#include <fp12_2over3over2_gadgets.hpp>

Inheritance diagram for libsnark::Fp12_2over3over2_square_gadget< Fp12T >:

Collaboration diagram for libsnark::Fp12_2over3over2_square_gadget< Fp12T >:

Public Types
using	FieldT = typename Fp12T::my_Fp

using	Fp6T = typename Fp12T::my_Fp6

Public Member Functions
	Fp12_2over3over2_square_gadget (protoboard< FieldT > &pb, const Fp12_2over3over2_variable< Fp12T > &A, const Fp12_2over3over2_variable< Fp12T > &result, const std::string &annotation_prefix)

const Fp12_2over3over2_variable< Fp12T > &	result () const

void	generate_r1cs_constraints ()

void	generate_r1cs_witness ()

Public Member Functions inherited from libsnark::gadget< Fp12T::my_Fp >
	gadget (protoboard< Fp12T::my_Fp > &pb, const std::string &annotation_prefix)

Public Attributes
Fp12_2over3over2_variable< Fp12T >	_A

Fp12_2over3over2_variable< Fp12T >	_result

Fp6_3over2_mul_gadget< Fp6T >	_compute_alpha

Fp6_3over2_mul_gadget< Fp6T >	_compute_beta

Additional Inherited Members
Protected Attributes inherited from libsnark::gadget< Fp12T::my_Fp >
protoboard< Fp12T::my_Fp > &	pb

const std::string	annotation_prefix

Detailed Description

template<typename Fp12T>
class libsnark::Fp12_2over3over2_square_gadget< Fp12T >

Follows implementation in libff::Fp12_2over3over2_model, which is based on Section 3 of [DOSD06].

Let (a0, a1) = a0 + a1 * w be an element of Fp12, where a0, a1 in Fp6 and w = v^2 for v in Fp6. By simple expansion of terms: (a0, a1)^2 = (a0^2 + a1^2 * v, 2 * a0 * a1) However, since a0^2 + a1^2 * v = (a0 + a1)*(a0 + a1 * v) - (a0 * a1) * v - a0 * a1, it follows that (a0, a1)^2 can be computed with just 2 full multiplications in Fp6. (Note that multiplications by v are free in an arithmetic circuit - see mul_by_non_residue).

Definition at line 92 of file fp12_2over3over2_gadgets.hpp.

Member Typedef Documentation

◆ FieldT

template<typename Fp12T >

using libsnark::Fp12_2over3over2_square_gadget< Fp12T >::FieldT = typename Fp12T::my_Fp

Definition at line 95 of file fp12_2over3over2_gadgets.hpp.

◆ Fp6T

template<typename Fp12T >

using libsnark::Fp12_2over3over2_square_gadget< Fp12T >::Fp6T = typename Fp12T::my_Fp6

Definition at line 96 of file fp12_2over3over2_gadgets.hpp.

Constructor & Destructor Documentation

◆ Fp12_2over3over2_square_gadget()

template<typename Fp12T >

libsnark::Fp12_2over3over2_square_gadget< Fp12T >::Fp12_2over3over2_square_gadget	(	protoboard< FieldT > &	pb,
		const Fp12_2over3over2_variable< Fp12T > &	A,
		const Fp12_2over3over2_variable< Fp12T > &	result,
		const std::string &	annotation_prefix
	)