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What are ZK-SNARKs?

You may have come across the term “ZK-SNARK” in discussions about blockchain, web3, and other emerging technologies. But what exactly are they? Let’s break it down in simple terms.

ZK-SNARK stands for “Zero-Knowledge Succinct Non-Interactive Argument of Knowledge.” It’s a type of cryptographic proof that allows someone to prove they have certain information or knowledge, without actually revealing that information.

Here’s how it works:

Zero-Knowledge: The person making the proof (the “prover”) can convince the person verifying the proof (the “verifier”) that a statement is true, without revealing any additional details about the statement. For example, the prover could prove they know a secret password, without telling the verifier what the password is.

Succinct: The proof itself is very compact, usually just a few hundred bytes long. This means it can be verified quickly, even for complex statements.

Non-Interactive: The prover can generate the proof on their own, without any back-and-forth communication with the verifier. The verifier can then check the proof at any time, without needing the prover to be present.

Argument of Knowledge: If the statement being proven is true, the verifier is guaranteed to accept the proof. If the statement is false, the verifier will reject the proof. This ensures the prover actually has the knowledge they claim to have.

In practical terms, ZK-SNARKs allow for all kinds of powerful applications, like privacy-preserving transactions, verifiable computations, and more. They’re a key building block for many blockchain and web3 technologies. The ability to prove things without revealing sensitive information has a lot of potential uses in the digital world.

How are ZK-SNARKs Constructed?

Building a ZK-SNARK system involves three main components:

1. Arithmetization: The first step is to represent the problem or computation that the prover wants to prove in a way that’s suitable for the ZK-SNARK system. This involves converting the problem into a set of polynomial equations.

The idea is that any program or algorithm, no matter how complex, can ultimately be broken down into a series of simple arithmetic operations, like addition and multiplication. In a ZK-SNARK system, these arithmetic operations are represented using “gates” — similar to how a computer’s CPU uses logic gates to execute instructions. By representing the problem as a circuit of these arithmetic gates, it can be translated into a set of polynomial equations that must be satisfied.

2. Proof System: Once the problem has been arithmetized, the prover needs to generate a cryptographic proof that they know a valid solution to the polynomial equations, without revealing the actual solution.

This is done using a special type of proof system called an “Interactive Oracle Proof” (IOP). The prover and verifier engage in a interactive protocol where the prover demonstrates knowledge of the solution, but the verifier never learns the actual solution. This interactive proof can then be converted into a non-interactive proof using a technique called the Fiat-Shamir transformation.

3. Commitment Scheme: The final component is a commitment scheme, which allows the prover to “commit” to their solution in a way that is both binding (the prover can’t change it later) and hiding (the verifier can’t see the actual solution).

Conceptually, you can think of this like the prover writing their solution on a piece of paper, locking it in a box, and sending the box to the verifier. The verifier can’t see the contents, but the prover can’t change it either. When the prover is ready, they provide the key to open the box, allowing the verifier to check the solution.

In practice, the commitment is implemented using cryptographic techniques like encryption, rather than a literal physical box.

By combining these three components — arithmetization, a proof system, and a commitment scheme — ZK-SNARK systems are able to construct succinct, non-interactive proofs that demonstrate knowledge of a solution, without revealing the solution itself. This is the core innovation that makes ZK-SNARKs so powerful and useful in a wide range of applications.

Putting ZK-SNARKs to Use

Now that we understand the core components of a ZK-SNARK system, the next question is: How can we actually use this technology to prove our own ideas or claims?

The process looks something like this:

Idea: Start with the idea or problem you want to prove.

Program: Translate that idea into a computer program that can be executed to solve the problem.

Circuit: Convert the program into a “circuit” — a network of simple arithmetic operations that can be represented as polynomial equations.

Parameters: Generate the cryptographic parameters needed for the ZK-SNARK proof system.

Proof: Using the circuit and parameters, the prover can generate a succinct, non-interactive proof that they know a valid solution.

Verification: The verifier can then check the proof to confirm the validity of the prover’s claim, without learning the actual solution.

An anatomy of a typical ZK-SNARK system

So how do we bridge the gap between a regular computer program and the circuit representation required for ZK-SNARKs? There are a few different approaches:

Hardware Description Languages (HDLs): Tools like Circom allow you to directly program the circuit using a language similar to how integrated circuits are designed. This gives you fine-grained control over the circuit, but requires learning a new domain-specific language.

Libraries: Frameworks like Bellman (Rust) and Gadgetlib (C++) provide programming libraries that let you build circuits using familiar programming languages. This is more accessible for developers, but you still need to understand the circuit-level constraints.

Compilers: Some new programming languages, like Zinc, are designed specifically for ZK-SNARK applications. They allow you to write high-level code that gets automatically compiled down to the required circuit representation. This is the most user-friendly approach, but may have performance trade-offs compared to the other methods.

Ultimately, the choice of approach depends on your specific needs and the level of control you require over the circuit representation. Developers with a strong background in hardware design may prefer the HDL route, while those more comfortable with general-purpose programming languages may find the library or compiler options more accessible.

Regardless of the approach, the key is being able to translate your idea or problem into a form that can be efficiently represented as a ZK-SNARK circuit. This unlocks the power of ZK-SNARKs to prove the validity of your claims without revealing sensitive information.

Verifying Machine Learning with ZK-SNARKs

As machine learning (ML) models have become more complex and powerful, a new challenge has emerged: how can we verify that the predictions made by these models are correct, especially when the models are being served by a third-party provider in an “ML-as-a-Service” (MLaaS) scenario?

This is where verifiable machine learning (VML) comes into play. The idea is to use ZK-SNARKs to allow an ML model provider to prove to a consumer that the model is behaving correctly, without revealing the sensitive details of the model itself.

So how do we go about generating a ZK-SNARK proof for a machine learning model? There are a few different approaches:

Direct Circuit Representation: The most straightforward way is to use the tools we discussed earlier, like Circom, to translate the ML model into a circuit representation that can be used to generate a ZK-SNARK proof. However, this approach can be quite inefficient, as the size of the circuit and the time required to generate the proof can grow quickly as the model complexity increases.

Specialized ZK-SNARK Protocols: To address the performance challenges of the direct approach, researchers have developed ZK-SNARK protocols that are specifically optimized for machine learning use cases. One example is Halo2, used in the Zcash cryptocurrency. Halo2 includes features like lookup tables and custom gates that make it much more efficient for handling the non-linear operations common in ML models.

ML-Focused Frameworks: Building on these specialized ZK-SNARK protocols, there are now frameworks like EZKL and ZKML that provide higher-level tools for constructing ZK-SNARK proofs for ML models. These frameworks allow developers to work directly with common ML model formats like PyTorch and TensorFlow Lite, without needing to worry about the low-level circuit representation.

Hybrid Approaches: Another option is to combine the strengths of different approaches. For example, the Circom HDL language, while not as optimized as Halo2 for ML, provides very fast verification times and short proofs. The Circomlib-ML library provides some pre-built circuit templates for common ML operations that can be used as a starting point.

Ultimately, the choice of approach will depend on the specific requirements of the application, the complexity of the ML model, and the trade-offs between proof generation time, proof size, and verification performance.

The key takeaway is that ZK-SNARKs provide a powerful tool for verifying the behavior of machine learning models, especially in scenarios where the models are being served by a third-party provider. By generating succinct, non-interactive proofs, the model consumer can have confidence in the correctness of the predictions, without needing to reveal the sensitive details of the model itself.

References

For further information on ZK-SNARKs and their applications in machine learning, here are some helpful resources:

Zero Knowledge Proofs MOOC: https://zk-learning.org/

A comprehensive online course on zero knowledge proofs and their construction.

ZKCNN Paper: https://eprint.iacr.org/2021/673

A research paper introducing a specialized ZK-SNARK protocol for verifying convolutional neural network (CNN) models.

ZKML Community: https://github.com/zkml-community/awesome-zkml

A curated list of resources, tools, and projects related to verifiable machine learning using ZK-SNARKs.

Daniel Kang’s Medium: https://medium.com/@danieldkang

A collection of articles by Daniel Kang, a researcher in the field of ZK-SNARKs and their applications.

Daniel Kang’s Paper: https://arxiv.org/abs/2210.08674

A research paper by Daniel Kang on using ZK-SNARKs for verifiable machine learning.

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