Prover output (evalutation pair, witness) that can be passed on to Shplonk batch opening. More...

Functions
template<class Fr >
std::vector< Fr >	powers_of_rho (const Fr rho, const size_t num_powers)
	Compute powers of challenge ρ

template<class Fr >
std::vector< Fr >	powers_of_evaluation_challenge (const Fr r, const size_t num_squares)
	Compute squares of folding challenge r.

Detailed Description

Prover output (evalutation pair, witness) that can be passed on to Shplonk batch opening.

Evaluation pairs {r, A₀₊(r)}, {-r, A₀₋(-r)}, {r^{2^j}, Aⱼ(r^{2^j)}, {-r^{2^j}, Aⱼ(-r^{2^j)}, j = [1, ..., m-1] and witness (Fold) polynomials [ A₀₊(X) = F(X) + r⁻¹⋅G(X) A₀₋(X) = F(X) - r⁻¹⋅G(X) A₁(X) = (1-u₀)⋅even(A₀)(X) + u₀⋅odd(A₀)(X) ... Aₘ₋₁(X) = (1-uₘ₋₂)⋅even(Aₘ₋₂)(X) + uₘ₋₂⋅odd(Aₘ₋₂)(X) ]

Template Parameters

Curve CommitmentScheme parameters

Function Documentation

◆ powers_of_evaluation_challenge()

template<class Fr >

std::vector< Fr > bb::gemini::powers_of_evaluation_challenge	(	const Fr	r,
		const size_t	num_squares
	)

inline

Compute squares of folding challenge r.

Parameters

r
num_squares	The number of foldings

Returns: std::vector<typename Curve::ScalarField>

Definition at line 94 of file gemini.hpp.

◆ powers_of_rho()