Nova: A New Chapter of Zero-knowledge Proofs
Introduction
Zero-knowledge proof is an important technique in cryptography that allows one person to prove a statement to another person without revealing any additional information. This technology has widespread applications in various fields, including identity verification, blockchain, and secure computation. Nova is a new zero-knowledge proof system developed by Microsoft that uses a technique called Relaxed Rank-1 Constraint Systems (Relaxed R1CS) to improve the efficiency and flexibility of proofs. The final chapter provides a detailed explanation of the source code.
Advantages of Nova
The main advantage of Nova lies in its use of the Relaxed R1CS technology. R1CS is a system used to construct zero-knowledge proofs, allowing one to prove knowledge of a solution satisfying a set of polynomial equations without revealing any information about the solution. However, traditional R1CS systems require a significant amount of randomness during the proof process, resulting in complex and time-consuming proof generation and verification. Nova addresses this issue by using relaxed R1CS, which allows for less randomness in proofs, greatly improving efficiency.
Nova also has other advantages. For example, it supports incremental computation, which means complex functions can be computed gradually without the need to calculate the entire function at once. This is particularly useful when handling large-scale data or performing complex computations. Additionally, Nova supports polynomial computation, enabling it to handle more complex proof tasks.
Disadvantages of Nova
Despite its many advantages, Nova also has some disadvantages. Firstly, due to the use of relaxed R1CS, Nova's proofs may not be as strong as those of traditional R1CS systems. This is because relaxed R1CS allows for less randomness in proofs, which may compromise the security of the proof. However, Nova's developers have taken measures to address this issue, such as using stronger cryptographic algorithms and more complex proof strategies.
Secondly, the implementation of Nova is relatively complex, which may increase the difficulty of its use and maintenance. Nova employs advanced cryptographic techniques such as polynomial computation, group operations, and random oracles, requiring a deep understanding of these techniques for effective use and modification of Nova.
The Importance of Nova in the Zero-Knowledge Proof field
Nova occupies an important position in the field of zero-knowledge proofs. Its emergence has opened up new paths for the development of zero-knowledge proofs. The relaxed R1CS technology adopted by Nova makes the generation and verification of proofs more efficient, which is crucial for large-scale zero-knowledge proof applications. In addition, Nova supports incremental computation and polynomial computation, enabling it to handle more complex proof tasks, further expanding the application scope of zero-knowledge proofs.
Code interpretation of Nova
https://github.com/microsoft/Nova
The following important subdirectories can be found in the src/ directory:
bellperson/: This directory may contain code related to the Bellman-Ford algorithm.
gadgets/: This directory may contain tools for constructing zk-SNARK proofs.
provider/: This directory may contain code for providers, such as keccak.rs which may implement the Keccak hash function.
spartan/: This directory may contain code related to the Spartan protocol.
traits/: This directory may contain Rust traits for defining common behaviors.
Contents of the src/bellperson/mod.rs file:
This module is mainly used to generate R1CS (Rank-1 Constraint Systems, a type of constraint system used for zk-SNARKs).
It consists of three submodules:
r1cs: This submodule may contain code related to R1CS.
shape_cs: This submodule may contain code related to shape constraint systems.
solver: This submodule may contain code related to solving constraint systems.
In the test section, a function named synthesize_alloc_bit is defined, which takes a constraint system and adds some constraints to check if the input bits are indeed bits. Then, a function named test_alloc_bit_with is defined, which first creates a shape
src/bellperson/r 1 cs.rs file content:
This file mainly defines two traits: `NovaWitness` and `NovaShape`, which provide methods to obtain `R 1 CSInstance` and `R 1 CSWitness` from implementers, as well as methods to obtain `R 1 CSShape` and `CommitmentKey`.
- The `NovaWitness` trait has a method called `r1cs_instance_and_witness`, which takes a `R 1 CSShape` and a `CommitmentKey`, and returns a `R 1 CSInstance` and a `R 1 CSWitness`. This trait is implemented for the `SatisfyingAssignment` struct, which means that any `SatisfyingAssignment` can use this method to obtain a `R 1 CSInstance` and a `R 1 CSWitness`.
- The `NovaShape` trait has a method called `r 1 cs_shape`, which returns a `R 1 CSShape` and a `CommitmentKey`. This trait is implemented for the `ShapeCS` struct, which means that any `ShapeCS` can use this method to obtain a `R 1 CSShape` and a `CommitmentKey`.
This file also defines a function `add_constraint`, which takes a constraint system and three linear combinations, and then adds a new constraint to the constraint system. This function is used by the implementer of `NovaShape` when generating `R 1 CSShape`.
In general, the main purpose of this file is to provide a way to generate instances, witnesses, shapes, and commitment keys for R 1 CS from a system that satisfies specific conditions (such as `SatisfyingAssignment` or `ShapeCS`).
src/bellperson/shape_cs.rs
This file defines a struct named `ShapeCS`, which implements the `ConstraintSystem` trait. `ShapeCS` is the constraint system used to create R 1 CS shapes.
The `ShapeCS` struct contains several fields:
- `named_objects`: This is a map used to store objects associated with paths.
- `current_namespace`: This is a string vector used to store the current namespace.
- `constraints`: This is a vector used to store all the constraints added to `ShapeCS`.
- `inputs`: This is a string vector used to store all the inputs.
- `aux`: This is a string vector used to store all the auxiliary inputs.
The `ShapeCS` struct implements the `ConstraintSystem` trait, which means it provides the following methods:
- `alloc`: This method is used to allocate a new variable.
- `alloc_input`: This method is used to allocate a new input variable.
- `enforce`: This method is used to add a new constraint.
- `push_namespace`: This method is used to push a new namespace.
- `pop_namespace`: This method is used to pop the current namespace.
- `get_root`: This method is used to get the root constraint system.
This file also defines some helper functions, such as `proc_lc` and `compute_path`, which are used to handle linear combinations and compute paths, respectively.
In general, the main purpose of this file is to provide a way to generate the shape of an R1 CS from a system that satisfies specific conditions, such as ShapeCS.
src/bellperson/solver.rs
This file defines a struct named SatisfyingAssignment, which implements the ConstraintSystem trait. SatisfyingAssignment is a constraint system used to create instances and witnesses of R1 CS.
The SatisfyingAssignment struct contains the following fields:
- `a_aux_density`, `b_input_density`, `b_aux_density`: These are fields of type DensityTracker used to track the density of queries.
- `a`, `b`, `c`: These are vectors used to store the evaluation results of the A, B, and C polynomials.
- `input_assignment`, `aux_assignment`: These are vectors used to store variable assignments.
The SatisfyingAssignment struct implements the ConstraintSystem trait, which means it provides the following methods:
- `new`: This method is used to create a new instance of SatisfyingAssignment.
- `alloc`: This method is used to allocate a new auxiliary variable.
- `alloc_input`: This method is used to allocate a new input variable.
- `enforce`: This method is used to add a new constraint.
- `push_namespace`, `pop_namespace`: These methods are used to manipulate namespaces, but they don't have any actual effect in this context.
- `get_root`: This method is used to get the root constraint system.
- `is_extensible`, `extend`: These methods are used to extend the constraint system.
In general, the main purpose of this file is to provide a way to generate instances and witnesses of R1CS circuits from a system that satisfies specific conditions, such as `SatisfyingAssignment`.
"src/circuit.rs" defines the Augmented Circuit in the Nova protocol. This circuit includes a Step Circuit and a Verifier Circuit in the non-interactive folding scheme of Nova.
The file defines several main structures and methods:
- `NovaAugmentedCircuitParams`: This structure contains the parameters of the circuit, including limb width, limb count, and a boolean value indicating whether it is the main circuit.
- `NovaAugmentedCircuitInputs`: This structure contains the inputs of the circuit, including parameters, i, z0, zi, U, u, and T.
- `NovaAugmentedCircuit`: This structure is the main definition of the Nova augmented circuit. It includes the circuit parameters, read-only constants, inputs, and the Step Circuit. It also defines methods such as `alloc_witness`, `synthesize_base_case`, and `synthesize_non_base_case`.
- `synthesize` method: This is the main synthesis method of the Nova augmented circuit. It first allocates all the witnesses, then synthesizes the circuit based on whether it is a base case or not, and finally outputs the computed hash value and u.X[1].
The file also contains some test code to test the functionality of the recursive circuit.
In summary, the main purpose of this file is to define the augmented circuit in the Nova protocol, which is a core part of the Nova protocol. It includes a Step Circuit and a Verifier Circuit, and provides a way to synthesize this circuit.
"src/constants.rs" defines some constants that are widely used throughout the project. Here are the meanings of these constants:
- `NUM_CHALLENGE_BITS`: This constant defines the number of bits for the challenge, with a value of 128. The challenge is usually a random number generated by the prover and is used in the interactive steps of the zk-SNARK proving process.
- `NUM_HASH_BITS`: This constant defines the number of bits for the hash, with a value of 250. A hash function is a function that maps input data of arbitrary length to a fixed-length output, and in this case, the output length is 250 bits.
- `BN_LIMB_WIDTH`: This constant defines the limb width of the big number, with a value of 64. In computer science, big numbers are those numbers that fall outside the range representable by standard data types, and they are usually decomposed into multiple "limbs" for storage and operations.
- `BN_N_LIMBS`: This constant defines the number of limbs for the big number, with a value of 4. This means that each big number is decomposed into 4 limbs for storage and operations.
- `NUM_FE_WITHOUT_IO_FOR_CRHF`: This constant defines the number of field elements (FE) for the collision-resistant hash function (CRHF), excluding the input/output, with a value of 17.
- `NUM_FE_FOR_RO`: This constant defines the number of field elements (FE) for the random oracle (RO), with a value of 24.
These constants play a crucial role in the implementation of the Nova protocol, as they define important parameters such as the number of challenge bits, hash bits, big number limb width, and limb count.
"src/errors.rs" defines the error types that the Nova library may return. These error types are encapsulated in an enumeration called `NovaError`. Here are the meanings of these error types:
- `InvalidIndex`: This error is returned if the provided row or column is out of range in the (row, col, val) tuple.
- `OddInputLength`: This error is returned if the provided input length is not even.
- `InvalidInputLength`: This error is returned if the provided input length is incorrect.
- `InvalidWitnessLength`: This error is returned if the provided witness length is incorrect.
- `UnSat`: This error is returned if the provided witness does not satisfy the given shape and instance.
- `DecompressionError`: This error is returned if the provided compressed commitment cannot be decompressed.
- `ProofVerifyError`: Returned if proof verification fails.
- `InvalidNumSteps`: Returned if the provided number of steps is zero.
- `InvalidIPA`: Returned if an invalid inner product parameter is provided.
- `InvalidSumcheckProof`: Returned if an invalid sumcheck proof is provided.
- `InvalidInitialInputLength`: Returned if the initial input for incremental computation does not match the previously declared arity.
- `InvalidStepOutputLength`: Returned if the output length produced by the step execution does not match the previously declared arity.
- `InternalTranscriptError`: Returned if the transcript engine encounters a round overflow.
- `InvalidMultisetProof`: Returned if the multiset check fails.
- `InvalidProductProof`: Returned if the product proof check fails.
- `IncorrectWitness`: Returned if consistency between the public IO and the assignment used fails.
These error types cover various issues that may occur in the Nova library, including input errors, proof errors, and internal errors. When functions in the Nova library encounter issues, they return these errors so that callers can understand what went wrong and take appropriate actions.
"ecc.rs", which is written in Rust language. This file mainly contains implementations related to Elliptic Curve Cryptography (ECC) in the Nova framework.
Elliptic Curve Cryptography (ECC) is a public key encryption technique that offers the advantage of using shorter keys while providing the same level of security. This means that ECC can utilize smaller computational resources and power, which is crucial for many devices, especially mobile devices and embedded systems.
In this file, you will see the definitions of some Rust structs and implementations that are aimed at implementing ECC functionalities. For example, you will come across `struct EccGadget`, which is the main implementation of ECC and includes fields such as `value` and `pb_variable` to store the state and associated variables of ECC.
In addition, you will also see the definitions of some functions, which are used to implement various operations of ECC, such as encryption, decryption, etc. For example, `fn encrypt` is an encryption function that takes a plaintext and a public key, and returns an encrypted ciphertext.
Overall, this file is a key part of implementing ECC functionality in the Nova framework.
"src/gadgets/mod.rs", it is a module in the Nova framework, mainly used to implement the necessary "gadgets" for Nova and applications built with Nova.
In cryptography, "gadget" is a general term used to describe a code block that implements a specific functionality. In zk-SNARKs (zero-knowledge succinct non-interactive argument of knowledge), a gadget typically refers to a proof system that implements a specific algorithm or protocol.
In this file, you will see the following submodules:
- `ecc`: This module may contain gadgets related to elliptic curve cryptography.
- `nonnative`: This module may contain gadgets related to non-native fields.
- `r 1 cs`: This module may contain gadgets related to R 1 CS (Rank-1 Constraint Systems).
- `utils`: This module may contain some utility functions or classes.
Together, these submodules provide various functionalities required by the Nova framework.
"bignat.rs", it is part of the Nova project, mainly used to implement operations on big integers (BigNat).
In computer science, a big integer (or arbitrary-precision integer) is an integer that can represent and operate on a range beyond what regular integer types (such as int or long) can represent. This is very useful in many fields, including cryptography, computer graphics, large number calculations, etc.
Let's take a closer look at some key parts of this file:
1. `use super::super::gadgets::GadgetCaller;`: This line of code imports GadgetCaller, which is a trait for invoking other gadgets.
2. `pub struct BigNatGadget;`: This line of code defines a structure named BigNatGadget. In Rust, structures are used to create complex data types.
3. `impl GadgetCaller for BigNatGadget`: This is an implementation of the GadgetCaller trait for the BigNatGadget structure. This means that BigNatGadget must provide implementations for all the methods required by the GadgetCaller trait.
4. In this implementation, we can see some methods such as `add`, `sub`, `mul`, `div`, `rem`, etc., which are basic operations for big integer arithmetic.
5. `pub fn from(&self, val: u64) -> Self`: This method is used to create a BigNatGadget from a value of type u64.
6. `pub fn to_u64(&self) -> u64`: This method is used to convert a BigNatGadget to a value of type u64.
7. `pub fn eq(&self, other: &Self) -> bool`: This method is used to determine whether two BigNatGadget objects are equal.
In summary, this file provides a utility for working with big integers, including creating big integers, converting big integers to other types of values, and performing basic operations on big integers.
"mod.rs", located in the "src/gadgets/nonnative/" directory. This file is primarily used to implement arithmetic operations on non-native fields.
In cryptography, non-native fields typically refer to fields that are not directly supported by hardware. For example, certain cryptographic algorithms may require arithmetic operations on fields larger than 64 bits, but most modern computer hardware only directly supports operations on up to 64 bits. In such cases, we need to use arithmetic operations on non-native fields.
In this file, you will see the following main sections:
1. `OptionExt` trait: This trait adds two methods, `grab` and `grab_mut`, to the `Option` type. They attempt to retrieve the value from the `Option`, and if the `Option` is `None`, return an error.
2. `BitAccess` trait: This `trait` provides a method `get_bit`, which accepts an index `i` and then returns whether the bit at that index is `1`.
3. `impl BitAccess for Scalar`: This is an implementation of the `BitAccess` trait for the `Scalar` type, where `Scalar` is a type representing a prime field.
4. `pub mod bignat;` and `pub mod util;`: These two lines of code import the `bignat` and `util` sub-modules, which may contain functions or classes for performing arithmetic operations on non-native fields.
In summary, this file provides a method for performing arithmetic operations on non-native fields, which is important for implementing certain cryptographic algorithms.
"util.rs", located in the "src/gadgets/nonnative/" directory. This file is mainly used for implementing utility functions for operations on non-native fields.
Here are some key parts of this file:
1. `Bit` struct: This struct represents a bit and includes a linear combination and a value, which is populated during witness time.
2. `Bitvector` struct: This struct represents a bit vector and includes a vector of linear combinations, a vector of values, and an assigned bit vector.
3. `Num` struct: This struct represents a number and includes a linear combination and a value.
4. `alloc` method for the `Bit` struct: This method allocates a variable in the constraint system that can only be a boolean value.
5. `fits_in_bits` method for the `Num` struct: This method checks if a number can be represented with a given number of bits.
6. `is_equal` method for the `Num` struct: This method checks if a number is equal to a natural number represented as a bit vector.
7. `decompose` method for the `Num` struct: This method decomposes a number into a bit vector.
8. `as_allocated_num` method for the `Num` struct: This method converts a number into an allocated number.
9. `f_to_nat` function: This function converts a field element into a natural number.
10. `nat_to_f` function: This function converts a natural number into a field element.
In general, this file provides some utility functions that can operate on non-local fields, such as allocating variables, checking if a number can be represented with a given number of bits, decomposing a number into a bit vector, and so on.
"r 1 cs.rs", which is located in the "src/gadgets/" directory. This file is mainly used to implement various gadgets for Rank-1 Constraint Systems (R 1 CS).
R 1 CS is a proof system used to describe algorithms or protocols. It is the basis for many zero-knowledge proof systems, including zk-SNARKs.
Here are some main parts of this file:
1. The `AllocatedR 1 CSInstance` structure: This structure represents an allocated R 1 CS instance, including a point `W` and two numbers `X 0 ` and `X 1 `.
2. The `AllocatedR1CSInstance::alloc` method: This method is used to allocate an R 1 CS instance in the constraint system.
3. The `AllocatedR1CSInstance::absorb_in_ro` method: This method is used to absorb an R 1 CS instance into a random oracle (RO).
4. The `AllocatedRelaxedR1CSInstance` structure: This structure represents an allocated relaxed R 1 CS instance, including two points `W` and `E`, a number `u`, and two large integers `X 0 ` and `X 1 `.
5. The `AllocatedRelaxedR1CSInstance::alloc` method: This method is used to allocate a relaxed R 1 CS instance in the constraint system.
6. The `AllocatedRelaxedR1CSInstance::default` method: This method is used to allocate a default relaxed R 1 CS instance in the constraint system.
7. The `AllocatedRelaxedR1CSInstance::from_r 1 cs_instance` method: This method is used to convert an R 1 CS instance to a relaxed R 1 CS instance.
8. The `AllocatedRelaxedR1CSInstance::absorb_in_ro` method: This method is used to absorb the relaxed R 1 CS instance into a random oracle (RO).
9. The `AllocatedRelaxedR 1 CSInstance::fold_with_r 1 cs` method: This method is used to fold the relaxed R 1 CS instance with an R 1 CS instance and return the result.
10. The `AllocatedRelaxedR1CSInstance::conditionally_select` method: This method is used to select one of the two relaxed R 1 CS instances based on a condition.
In general, this file provides some tools for working with R 1 CS, including creating an R 1 CS instance, converting an R 1 CS instance to a relaxed R 1 CS instance, absorbing an R 1 CS instance into a random oracle, and folding a relaxed R 1 CS instance with an R 1 CS instance.
This file is named "utils.rs" and is located in the "src/gadgets/" directory. This file is mainly used to implement some low-level utility functions that are helpful in building higher-level cryptographic protocols and algorithms.
Here are some key sections in this file:
1. The `le_bits_to_num` function: This function takes a little-endian representation of a bit array and returns the corresponding value.
2. The `alloc_zero` and `alloc_one` functions: These two functions are used to allocate a variable with the value zero and one, respectively, in the constraint system.
3. The `alloc_scalar_as_base` function: This function is used to allocate a scalar as a base in the constraint system.
4. `scalar_as_base` function: This function is used to interpret a scalar as a base.
5. `alloc_bignat_constant` function: This function is used to allocate a big integer constant in the constraint system.
6. `alloc_num_equals` function: This function is used to check if two numbers are equal and return a bit.
7. `conditionally_select` function: This function is used to select one of two numbers based on a condition.
8. `conditionally_select_vec` function: This function is used to select one of two number arrays based on a condition.
9. `conditionally_select_bignat` function: This function is used to select one of two big integers based on a condition.
10. `conditionally_select2` function: This function is used to select one of two numbers based on a condition, where the condition is an allocated number.
11. `select_zero_or_num 2` and `select_num_or_zero 2` functions: These functions are used to set a number to zero or leave it unchanged based on a condition, where the condition is an allocated number.
12. `select_num_or_zero` function: This function is used to set a number to zero or leave it unchanged based on a condition, where the condition is a boolean value.
13. `select_one_or_num 2` and `select_num_or_one` functions: These functions are used to set a number to one or leave it unchanged based on a condition, where the condition is an allocated number and a boolean value.
In summary, this file provides some utility functions that allow for variable allocation, checking equality of numbers, and selecting one of two numbers based on a condition in the constraint system.
This is a Rust language source code file named "lib.rs", which is a main component of the Nova project. This file mainly defines the public interface and some core functionalities of the Nova library. Here is a detailed explanation of the file:
1. `pub mod ast`: This line of code imports a module named "ast". "ast" is short for "Abstract Syntax Tree", which is a data structure used to represent the structure of source code. In the Nova project, the "ast" module may contain various data structures and functions for parsing and processing Nova language source code.
2. `pub mod parser`: This line of code imports a module named "parser". The module may contain functions and classes for parsing the source code of the Nova language.
3. `pub mod codegen`: This line of code imports a module named "codegen". The module may contain functions and classes for converting the abstract syntax tree of the Nova language into target code (such as LLVM IR or machine code).
4. `pub mod types`: This line of code imports a module named "types". The module may contain the type system of the Nova language, including representations and operations for various built-in types and user-defined types.
5. `pub mod util`: This line of code imports a module named "util". The module may contain various utility functions and classes, such as error handling, logging, file I/O, and so on.
6. `pub mod driver`: This line of code imports a module named "driver". In a compiler project, "driver" usually refers to the module that controls the entire compilation process, including steps like source code reading, parsing, type checking, code generation, optimization, and output.
7. `pub mod error`: This line of code imports a module named "error". The module may contain the error handling system of the Nova language, including representations and operations for various compilation errors and runtime errors.
8. `pub mod config`: This line of code imports a module named "config". The module may contain the configuration system of the Nova language, including representations and operations for compilation options, runtime options, and so on.
The main purpose of this file is to organize various components of the Nova language (such as the parser, code generator, type system, error handling system, etc.) into a complete compiler library.
This file is named "nifs.rs" and it is located in the "src/" directory. This file implements a Non-Interactive Folding Scheme (NIFS), which is a cryptographic protocol used to prove the correctness of each step in incremental computation.
The following are some key parts of this file:
1. The `NIFS` struct: This struct represents a SNARK, which holds the proof for one step of incremental computation. It contains a field called `comm_T`, which is a compressed commitment.
2. The `prove` method: This method takes in loose R 1 CS instance-witness pairs `(U 1, W 1)` and (U 2, W 2) for the same structure `shape` with respect to the same `ck` definition. It then outputs a folded loose R 1 CS instance-witness pair (U, W) with the same structure `shape`. If `W 1 ` satisfies `U 1 ` and `W 2 ` satisfies `U 2 `, the folded witness W satisfies the folded instance `U`.
3. The `verify` method: This method takes in a loose R 1 CS instance `U 1 ` and a R 1 CS instance `U 2 `, both having the same structure and with respect to the same parameter definition. It then outputs a folded instance U with the same structure. If `U 1 ` and `U 2 ` are satisfiable, then the folded instance U is satisfiable.
4. The testing module: This module contains some test functions to test the `prove` and `verify` methods of the `NIFS` struct.
In summary, this file implements a non-interactive folding scheme, which is a cryptographic protocol used to prove the correctness of each step in incremental computation. The main advantage of this scheme is that it can fold multiple proofs into a single proof, reducing the storage and transmission costs of the proof.
The filename of this file is "ipa_pc.rs" and it is located in the "src/provider/" directory. This file implements an evaluation engine using a polynomial commitment scheme based on IPA (Inner Product Argument).
The following are some key parts of this file:
1. `ProverKey` struct: This struct represents a prover key, which includes a commitment key `ck_s`.
2. `VerifierKey` struct: This struct represents a verifier key, which includes two commitment keys `ck_v` and `ck_s`.
3. `EvaluationArgument` struct: This struct represents a polynomial evaluation argument, which includes an inner product parameter `ipa`.
4. `EvaluationEngine` struct: This struct represents an evaluation engine using IPA.
5. Implementation of the `EvaluationEngineTrait` trait: This implementation provides the main functionalities of a polynomial evaluation engine, including setup, proving, and verification.
6. `inner_product` function: This function calculates the inner product of two vectors.
7. `InnerProductInstance` struct: This struct represents an inner product instance, which includes a commitment `comm_a_vec` for vector `a`, another vector `b_vec`, and a claimed value `c =
8. `InnerProductWitness` struct: This struct represents an inner product witness, which includes a vector `a_vec`.
9. `InnerProductArgument` struct: This struct represents an inner product argument, which includes two compressed commitment vectors `L_vec` and `R_vec`, and a scalar `a_hat`.
In summary, this file implements an evaluation engine using a polynomial commitment scheme based on IPA. This is a cryptographic protocol used for proving the evaluation value of a polynomial at a specific point in zero-knowledge proofs. The main advantage of this scheme is that it can prove the evaluation value of a polynomial without revealing the polynomial itself, thus preserving the privacy of the polynomial.
The file is named "keccak.rs" and is located in the "src/provider/" directory. This file implements a TranscriptEngineTrait using the Keccak 256 hash function. TranscriptEngineTrait is a trait used to handle transcripts in zero-knowledge proof processes. A transcript is a data structure that records all interactive steps in the proof process.
Here are some main parts of this file:
1. `Keccak 256 Transcript` struct: This struct implements the TranscriptEngineTrait and uses Keccak 256 hash function to handle the transcript. It contains a round field to record the current round, a state field to store the current hash state, a transcript field to store the transcript, and a _p field to store the type information.
2. `compute_updated_state` function: This function takes an input and computes the updated hash state.
3. Implementation of TranscriptEngineTrait: The implementation of this trait provides the main functions for handling the transcript, including creating a new transcript, extracting a challenge from the transcript, adding an element to the transcript, and adding a domain separator.
4. Testing module: This module contains some test functions to test the functionality of the `Keccak 256 Transcript` struct.
In summary, this file implements a TranscriptEngineTrait using the Keccak 256 hash function, which is a tool for handling transcripts in the zero-knowledge proof process. The main advantage of this tool is that it can handle transcripts without revealing the interactive steps of the proof process, thus protecting the privacy of the proof process.
This file is named "mod.rs" and is located in the "src/provider/" directory. This file is mainly used to import various implementation modules in the Nova project, which provide various functionalities required by the Nova project.
Here are some main parts of this file:
1. `pub mod ipa_pc;`: This line of code imports a module named "ipa_pc". This module implements an evaluation engine using the Inner Product Argument (IPA) based polynomial commitment scheme.
2. `pub mod keccak;`: This line of code imports a module named "keccak". This module implements a TranscriptEngineTrait that uses the Keccak 256 hash function.
3. `pub mod pasta;`: This line of code imports a module named "pasta". This module may contain functions and classes that use the Pasta curve.
4. `pub mod pedersen;`: This line of code imports a module named "pedersen". This module may contain functions and classes that use the Pedersen commitment.
5. `pub mod poseidon;`: This line of code imports a module named "poseidon". This module may contain functions and classes that use the Poseidon hash function.
In summary, the main purpose of this file is to organize the various components of the Nova project (such as the evaluation engine, TranscriptEngineTrait, Pasta curve, Pedersen commitment, Poseidon hash function, etc.) to form a complete cryptographic library.
File name: `src/r 1 cs.rs`
This file defines types and methods related to the Rank-1 Constraint System (R 1 CS). R 1 CS is a constraint system widely used in zero-knowledge proof systems.
It primarily defines the following structures and their methods:
1. `R 1 CS
2. `R 1 CSShape
3. `R 1 CSWitness
4. `R 1 CSInstance
5. `RelaxedR 1 CSWitness
6. `RelaxedR 1 CSInstance
Filename: `src/spartan/math.rs`
This file defines a trait called `Math`, as well as implementations for the `usize` type. This trait defines some mathematical operations, including calculating powers of 2, retrieving binary bits, and computing logarithms.
1. The `Math` trait defines the following methods:
- `pow 2(self) -> usize`: Calculates 2 raised to the power of self.
- `get_bits(self, num_bits: usize) -> Vec
- `log_ 2(self) -> usize`: Computes the logarithm of self to the base 2.
2. For the `usize` type, all methods of the `Math` trait are implemented:
- `pow 2(self) -> usize`: Calculates 2 raised to the power of self using the built-in `pow` function.
- `get_bits(self, num_bits: usize) -> Vec
- `log_ 2(self) -> usize`: If self is a power of 2, calculate the logarithm of self with base 2 using the `leading_zeros` method; otherwise, calculate the logarithm of self with base 2 using the `leading_zeros` method and the `leading_zeros` method of the maximum value of usize.
This file provides some basic mathematical operations that may be used by other parts of the code to implement more complex functionalities.
File name: src/spartan/mod.rs
This module implements the RelaxedR1CSSNARKTrait using Spartan, which is a generic Polynomial Commitment Scheme and Evaluation Parameters (PCS).
The following are some key structures and functions:
1. `PolyEvalWitness`: This is a structure that contains the proof of a polynomial.
2. `PolyEvalInstance`: This is a structure that contains an instance of polynomial evaluation.
3. `ProverKey` and `VerifierKey`: These two structures represent the prover's key and the verifier's key, respectively.
4. `RelaxedR 1 CSSNARK`: This structure represents a succinct proof of knowledge of a relaxed R 1 CS instance. The proof is generated using the combination of Spartan's sum-check and vector considered as polynomial commitment.
5. `setup`: This function is used to set up the proof and verification keys.
6. `prove`: This function is used to generate a succinct proof of the satisfiability of a relaxed R 1 CS instance.
7. `verify`: This function is used to verify the proof of satisfiability of a relaxed R 1 CS instance.
This module's code mainly involves zero-knowledge proofs in cryptography, especially the proofs about R1CS (Rank-1 Constraint Systems). R1CS is a system used for constructing zero-knowledge proofs that enable a person to prove knowledge of a solution satisfying a set of polynomial equations without revealing any information about the solution. Spartan is a specific zero-knowledge proof system that utilizes a "relaxed" form of R1CS. This system allows the use of randomness in the proofs, which improves efficiency.
Filename: src/spartan/polynomial.rs
This file defines some basic types and operations related to polynomials. These types and operations are used for polynomial calculations in the Spartan protocol.
Here are some key parts of this file:
1. `EqPolynomial`: This structure represents an equality polynomial. It includes a `new` method for creating a new polynomial, an `evaluate` method for evaluating the polynomial at a specified point, and an `evals` method for calculating evaluations of the polynomial on all Boolean inputs.
2. `MultilinearPolynomial`: This structure represents a multilinear polynomial. It includes a `new` method for creating a new polynomial, a `get_num_vars` method for getting the number of variables in the polynomial, a `bound_poly_var_top` method for binding variables of the polynomial to the top, and an `evaluate` method for evaluating the polynomial at a specified point.
3. `SparsePolynomial`: This structure represents a sparse polynomial. It includes a `new` method for creating a new polynomial and an `evaluate` method for evaluating the polynomial at a specified point.
The code in this file mainly deals with polynomial calculations in cryptography, especially calculations involving multilinear polynomials and sparse polynomials. These calculations play an important role in zero-knowledge proof systems as they can be used to construct complex proofs without revealing any information about the proofs.
`src/spartan/pp.rs` is a Rust file in the Nova project. This file implements the functionality of the preprocessor in Nova. The preprocessor is a stage in the compilation process that performs some processing on the code before the actual compilation.
The main structures and functions in this file include:
1. `struct Preprocessor`: This is a structure of the preprocessor, which contains some states and data that the preprocessor needs.
2. `impl Preprocessor`: This is the implementation of the `Preprocessor` structure, which includes some methods.
3. `fn new(source: String) -> Self`: This is the constructor of `Preprocessor`, used to create a new instance of `Preprocessor`.
4. `fn preprocess(&mut self) -> Result<(), Error>`: This is the main function of the preprocessor, which preprocesses the input source code and returns the processing result. If an error occurs during the processing, it will return an error.
5. `fn next_token(&mut self) -> Result
6. `fn skip_whitespace(&mut self)`: This function skips whitespace characters in the source code.
7. `fn skip_comment(&mut self) -> Result<(), Error>`: This function skips comments in the source code. If an error occurs during the processing, it will return an error.
8. `fn read_number(&mut self) -> Result
9. `fn read_identifier(&mut self) -> Result
10. `fn read_string(&mut self) -> Result
In summary, the `src/spartan/pp.rs` file implements the preprocessor in Nova, which preprocesses the source code, including skipping whitespace and comments, and reading numbers, identifiers, and strings.
Filename: src/spartan/sumcheck.rs
This file implements the Sumcheck algorithm in the Spartan protocol. The Sumcheck algorithm is an algorithm used to verify polynomial summation and has wide applications in zero-knowledge proof systems.
Here are some main parts of this file:
1. `SumcheckProof`: This struct represents a Sumcheck proof. It includes a method `new` for creating a new proof, a method `verify` for verifying the proof, and several `prove` methods for generating the proof.
2. `UniPoly` and `CompressedUniPoly`: These two structs represent univariate polynomials and compressed univariate polynomials. They include methods for creating polynomials, evaluating polynomials, evaluating polynomials at specified points, as well as compressing and decompressing polynomials.
3. `TranscriptReprTrait`: This trait defines a method `to_transcript_bytes` for converting an object to a byte sequence. This is a common operation in zero-knowledge proof systems as it can be used to add the representation of an object to the transcript of a proof.
The code in this file mainly involves the Sumcheck algorithm in cryptography, particularly the computation and proof of polynomials. These computations play an important role in zero-knowledge proof systems as they can be used to construct complex proofs without revealing any information about the proof.
File Name: src/traits/circuit.rs
This file defines a trait called `StepCircuit` and a struct `TrivialTestCircuit` that implements this trait. Both the trait and the struct are related to the step function in incremental computation.
Here are some main parts of this file:
1. `StepCircuit` trait: This trait defines the methods that an incremental computation step function must implement. These methods include:
- `arity`: Returns the number of inputs or outputs for each step.
- `synthesize`: Performs synthesis on a computational step and returns the variables corresponding to the step outputs.
- `output`: Returns the output of the step when the input for the step is provided.
2. `TrivialTestCircuit` struct: This struct implements the `StepCircuit` trait and simply returns the input. This struct may be used for testing or as a basic step function.
This file mainly involves the step function of incremental computation. In cryptography, incremental computation is a common technique that can be used to calculate complex functions step by step without calculating the entire function at once. This technique is particularly useful in zero-knowledge proof systems, as it can be used to construct complex proofs without generating the entire proof at once.
File name: src/traits/commitment.rs
This file defines traits related to commitments. In cryptography, a commitment is a mechanism that allows a person to commit to a value without immediately revealing it. This is necessary in many cryptographic protocols, such as zero-knowledge proofs.
The following are some key parts of this file:
1. `CommitmentOps` trait: This trait defines basic operations for commitments, including addition and assignment.
2. `CommitmentOpsOwned` trait: This trait defines basic operations for references to owned commitments.
3. `ScalarMul` trait: This trait defines multiplication operations between commitments and scalars.
4. `CommitmentTrait` trait: This trait defines the behavior of commitments, including cloning, copying, defaulting, comparing, sending, synchronizing, serializing, deserializing, absorbing, operating, compressing, and decompressing.
5. `CommitmentEngineTrait` trait: This trait binds together different parts generated by commitments, including commitment keys, commitments, settings, and commitments.
This file mainly involves commitments in cryptography. These commitments play an important role in zero-knowledge proof systems as they can be used to construct complex proofs without revealing any information about the proof.
File name: src/traits/evaluation.rs
This file defines a trait named `EvaluationEngineTrait`. This trait defines the behavior of a polynomial evaluation engine, including setup, proving, and verification.
The following are some key parts of this file:
1. `EvaluationEngineTrait` trait: This trait defines methods that a polynomial evaluation engine must implement. These methods include:
- `setup`: This method is used for any additional setup required to generate evaluation proofs.
- `prove`: This method is used to prove the evaluation of a multilinear polynomial.
- `verify`: This method is used to verify the proof of the evaluation of a multilinear polynomial.
This trait also defines some associated types, including:
- `CE`: This is the type associated with the commitment engine.
- `ProverKey`: This is the type of the prover's key.
- `VerifierKey`: This is the type of the verifier's key.
- `EvaluationArgument`: This is the type of the evaluation argument.
The code in this file mainly deals with polynomial evaluation in cryptography. This is an important step in zero-knowledge proof systems, as it can be used to prove that a person knows a solution that satisfies a set of polynomial equations without revealing any information about the solution.
File Name: src/traits/mod.rs
This file is the main entry point for the `traits` module in the Nova project. It mainly defines traits for cryptographic operations. Traits are a key feature in Rust that define an abstract type that can be implemented by multiple different concrete types. This allows us to write generic code that can handle values of any type that implements a specific trait.
Here are some key parts of this file:
1. `Group` trait: This trait defines basic operations for a group, including cloning, copying, default, comparison, sending, syncing, serialization, deserialization, absorption, operation, compression, decompression, etc.
2. `CompressedGroup` trait: This trait defines basic operations for a compressed group, including cloning, copying, comparison, sending, syncing, serialization, deserialization, etc.
3. `AbsorbInROTrait` trait: This trait defines a method `absorb_in_ro` for absorbing an object into a random oracle.
4. `ROTrait` trait: This trait defines the behavior of a random oracle, including initialization, absorption, and squeezing.
5. `ROConstantsTrait` trait: This trait defines the constants of a random oracle.
6. `GroupOps` trait: This trait defines group operations, including addition, subtraction, addition assignment, and subtraction assignment.
7. `ScalarMul` trait: This trait defines scalar multiplication operation.
8. `TranscriptReprTrait` trait: This trait defines a method `to_transcript_bytes` for converting an object to a byte sequence.
9. `TranscriptEngineTrait` Trait: This trait defines the behavior of the transcript engine, including initialization, squeezing, absorbing, and adding domain separators.
The code in this file mainly involves group operations, random oracles, and transcript engines in cryptography. These play an important role in zero-knowledge proof systems because they can be used to construct complex proofs without revealing any information about the proof.
Filename: src/traits/snark.rs
This file defines a trait called `RelaxedR1CSSNARKTrait`. This trait defines the behavior of a zero-knowledge succinct non-interactive argument of knowledge (zkSNARK), specifically for Relaxed Rank-1 Constraint Systems (Relaxed R 1 CS).
Here are some key parts of this file:
1. `RelaxedR1CSSNARKTrait` Trait: This trait defines methods that a zkSNARK must implement. These methods include:
- `setup`: This method is used to generate keys for the prover and verifier.
- `prove`: This method is used to generate a succinct proof of satisfiability for a relaxed R 1 CS instance.
- `verify`: This method is used to verify a proof of satisfiability for a relaxed R 1 CS instance.
This trait also defines some associated types, including:
- `ProverKey`: This is the type of the prover's key.
- `VerifierKey`: This is the type of the verifier's key.
The code in this file mainly involves zero-knowledge proofs in cryptography, specifically about R 1 CS proofs. R 1 CS is a system used to construct zero-knowledge proofs that can prove that a person knows a solution to a set of polynomial equations without revealing any information about the solution. zkSNARK is a specific zero-knowledge proof system that provides an efficient way to generate and verify proofs.
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