Author: shuangcrypto.com

Take example circuit in figure 1, following the Arithmetization described in post, a step by step description of GKR arithmetication of a concrete example.

Notations representing index of gates

\(q’\in \{0,1\}^{b_N}\): The index of one of the \(N\) identical copies of the base circuit \(C_0\) within \(C\).…

To understand the attack on Nova, I figure out I need to understand the role of the hash function and the validation check of hash function in Nova, from the first paper where the “cycle of curves” is not introduced, the circuit is illustrated as

to …

explain the multipoints opening of Halo 2, I don’t think Halo2 book explain this part clearly, and perhaps, neither my note.

the key, is the homomorphism of the commitment scheme. and combine the evaluation at different points, and combine the different polynomial evaluated at the same points. Later if I …

Stark can be described in 5 steps in a high level:

1. Computation program
2. generate an execution trace and a set of polynomial constraints, AIR (Algebraic Intermediate Representation) (no circuit)
3. Transfer the execution trace to be a polynomial, extend it to a larger domain
4. compute the composition polynomial, which is the

…

1. prover commit to \(f(x)\)

$$f(X)=f_E(X^2)+X\cdot f_O(X^2)$$

if we take an intermediate variant \(Y\) to replace the \(X^2\)

With a fixed \(Y\), then \(f(x)\) can be considered as one degree polynomial for \(X\), as

$$f(X)=f_E(Y)+X\cdot f_O(Y)$$

and for a given \(y\), it determineds a unique line (one degree polynomial)

and the …