Nova: New zk-SNARKs System

Nova is a new type of zk-SNARKs system developed by Microsoft. It utilizes Relaxed Rank-1 Constraint Systems ( Relaxed R1CS ) technology to improve the efficiency and flexibility of the proofs.

Advantages of Nova

The main advantage of Nova lies in its use of relaxed R1CS technology. Traditional R1CS systems require a significant amount of randomness during the proof process, resulting in a complex and time-consuming proof generation and verification process. Nova, by using relaxed R1CS, allows for less randomness in the proof, greatly improving proof efficiency.

Nova also supports incremental computation, allowing for the gradual calculation of complex functions without the need to compute the entire function at once. This is particularly useful when dealing with large-scale data or complex computations. Additionally, Nova supports polynomial computation, enabling it to handle more complex proof tasks.

Disadvantages of Nova

Although Nova has many advantages, it also has some disadvantages:

1. Due to the use of relaxed R1CS, Nova's proofs may not be as robust as traditional R1CS systems. Relaxed R1CS allows for less randomness, which may compromise proof security. However, the developers of Nova have taken measures to address this issue, such as employing stronger cryptographic algorithms and more complex proof strategies.

2. The implementation of Nova is relatively complex, which may increase the difficulty of use and maintenance. Nova employs many advanced cryptographic techniques, such as polynomial computation, group operations, and random oracles, which require a deep understanding of these technologies to use and modify Nova effectively.

The Important Position of Nova in the Field of zk-SNARKs

Nova occupies an important position in the field of zk-SNARKs. Its emergence has opened new avenues for the development of zk-SNARKs. The relaxed R1CS technology adopted by Nova makes the process of generating and verifying proofs more efficient, which is crucial for large-scale zk-SNARKs applications. In addition, Nova also supports incremental computation and polynomial computation, allowing it to handle more complex proof tasks, further expanding the application scope of zk-SNARKs.

Interpretation of Nova's Source Code

The main source code structure of Nova is as follows:

• src/bellperson/: Implemented the generation of R1CS( Rank-1 Constraint Systems).
• src/gadgets/: Contains tools for constructing zk-SNARKs proofs.
• src/provider/: Contains some provider code, such as the implementation of the Keccak hash function.
• src/spartan/: Contains the code related to the Spartan protocol.
• src/traits/: Contains some Rust traits that define common behaviors.

The functions of the main modules and files are as follows:

• bellperson/mod.rs: Defines the functions related to the generation of R1CS.
• bellperson/r1cs.rs: Defines two traits, NovaWitness and NovaShape, for obtaining R1CS instances, witnesses, shapes, and commitment keys.
• bellperson/shape_cs.rs: defines the ShapeCS structure, used to create R1CS shape constraint systems.
• bellperson/solver.rs: defines the SatisfyingAssignment structure, used to create R1CS instances and the constraint system of the prover.
• circuit.rs: defines the enhanced circuits in the Nova protocol, including the step circuit and the verifier circuit.
• constants.rs: Defines some constants, such as the challenge bit length, hash bit length, etc.
• errors.rs: Defines the error types that the Nova library may return.
• nifs.rs: implemented a non-interactive folding scheme ( NIFS ).
• r1cs.rs: Defines types and methods related to R1CS.
• spartan/math.rs: Defines the Math trait and its implementation for the usize type, including some basic mathematical operations.
• spartan/mod.rs: Implemented the RelaxedR1CSSNARKTrait using Spartan.
• spartan/polynomial.rs: Defines the basic types and operations related to polynomials.
• spartan/sumcheck.rs: Implements the Sumcheck algorithm in the Spartan protocol.
• traits/circuit.rs: Defines the StepCircuit trait, used for incremental computation of step functions.
• traits/commitment.rs: defines the traits related to the commitment ( commitment ).
• traits/evaluation.rs: Defines the EvaluationEngineTrait trait for polynomial evaluation engine.
• traits/mod.rs: Defines some traits used for cryptographic operations.
• traits/snark.rs: Defines the RelaxedR1CSSNARKTrait trait, used for zk-SNARKs (.

The source code of Nova implements a complete zk-SNARKs system, including the generation of R1CS, the construction of constraint systems, polynomial computation, commitment schemes, evaluation engines, and several other modules. These modules work together to achieve efficient zk-SNARKs generation and verification functions.