us going, I want to talk a little bit about two of my ideas around Bitcoin. There are two questions that every decentralized cryptocurrency must answer. First of them is where does the money come from. The second question is, if money is digital, if I have my digital $1 bill, can I copy it? What prevents it from double spending?

Bitcoin has answers to both of them. Money comes from work for solving hard puzzles. Double spending is prevented by using a public consensus protocol that uses puzzles. It maintains a public ledger. This ledger has sparked tremendous innovation.

If you have a public ledger, it is easy to track whether you are double spending. This innovation is also a liability for Bitcoin. Because it presents a privacy issue. Bitcoin is not really anonymous. A simplified example is the blockchain where you see a "from" address and a to address and amount. All transactions will be there forever.

People may say, "those are just addresses" and "what can you get from them". It's true that it is not a first or last name. But it is just like a nickname. By design, those who you interact with know thos eaddresses. Anyone else can mine the ledger.

There has been extensive academic work of doing just that. You might say that the academic work is not really there. Methods of analysis get stronger as time goes by. But your history will be saved forever. This is like something you see in the news.

You might say it's not private, do we care? My answer is yes, because there are serious consequences for the Bitcoin economy. It limits adoption because consumers have purchases visible to everyone. If a United States merchants decides to go all Bitcoin, then their cashflow is exposed to competitors. Even more so, it threatens the Bitcoin economy because it's a threat to fungibility. Say I go to a coffee shop and get change, but it happens to be stolen from MtGox, it has now tainted my wallet. Maybe sometime later they will stop accepting my Bitcoin because of that.

For many users, Bitcoin is in a sense worse than a bank. In a regular currency you leave everything to a bank. Do you have to reveal everything to everyone? We think no.

Our goal is to preserve privacy and also have decentralization. Our result is zerocash. We can sit on top of any ledger system. You can have zerocash for Bitcoin or even for Litecoin. It provably hides all metadata about all transactions. Unlike previous approaches, zerocash is also efficient. Transactions are small, easy to produce and easy to verify.

We have essentially what I would call a perfect system. Nothing comes for free. There is a caveat. We need one-time trusted setup to generate public parameters for the system. And we need additional cryptographic assumptions. The trusted setup limitation can be removed, and I am going to talk about that later in the talk.

Now, let's have like a 10k foot overview of how zerocash works. What it amounts to is how to ensure integrity when everything is hidden. You cannot just look at tihngs to ensure integrity, because there is nothing to look at. Let's say there's an Alice and a Bob, and Alice wants to send 10 coins to Bob. He wants to know whether it's valid. He can't look at the ledger.

Alice knows for a fact tha tthe transaction is valid. She knows she got 10 BTC from Carol. She knows she didn't spend them. Therefore the transaction must be valid. So she can send all of her books over to Bob. He can examine her entire financial history. Well, this is not private. This is what Bitcoin does though.

We need to do better. Let's use a trusted accountant. Alice has access to a trusted account. She can send her books to the accountant, the accountant will look and say yes it checks out, and produce a signature that says the transaction you are about to receive is valid. Bob can look at that signature and be convinced.

But where do you get such an accountant? Accountants are humans, they don't really scale to billions of transactions and real-time operation. We would like to somehow digitize this accountant and have it as a program with integrity you can computationally verify.

You can imagine a virtual accountant in Alice's head that she presents all transactions to. Later we get cryptographic proof that this account accepted. We can post that proof on a ledger. And now Bob is happy. He gets his coins and he can prove those are really unspent. So his question goes away.

From a high level, this is what zerocash does. We can produce public transactions with zero knowledge proofs. But what kind of proof do we need? There are many cryptographic proof systems.

There must be proof. We also want this to be zero knowledge. Bob must not learn a nything about Alice's transaction history by examining the proof. It must be non-interactive, which means that Bob can verify the correctness without interacting with any accountant digital or real. It must be posted on the ledger. It must be succinct. Small and easy to verify. Finally, we want the cryptographic property known as proof-of-knowledge. We want to ensure that Alice knows the secret behind the transaction. What does it mean that there exists a signature? We want to know that Alice knows the signing key for such a signature.

All of those properties when taken together are actually impossible. So we relax this from being a proof to being an argument. It holds if cryptography is not broken. If you take all of them together now, a succinct non-interactive proof of knowledge, called snark. This is call zkSNARK when put together.

Having identified what we want, can we get it? In a beautiful line of early work by Killian92 and Mical92, Mical00, they are efficient enough to be implemented.

PGHR13, BCGTV13, BCTV14b, KPPSST14, ZPK14, CFHKPKNPZ14, BCTV14,

We chose one of those systems, libsnark, that we believe is best. Our implementation we chose is fast. It's also very versatile. It supports low-level concepts like circuits and high-level concepts like random access machines. It is MIT licensed.

https://github.com/scipr-lab/libsnark

SNARK is just a tool. It will not be plug and play. A great deal of work goes into characterizing how do we use this tool to build an anonymous payment scheme? That's the main contribution of "SNARKS for C" paper.

We need to introduce a notion of decentralized anonymous payments. These are specified by algorithms that specify some security properties. Everything is hidden, so we need to define them a new. The algorithms we need are setting up the parameters, for users to create addresses, mint coins, send them to other users, for miners to verify transactions, and if everything is hidden on the blockchain then we need an algorithm that scans the blockchain and receives your coins.

The security requirements are those. We want these to be private. This must be ledger indistinguishability. Nothing revealed besides public information on the ledger, even by chosen-transaction adversary. This should hold even if the adversary can choose transactions.

Since everything is hidden, we need to ensure balance. No money from thin air. You can only spend what you have minted or received. Finally, we need non-malleability, the transactions must not be modified while in route to the ledger.

Now we can build up from an insecure scheme to something more secure, completely secure, then we can add functionality.

Let's build a basic anonymous ecash. Our coins are going to be identified by serial numbers. What we need to integrate are coins in the Bitcoin ecosystem. So we add new transactions. One is minting, it uses up 1 BTC to create a coin with a specified serial number. And here they are. You can scan the ledger for them.

How do you use this coin? Well that's spending. The semantics is using up a coin with a unique serial number, and a BTC appears in the result. This scheme is horribly broken in multiple ways. It is not private. Anyone can steal your coins. But it's a start. So let's try better.

In 1999, Sander and Ta-Shma used the idea of commitment schemes that my coin is going to be identified by a coin commitment that commits to a serial number. The commitment scheme is like a hash function that essentially ensures two properties, that it is hard to go back from commitment to the serial number even if you know the, it's hard to go from commitment to serial number, and it's also hard to claim a different serial number with a different commitment randomness for the same coin commitment. Main thing will be, I hereby spend 1 BTC to create this anonymous coin with a coin commitment. And coin commitments are here, and spending a coin would mean I'm using up a coin with a unique serial number so that you can verify that I am not double spending. So here is the commitment and randomness. So you can check if it really was there. The scheme is again horribly insecure, but we have made some progress.

So what ... proposes is to build a merkle tree over all coin commitments, and then you still reveal the unique serial number, but instead of revealing coin commitment and randomness, you prove in zero knowledge that you know them. That essentially unlinks the minting the coin from the act of spending the coin. Integrity is ensured under the seal of zero knowledge proof.

This only supports single denomination. If I want to spend you 10 BTC, I will need 10 transactions. This is not hard to fix. Use iterated coin commitments where the outer one contains a value, the inner one contains serial number, and then you mint, you post publicly how much you want to spend in Bitcoin, then you post two values k and r to prove consistency but you don't post the serial number. To spend against, you post the coin value and that proves, and the serial number, and this proves that you know the coin is a hash tree that corresponded to it.

You can go on. All transactions must go through the Bitcoin network. If you are totally unique values, and they will appear on the network, so we will add an additional thing, that users can send coins directly from one to another. To do that, we need to ensure that a coin after it is sent cannot be spent by the sender. So we are going to make a scheme where the serial number is unknown to the sender. There is going to be an address in public, and a secret key pair for every participant in the system. You can send to anyone's public key, but to spend it, someone needs to know the corresponding secret key to produce a serial number. Those secrets can be sent either out of band to send someone a coin, or posted encrypted to the ledger.

So that takes care of direct paymetns. But that doesn't let you split coin apart or join two coins together. Or convert to Bitcoin after the fact.

What we are going to introduce is a concept that unifies these notions. Pouring. Zerocash coins go out, two coins go out, and there's a public Bitcoin output that can be split up for a transaction fee or just going to the Bitcoin ledger. This algorithm needs to know what are the values, how you want to split it up, and what the destinations are. It will produce the correct coins and a proof that ensures the transaction was valid. That the blaances match out.

What will be posted on the ledger is the serial numbers for the old coins, and commitments for the new coins, and the proof. Let's take a deep breath. So this covers most of the technical part. If you want more detail, this is in the paper. This is actually a simplified version of our construction.

So a nice theoretical construction, but can it be implemented? Yes, we did implement it. We started from libsnark, we integrated with bitcoind, we made libzerocash. We found out that the preformance for our clients is good and that the latency in block propagation time is negligble. So it really works.

However, I will address this caveat of this trusted setup. So what is this? Our zkSNARK trusted setup is for initial public parameters of the system. It only happens at genesis time. After that, no trust is required in the system ever. However, if the trusted setup is compromised, then an attacker can fake new coins and could totally trash your economy. An attacker cannot break your anonymity or steal your coins. That said, we would like to get rid of trusted setup.

There is a paper by some of us which will be appearing soon (BCGTV15) where we propose a multi-party protocol for sampling the parameters. Efficient MPC protocol. If just one is honest, then parameters are going to be completely secure, meaning that an attacker needs to compromise every single one of the participants presumably on the different continents, to break the setup assumptions.

Another way around trusted setup is using PCP (probabilistically checkable proofs), but this is a topic for a different talk. (Multi-party computation?)

Yesterday we saw this wonderful table by Charlie Lee that gratefully allowed me to reproduce it here, thank you. Zerocash is everything that Bitcoin is, in those terms, plus the fungibility issue is solved. So maybe zerocash is the perfect currency.

You can go beyond privacy and fungibility. You can use zero knowledge to get more public oversight. The current statements we are proving is stuff like the balances match but I wont tell you more. Zerocash stops here, but you can extend it. You can prove to you that the money went to a non-profit. I am not going to tell anyone which non-profit it was.

Public oversight example: I know the private keys that control a large amount of Bitcoin, but I am not going to tell you which address. This is an interesting public policy question. Which policies are feasible and which ones are desirable?

To wrap-up, our approach is http://zca.sh/ we have our whitepaper there. The zkSNARK library is from http://scipr-lab.org/

We were wondering what's next for zerocash. So we needed to solve this annoying trusted setup problem. We think we have this down now. The next thing is to just to deploy. Thank you.

Questions: - what do you think of libsnark?