Huobi Ventures' Latest Research Report: Hardcore Analysis of the Latest Meme $NOVA
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Huobi Ventures' Latest Research Report: Hardcore Analysis of the Latest Meme $NOVA
This article provides a hardcore analysis of the underlying technology behind Nova, setting aside captivating narratives and returning to the code itself.
Navigating Web3 tides with focused insightsAuthor: Xie Jinbin, Senior Researcher at Huobi Ventures
The hottest memecoin today—Nova—has emerged as the "savior" of the NFT world.
According to its official website, the smart contract code for the meme project NOVA was written by ChatGPT and officially launched on July 10. NOVA plans to distribute airdrops to all blue-chip NFT holders. The contract includes a 9% sell tax (0% buy tax), with 3% automatically used to purchase ETH and distributed to holders of the top 30 blue-chip NFT projects. Official data shows that in its first phase, NOVA will distribute 10,000 ETH to support major blue-chip NFT holders.
This article provides a hardcore technical analysis of Nova’s underlying technology, stripping away the captivating narrative to focus purely on the code itself.
This research report is published by Huobi Ventures, the global investment arm of Huobi, integrating investment, incubation, and research to identify the most outstanding and promising projects worldwide.
Introduction
Zero-knowledge proofs are an important cryptographic technique allowing one party to prove to another that a statement is true without revealing any additional information. This technology has broad applications in areas such as authentication, 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 proof efficiency and flexibility. The final section provides a detailed source code analysis.
Nova's Advantages
Nova's primary advantage lies in its use of relaxed R1CS. R1CS is a system used to construct zero-knowledge proofs, capable of proving knowledge of solutions satisfying a set of polynomial equations without disclosing any information about the solution. However, traditional R1CS systems require significant randomness during proof generation, making the process complex and time-consuming. Nova addresses this by using relaxed R1CS, which reduces the amount of randomness required, significantly improving proof efficiency.
Nova also offers other benefits. For example, it supports incremental computation, enabling step-by-step evaluation of complex functions rather than computing the entire function at once—particularly useful when handling large-scale data or performing complex calculations. Additionally, Nova supports polynomial computations, allowing it to handle more complex proof tasks.
Nova's Disadvantages
Despite its many advantages, Nova has some drawbacks. First, because it uses relaxed R1CS, its proofs may not be as strong as those from traditional R1CS systems. The reduced randomness allowed in relaxed R1CS could potentially lower proof security. However, Nova's developers have implemented measures to mitigate this, such as using stronger cryptographic algorithms and more sophisticated proof strategies.
Second, Nova's implementation is relatively complex, increasing usage and maintenance difficulty. It employs advanced cryptographic techniques like polynomial computation, group operations, and random oracles, requiring deep expertise to use and modify effectively.
Nova's Significance in Zero-Knowledge Proofs
Nova holds a significant position in the field of zero-knowledge proofs. Its emergence opens new pathways for development in this domain. By adopting relaxed R1CS, Nova makes proof generation and verification more efficient—crucial for large-scale zero-knowledge proof applications. Furthermore, its support for incremental and polynomial computations expands the scope of applicable proof tasks, broadening the overall application range of zero-knowledge proofs.
Source Code Analysis of Nova
https://github.com/microsoft/Nova
Within the src/ directory, several key subdirectories exist:
bellperson/: This directory likely contains code related to the Bellman-Ford algorithm.
gadgets/: This directory likely contains tools for constructing zk-SNARK proofs.
provider/: This directory likely contains provider-related code; keccak.rs may implement the Keccak hash function.
spartan/: This directory likely contains code related to the Spartan protocol.
traits/: This directory likely contains Rust traits defining common behaviors.
Contents of src/bellperson/mod.rs:
This module primarily generates R1CS (Rank-1 Constraint Systems), a constraint system used in zk-SNARKs.
It includes three submodules:
r1cs: Likely contains R1CS-related code.
shape_cs: Likely contains code related to shape constraint systems.
solver: Likely contains code for solving constraint systems.
In the test section, it defines a function synthesize_alloc_bit, which takes a constraint system and adds constraints to verify that two input bits are indeed binary values. Then it defines a function test_alloc_bit_with, which first creates a shape
Contents of src/bellperson/r1cs.rs:
This file mainly defines two traits: `NovaWitness` and `NovaShape`, providing methods to obtain `R1CSInstance` and `R1CSWitness`, and `R1CSShape` and `CommitmentKey` respectively.
- The `NovaWitness` trait has a method `r1cs_instance_and_witness` that accepts a `R1CSShape` and a `CommitmentKey`, returning an `R1CSInstance` and an `R1CSWitness`. This trait is implemented for the `SatisfyingAssignment` struct, meaning any `SatisfyingAssignment` can use this method to retrieve an `R1CSInstance` and an `R1CSWitness`.
- The `NovaShape` trait has a method `r1cs_shape` that returns a `R1CSShape` and a `CommitmentKey`. This trait is implemented for the `ShapeCS` struct, meaning any `ShapeCS` can use this method to retrieve a `R1CSShape` and a `CommitmentKey`.
This file also defines a function `add_constraint`, which takes a constraint system and three linear combinations, adding a new constraint into the system. This function is used by implementations of `NovaShape` when generating `R1CSShape`.
Overall, this file provides a way to generate instances, witnesses, shapes, and commitment keys of R1CS from systems meeting specific conditions (such as `SatisfyingAssignment` or `ShapeCS`).
src/bellperson/shape_cs.rs
This file defines a structure named `ShapeCS` that implements the `ConstraintSystem` trait. `ShapeCS` is a constraint system used to create R1CS shapes.
The `ShapeCS` structure contains the following fields:
- `named_objects`: A map storing objects associated with paths.
- `current_namespace`: A vector of strings storing the current namespace.
- `constraints`: A vector storing all constraints added to `ShapeCS`.
- `inputs`: A vector of strings storing all inputs.
- `aux`: A vector of strings storing all auxiliary inputs.
The `ShapeCS` structure implements the `ConstraintSystem` trait, providing the following methods:
- `alloc`: Allocates a new variable.
- `alloc_input`: Allocates a new input variable.
- `enforce`: Adds a new constraint.
- `push_namespace`: Pushes a new namespace.
- `pop_namespace`: Pops the current namespace.
- `get_root`: Retrieves the root constraint system.
The file also defines helper functions like `proc_lc` and `compute_path`, which handle linear combinations and compute paths, respectively.
Overall, this file provides a way to generate R1CS shapes from systems meeting specific conditions (such as `ShapeCS`).
src/bellperson/solver.rs
This file defines a structure named `SatisfyingAssignment` that implements the `ConstraintSystem` trait. `SatisfyingAssignment` is a constraint system used to create R1CS instances and witnesses.
The `SatisfyingAssignment` structure contains the following fields:
- `a_aux_density`, `b_input_density`, `b_aux_density`: Fields of type `DensityTracker` used to track query density.
- `a`, `b`, `c`: Vectors storing evaluations of polynomials A, B, and C.
- `input_assignment`, `aux_assignment`: Vectors storing variable assignments.
The `SatisfyingAssignment` structure implements the `ConstraintSystem` trait, providing the following methods:
- `new`: Creates a new `SatisfyingAssignment` instance.
- `alloc`: Allocates a new auxiliary variable.
- `alloc_input`: Allocates a new input variable.
- `enforce`: Adds a new constraint.
- `push_namespace`, `pop_namespace`: Operate on namespaces but perform no actual operations in this context.
- `get_root`: Retrieves the root constraint system.
- `is_extensible`, `extend`: Used to extend the constraint system.
Overall, this file provides a way to generate R1CS instances and witnesses from systems meeting specific conditions (such as `SatisfyingAssignment`).
"src/circuit.rs" defines the augmented circuit in the Nova protocol.
This circuit includes a step circuit and the verifier circuit from Nova's non-interactive folding scheme.
The file defines the following main structures and methods:
- `NovaAugmentedCircuitParams`: Contains circuit parameters including limb width, number of limbs, and a boolean indicating whether it is the main circuit.
- `NovaAugmentedCircuitInputs`: Contains circuit inputs including parameters, i, z0, zi, U, u, and T.
- `NovaAugmentedCircuit`: The main definition of Nova's augmented circuit, containing circuit parameters, read-only constants, inputs, and the step circuit. It also defines methods such as `alloc_witness` (allocate witness), `synthesize_base_case` (synthesize base case), and `synthesize_non_base_case` (synthesize non-base case).
- `synthesize` method: The primary synthesis method for Nova's augmented circuit, which first allocates all witnesses, then synthesizes the circuit based on whether it is a base case, finally outputting the computed hash value and u.X[1].
The file also includes test code for testing recursive circuit functionality.
Overall, this file defines the augmented circuit in the Nova protocol—a core component comprising a step circuit and a verifier circuit—and provides a way to synthesize this circuit.
"src/constants.rs" defines constants widely used throughout the project.
Below are explanations of these constants:
- `NUM_CHALLENGE_BITS`: Defines the number of challenge bits, set to 128. Challenges are typically random numbers generated by provers during interactive steps in zk-SNARK proofs.
- `NUM_HASH_BITS`: Defines the number of hash bits, set to 250. Hash functions map arbitrary-length inputs to fixed-length outputs; here the output length is 250 bits.
- `BN_LIMB_WIDTH`: Defines the limb width for big numbers, set to 64. In computer science, big numbers exceed standard data types' representable ranges and are typically split into multiple "limbs" for storage and operations.
- `BN_N_LIMBS`: Defines the number of limbs for big numbers, set to 4. This means each big number is split into four limbs for storage and operations.
- `NUM_FE_WITHOUT_IO_FOR_CRHF`: Defines the number of field elements (FE) excluding I/O for collision-resistant hash functions (CRHF), set to 17.
- `NUM_FE_FOR_RO`: Defines the number of field elements (FE) for random oracles (RO), set to 24.
These constants play crucial roles in the Nova protocol implementation, defining key parameters such as challenge bit count, hash bit count, big number limb width and count.
"src/errors.rs" defines error types that the Nova library might return.
These error types are encapsulated in an enum named `NovaError`. Below are their meanings:
- `InvalidIndex`: Returned if provided row or column in a (row, col, val) tuple is out of bounds.
- `OddInputLength`: Returned if provided input length is odd.
- `InvalidInputLength`: Returned if provided input length is incorrect.
- `InvalidWitnessLength`: Returned if provided witness length is incorrect.
- `UnSat`: Returned if provided witness does not satisfy given shape and instance.
- `DecompressionError`: Returned if unable to decompress provided compressed commitment.
- `ProofVerifyError`: Returned if proof verification fails.
- `InvalidNumSteps`: Returned if provided number of steps is zero.
- `InvalidIPA`: Returned if invalid inner product argument is provided.
- `InvalidSumcheckProof`: Returned if invalid sumcheck proof is provided.
- `InvalidInitialInputLength`: Returned if initial input length for incremental computation differs from previously declared arity.
- `InvalidStepOutputLength`: Returned if output length produced by step execution differs from previously declared arity.
- `InternalTranscriptError`: Returned if transcript engine encounters round overflow.
- `InvalidMultisetProof`: Returned if multiset check fails.
- `InvalidProductProof`: Returned if product proof check fails.
- `IncorrectWitness`: Returned if consistency with public I/O and assigned values fails.
These error types cover various issues possible within the Nova library, including input errors, proof errors, internal errors, etc. When Nova library functions encounter problems, they return these errors so callers can understand what went wrong and take appropriate actions.
"ecc.rs", written in Rust,
primarily contains elliptic curve cryptography (ECC)-related implementations in the Nova framework.
Elliptic Curve Cryptography (ECC) is a public-key encryption technique offering equivalent security with shorter keys. This allows ECC to use less computational power and electricity—especially important for many devices, particularly mobile and embedded systems.
In this file, you'll see definitions of Rust structs and impls implementing ECC functionality. For example, `struct EccGadget` is a primary ECC implementation containing fields like `value` and `pb_variable` for storing ECC state and related variables.
Additionally, you'll see definitions of functions implementing various ECC operations such as encryption and decryption. For instance, `fn encrypt` is an encryption function accepting plaintext and a public key, returning an encrypted ciphertext.
Overall, this file is a key part of the Nova framework implementing ECC functionality.
"src/gadgets/mod.rs" is a module in the Nova framework primarily implementing various "gadgets" necessary for Nova and applications built using Nova.
In cryptography, "gadget" is a general term describing code blocks implementing specific functions. In zk-SNARKs (zero-knowledge succinct non-interactive arguments), gadgets typically refer to proof systems implementing specific algorithms or protocols.
In this file, you'll see the following submodules:
- `ecc`: May contain ECC-related gadgets.
- `nonnative`: May contain gadgets for non-native fields.
- `r1cs`: May contain R1CS (Rank-1 Constraint Systems) gadgets.
- `utils`: May contain utility functions or classes.
Together, these submodules provide various functionalities needed by the Nova framework.
"bignat.rs", part of the Nova project, primarily implements operations on big integers (BigNat).
In computer science, big integers (or arbitrary-precision integers) can represent and manipulate integers beyond conventional integer types (like int or long). This is very useful in many fields including cryptography, computer graphics, and large-number computations.
Let's examine some main parts of this file:
1. `use super::super::gadgets::GadgetCaller;`: This line imports GadgetCaller, a trait used to call other gadgets.
2. `pub struct BigNatGadget;`: This line defines a structure named BigNatGadget. In Rust, structs are used to create complex data types.
3. `impl GadgetCaller for BigNatGadget`: This is an implementation for the BigNatGadget struct, implementing the GadgetCaller trait. This means BigNatGadget must provide implementations for all methods required by the GadgetCaller trait.
4. Within this implementation, we see methods like `add`, `sub`, `mul`, `div`, `rem`, etc., which are basic operations for big integer arithmetic.
5. `pub fn from(&self, val: u64) -> Self`: This method creates a BigNatGadget from a u64 value.
6. `pub fn to_u64(&self) -> u64`: This method converts a BigNatGadget to a u64 value.
7. `pub fn eq(&self, other: &Self) -> bool`: This method checks whether two BigNatGadgets are equal.
Overall, this file provides a tool for handling big integers, including creating them, converting them to other types, and performing basic arithmetic operations.
"mod.rs" located in the "src/gadgets/nonnative/" directory.
This file primarily implements arithmetic operations on non-native fields.
In cryptography, non-native fields typically refer to fields not directly supported by hardware. For example, certain cryptographic algorithms may require operations over fields larger than 64 bits, but most modern computer hardware only directly supports up to 64-bit operations. In such cases, non-native field arithmetic is required.
In this file, you'll find the following main components:
1. `OptionExt` trait: This trait adds two methods, `grab` and `grab_mut`, to the `Option` type, attempting to extract values from `Option`, returning an error if `Option` is `None`.
2. `BitAccess` trait: This trait provides a method `get_bit` that takes an index `i` and returns whether the bit at that index is `1`.
3. `impl BitAccess for Scalar`: Implementation of the `BitAccess` trait for the `Scalar` type, representing prime field elements.
4. `pub mod bignat;` and `pub mod util;`: These lines import the `bignat` and `util` submodules, which may contain functions or classes implementing non-native field arithmetic.
Overall, this file provides a method for performing arithmetic on non-native fields, essential for implementing certain cryptographic algorithms.
"util.rs" located in the "src/gadgets/nonnative/" directory.
This file primarily implements utility functions for operations on non-native fields.
Below are some main parts of this file:
1. `Bit` struct: Represents a bit, containing a linear combination and a value filled during witness time.
2. `Bitvector` struct: Represents a bit vector, containing vectors of linear combinations, values, and allocated bits.
3. `Num` struct: Represents a number, containing a linear combination and a value.
4. `Bit` struct's `alloc` method: Allocates a variable in the constraint system restricted to Boolean values.
5. `Num` struct's `fits_in_bits` method: Checks whether a number can be represented with a given number of bits.
6. `Num` struct's `is_equal` method: Checks whether a number equals a natural number represented by a bit vector.
7. `Num` struct's `decompose` method: Decomposes a number into a bit vector.
8. `Num` struct's `as_allocated_num` method: Converts a number into an allocated number.
9. `f_to_nat` function: Converts a field element to a natural number.
10. `nat_to_f` function: Converts a natural number to a field element.
Overall, this file provides utility functions for various operations on non-native fields, such as allocating variables, checking bit representation capacity, decomposing numbers into bit vectors, etc.
"r1cs.rs" located in the "src/gadgets/" directory.
This file primarily implements various gadgets for Rank-1 Constraint Systems (R1CS).
R1CS is a proof system used to describe algorithms or protocols, forming the foundation of many zero-knowledge proof systems including zk-SNARKs.
Below are some main parts of this file:
1. `AllocatedR1CSInstance` struct: Represents an allocated R1CS instance, containing a point `W` and two numbers `X0` and `X1`.
2. `AllocatedR1CSInstance::alloc` method: Allocates an R1CS instance within the constraint system.
3. `AllocatedR1CSInstance::absorb_in_ro` method: Absorbs the R1CS instance into the Random Oracle (RO).
4. `AllocatedRelaxedR1CSInstance` struct: Represents an allocated relaxed R1CS instance, containing two points `W` and `E`, a number `u`, and two big integers `X0` and `X1`.
5. `AllocatedRelaxedR1CSInstance::alloc` method: Allocates a relaxed R1CS instance within the constraint system.
6. `AllocatedRelaxedR1CSInstance::default` method: Allocates a default relaxed R1CS instance within the constraint system.
7. `AllocatedRelaxedR1CSInstance::from_r1cs_instance` method: Converts an R1CS instance into a relaxed R1CS instance.
8. `AllocatedRelaxedR1CSInstance::absorb_in_ro` method: Absorbs the relaxed R1CS instance into the Random Oracle (RO).
9. `AllocatedRelaxedR1CSInstance::fold_with_r1cs` method: Folds the relaxed R1CS instance with an R1CS instance and returns the result.
10. `AllocatedRelaxedR1CSInstance::conditionally_select` method: Conditionally selects one of two relaxed R1CS instances based on a condition.
Overall, this file provides tools for handling R1CS, including creating R1CS instances, converting R1CS instances to relaxed R1CS instances, absorbing R1CS instances into RO, folding relaxed R1CS instances with R1CS instances, etc.
This file named "utils.rs" is located in the "src/gadgets/" directory.
This file primarily implements low-level utility functions useful when building higher-level cryptographic protocols and algorithms.
Below are some main parts of this file:
1. `le_bits_to_num` function: Accepts a little-endian bit array and returns the corresponding numerical value.
2. `alloc_zero` and `alloc_one` functions: Allocate variables with values zero and one, respectively, within the constraint system.
3. `alloc_scalar_as_base` function: Allocates a scalar as a base within the constraint system.
4. `scalar_as_base` function: Interprets a scalar as a base.
5. `alloc_bignat_constant` function: Allocates a big integer constant within the constraint system.
6. `alloc_num_equals` function: Checks whether two numbers are equal and returns a bit.
7. `conditionally_select` function: Selects one of two numbers based on a condition.
8. `conditionally_select_vec` function: Selects one of two number arrays based on a condition.
9. `conditionally_select_bignat` function: Selects one of two big integers based on a condition.
10. `conditionally_select2` function: Selects one of two numbers based on a condition, where the condition is an allocated number.
11. `select_zero_or_num2` and `select_num_or_zero2` functions: 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: Sets a number to zero or leaves it unchanged based on a Boolean condition.
13. `select_one_or_num2` and `select_num_or_one` functions: Set a number to one or leave it unchanged based on a condition, where the condition is an allocated number and a Boolean value, respectively.
Overall, this file provides utility functions for allocating variables within constraint systems, checking number equality, conditionally selecting between two numbers, etc.
This is a Rust source code file named "lib.rs," serving as a main component of the Nova project.
This file primarily defines the public interface and core functionalities of the Nova library. Below is a detailed explanation of this file:
1. `pub mod ast`: Imports a module named "ast." "ast" stands for "Abstract Syntax Tree," a data structure representing source code structure. In the Nova project, the "ast" module likely contains various data structures and functions for parsing and processing Nova language source code.
2. `pub mod parser`: Imports a module named "parser." The "parser" module likely contains functions and classes for parsing Nova language source code.
3. `pub mod codegen`: Imports a module named "codegen," short for "code generation." This module likely contains functions and classes for converting Nova language abstract syntax trees into target code (e.g., LLVM IR or machine code).
4. `pub mod types`: Imports a module named "types." This module likely contains the type system for the Nova language, including representations and handling of various built-in and user-defined types.
5. `pub mod util`: Imports a module named "util," short for "utilities." This module likely contains various utility functions and classes, such as error handling, logging, file reading/writing, etc.
6. `pub mod driver`: Imports a module named "driver." In compiler projects, "driver" typically refers to the module controlling the entire compilation process, including source code reading, parsing, type checking, code generation, optimization, and output.
7. `pub mod error`: Imports a module named "error." This module likely contains the error handling system for the Nova language, including representations and handling of various compile-time and runtime errors.
8. `pub mod config`: Imports a module named "config." This module likely contains the configuration system for the Nova language, including representations and handling of compilation options, runtime options, etc.
The main purpose of this file is to organize various components of the Nova language (e.g., parser, code generator, type system, error handling system) into a complete compiler library.
This file named "nifs.rs" is located in the "src/" directory.
This file implements a Non-Interactive Folding Scheme (NIFS)—a cryptographic protocol used to prove correctness at each step of incremental computation.
Below are some main parts of this file:
1. `NIFS` struct: Represents a SNARK that stores a proof for one step of incremental computation. It contains a field named `comm_T`, a compressed commitment.
2. `prove` method: Takes a relaxed R1CS instance-witness pair `(U1, W1)` and an R1CS instance-witness pair `(U2, W2)`, both having the same shape and defined relative to the same ck. It outputs a folded relaxed R1CS instance-witness pair `(U, W)` with the same shape. If `W1` satisfies `U1` and `W2` satisfies `U2`, then the folded witness `W` satisfies the folded instance `U`.
3. `verify` method: Takes a relaxed R1CS instance `U1` and an R1CS instance `U2`, both having the same shape and defined relative to the same parameters. It outputs a folded instance `U` with the same shape. If `U1` and `U2` are satisfiable, then the folded instance `U` is satisfiable.
4. Test module: Contains test functions for testing the `prove` and `verify` methods of the `NIFS` struct.
Overall, this file implements a non-interactive folding scheme—a cryptographic protocol used to prove correctness at each step of incremental computation. Its main advantage is reducing storage and transmission overhead by folding multiple proofs into one.
This file named "ipa_pc.rs" is located in the "src/provider/" directory.
This file implements an evaluation engine using an IPA (Inner Product Argument)-based polynomial commitment scheme.
Below are some main parts of this file:
1. `ProverKey` struct: Represents a prover key, containing a commitment key `ck_s`.
2. `VerifierKey` struct: Represents a verifier key, containing two commitment keys `ck_v` and `ck_s`.
3. `EvaluationArgument` struct: Represents a polynomial evaluation argument, containing an inner product argument `ipa`.
4. `EvaluationEngine` struct: Represents a polynomial evaluation engine using IPA.
5. Implementation of `EvaluationEngineTrait`: Provides main functionalities of the polynomial evaluation engine, including setup, proving, and verification.
6. `inner_product` function: Computes the inner product of two vectors.
7. `InnerProductInstance` struct: Represents an inner product instance, containing a commitment `comm_a_vec` to vector `a`, another vector `b_vec`, and a claimed value `c =
8. `InnerProductWitness` struct: Represents an inner product witness, containing a vector `a_vec`.
9. `InnerProductArgument` struct: Represents an inner product argument, containing two compressed commitment vectors `L_vec` and `R_vec`, and a scalar `a_hat`.
Overall, this file implements an evaluation engine using an IPA-based polynomial commitment scheme—a cryptographic protocol used in zero-knowledge proofs to prove polynomial evaluations at specific points without revealing the polynomial itself, thus protecting polynomial privacy.
This file named "keccak.rs" is located in the "src/provider/" directory.
This file implements a TranscriptEngineTrait using the Keccak256 hash function. TranscriptEngineTrait is a trait for handling transcripts in zero-knowledge proofs—data structures recording all interaction steps during the proof process.
Below are some main parts of this file:
1. `Keccak256Transcript` struct: Implements TranscriptEngineTrait using the Keccak256 hash function. It contains a `round` field to track the current round, a `state` field to store the current hash state, a `transcript` field to store the transcript, and an `_p` field to store type information.
2. `compute_updated_state` function: Accepts input and computes the updated hash state.
3. Implementation of TranscriptEngineTrait: Provides main transcript handling functionalities, including creating a new transcript, extracting a challenge from the transcript, appending an element to the transcript, and adding a domain separator.
4. Test module: Contains test functions for testing the `Keccak256Transcript` struct's functionality.
Overall, this file implements a TranscriptEngineTrait using the Keccak256 hash function—a tool for handling transcripts in zero-knowledge proofs. Its main advantage is processing transcripts without revealing interaction steps, thus protecting proof privacy.
This file named "mod.rs" is located in the "src/provider/" directory.
This file primarily imports various implementation modules in the Nova project, providing the functionalities needed by Nova.
Below are some main parts of this file:
1. `pub mod ipa_pc;`: Imports a module named "ipa_pc" implementing an evaluation engine using an IPA (Inner Product Argument)-based polynomial commitment scheme.
2. `pub mod keccak;`: Imports a module named "keccak" implementing a TranscriptEngineTrait using the Keccak256 hash function.
3. `pub mod pasta;`: Imports a module named "pasta" possibly containing functions and classes using Pasta curves.
4. `pub mod pedersen;`: Imports a module named "pedersen" possibly containing functions and classes using Pedersen commitments.
5. `pub mod poseidon;`: Imports a module named "poseidon" possibly containing functions and classes using the Poseidon hash function.
Overall, this file organizes various components of the Nova project (e.g., evaluation engine, TranscriptEngineTrait, Pasta curves, Pedersen commitments, Poseidon hash function) into a complete cryptographic library.
Filename: `src/r1cs.rs`
This file defines types and methods related to Rank-1 Constraint System (R1CS), a constraint system widely used in zero-knowledge proof systems.
Mainly defines the following structures and their methods:
1. `R1CS
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