250 lines
7.9 KiB
C++
250 lines
7.9 KiB
C++
/*
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* Copyright (c) 2012-2020 MIRACL UK Ltd.
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*
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* This file is part of MIRACL Core
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* (see https://github.com/miracl/core).
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*
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* Licensed under the Apache License, Version 2.0 (the "License");
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* you may not use this file except in compliance with the License.
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* You may obtain a copy of the License at
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*
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* http://www.apache.org/licenses/LICENSE-2.0
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*
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* Unless required by applicable law or agreed to in writing, software
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* distributed under the License is distributed on an "AS IS" BASIS,
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* WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
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* See the License for the specific language governing permissions and
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* limitations under the License.
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*/
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#ifndef ECP2_BN462_H
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#define ECP2_BN462_H
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#include "fp2_BN462.h"
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#include "config_curve_BN462.h"
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using namespace core;
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namespace BN462 {
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extern const B464_60::BIG Fra; /**< real part of BN curve Frobenius Constant */
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extern const B464_60::BIG Frb; /**< imaginary part of BN curve Frobenius Constant */
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}
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namespace BN462 {
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/**
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@brief ECP2 Structure - Elliptic Curve Point over quadratic extension field
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*/
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typedef struct
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{
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// int inf; /**< Infinity Flag */
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BN462::FP2 x; /**< x-coordinate of point */
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BN462::FP2 y; /**< y-coordinate of point */
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BN462::FP2 z; /**< z-coordinate of point */
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} ECP2;
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/* Curve Params - see rom*.cpp */
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extern const int CURVE_B_I; /**< Elliptic curve B parameter */
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extern const B464_60::BIG CURVE_B; /**< Elliptic curve B parameter */
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extern const B464_60::BIG CURVE_Order; /**< Elliptic curve group order */
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extern const B464_60::BIG CURVE_Cof; /**< Elliptic curve cofactor */
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extern const B464_60::BIG CURVE_Bnx; /**< Elliptic curve parameter */
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extern const B464_60::BIG CURVE_HTPC; /**< Hash to Point precomputation */
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/* Generator point on G1 */
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extern const B464_60::BIG CURVE_Gx; /**< x-coordinate of generator point in group G1 */
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extern const B464_60::BIG CURVE_Gy; /**< y-coordinate of generator point in group G1 */
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/* For Pairings only */
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/* Generator point on G2 */
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extern const B464_60::BIG CURVE_Pxa; /**< real part of x-coordinate of generator point in group G2 */
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extern const B464_60::BIG CURVE_Pxb; /**< imaginary part of x-coordinate of generator point in group G2 */
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extern const B464_60::BIG CURVE_Pya; /**< real part of y-coordinate of generator point in group G2 */
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extern const B464_60::BIG CURVE_Pyb; /**< imaginary part of y-coordinate of generator point in group G2 */
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/* ECP2 E(Fp2) prototypes */
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/** @brief Tests for ECP2 point equal to infinity
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*
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@param P ECP2 point to be tested
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@return 1 if infinity, else returns 0
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*/
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extern int ECP2_isinf(ECP2 *P);
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/** @brief Copy ECP2 point to another ECP2 point
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*
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@param P ECP2 instance, on exit = Q
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@param Q ECP2 instance to be copied
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*/
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extern void ECP2_copy(ECP2 *P, ECP2 *Q);
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/** @brief Set ECP2 to point-at-infinity
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*
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@param P ECP2 instance to be set to infinity
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*/
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extern void ECP2_inf(ECP2 *P);
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/** @brief Tests for equality of two ECP2s
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*
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@param P ECP2 instance to be compared
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@param Q ECP2 instance to be compared
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@return 1 if P=Q, else returns 0
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*/
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extern int ECP2_equals(ECP2 *P, ECP2 *Q);
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/** @brief Converts an ECP2 point from Projective (x,y,z) coordinates to affine (x,y) coordinates
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*
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@param P ECP2 instance to be converted to affine form
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*/
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extern void ECP2_affine(ECP2 *P);
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/** @brief Extract x and y coordinates of an ECP2 point P
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*
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If x=y, returns only x
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@param x FP2 on exit = x coordinate of point
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@param y FP2 on exit = y coordinate of point (unless x=y)
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@param P ECP2 instance (x,y)
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@return -1 if P is point-at-infinity, else 0
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*/
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extern int ECP2_get(BN462::FP2 *x, BN462::FP2 *y, ECP2 *P);
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/** @brief Formats and outputs an ECP2 point to the console, converted to affine coordinates
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*
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@param P ECP2 instance to be printed
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*/
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extern void ECP2_output(ECP2 *P);
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/** @brief Formats and outputs an ECP2 point to the console, in projective coordinates
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*
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@param P ECP2 instance to be printed
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*/
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extern void ECP2_outputxyz(ECP2 *P);
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/** @brief Formats and outputs an ECP2 point to an octet string
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*
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The octet string is created in the form x|y or just x if compressed
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Convert the real and imaginary parts of the x and y coordinates to big-endian base 256 form.
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If c is true, only the x coordinate is provided as in 0x2|x if y is even, or 0x3|x if y is odd
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@param S output octet string
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@param P ECP2 instance to be converted to an octet string
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@param c true for compression
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*/
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extern void ECP2_toOctet(octet *S, ECP2 *P, bool c);
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/** @brief Creates an ECP2 point from an octet string
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*
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The octet string is in the form x|y
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The real and imaginary parts of the x and y coordinates are in big-endian base 256 form.
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If in compressed form only the x coordinate is provided as in 0x2|x if y is even, or 0x3|x if y is odd
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@param P ECP2 instance to be created from the octet string
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@param S input octet string
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return 1 if octet string corresponds to a point on the curve, else 0
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*/
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extern int ECP2_fromOctet(ECP2 *P, octet *S);
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/** @brief Calculate Right Hand Side of curve equation y^2=f(x)
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*
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Function f(x)=x^3+Ax+B
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Used internally.
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@param r FP2 value of f(x)
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@param x FP2 instance
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*/
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extern void ECP2_rhs(BN462::FP2 *r, BN462::FP2 *x);
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/** @brief Set ECP2 to point(x,y) given x and y
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*
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Point P set to infinity if no such point on the curve.
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@param P ECP2 instance to be set (x,y)
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@param x FP2 x coordinate of point
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@param y FP2 y coordinate of point
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@return 1 if point exists, else 0
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*/
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extern int ECP2_set(ECP2 *P, BN462::FP2 *x, BN462::FP2 *y);
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/** @brief Set ECP to point(x,[y]) given x
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*
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Point P set to infinity if no such point on the curve. Otherwise y coordinate is calculated from x.
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@param P ECP instance to be set (x,[y])
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@param x BIG x coordinate of point
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@param s sign of y
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@return 1 if point exists, else 0
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*/
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extern int ECP2_setx(ECP2 *P, BN462::FP2 *x, int s);
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/** @brief Negation of an ECP2 point
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*
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@param P ECP2 instance, on exit = -P
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*/
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extern void ECP2_neg(ECP2 *P);
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/** @brief Doubles an ECP2 instance P
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*
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@param P ECP2 instance, on exit =2*P
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*/
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extern int ECP2_dbl(ECP2 *P);
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/** @brief Adds ECP2 instance Q to ECP2 instance P
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*
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@param P ECP2 instance, on exit =P+Q
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@param Q ECP2 instance to be added to P
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*/
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extern int ECP2_add(ECP2 *P, ECP2 *Q);
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/** @brief Subtracts ECP instance Q from ECP2 instance P
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*
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@param P ECP2 instance, on exit =P-Q
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@param Q ECP2 instance to be subtracted from P
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*/
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extern void ECP2_sub(ECP2 *P, ECP2 *Q);
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/** @brief Multiplies an ECP2 instance P by a BIG, side-channel resistant
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*
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Uses fixed sized windows.
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@param P ECP2 instance, on exit =b*P
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@param b BIG number multiplier
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*/
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extern void ECP2_mul(ECP2 *P, B464_60::BIG b);
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/** @brief Multiplies an ECP2 instance P by the internal modulus p, using precalculated Frobenius constant f
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*
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Fast point multiplication using Frobenius
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@param P ECP2 instance, on exit = p*P
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@param f FP2 precalculated Frobenius constant
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*/
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extern void ECP2_frob(ECP2 *P, BN462::FP2 *f);
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/** @brief Calculates P=b[0]*Q[0]+b[1]*Q[1]+b[2]*Q[2]+b[3]*Q[3]
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*
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@param P ECP2 instance, on exit = b[0]*Q[0]+b[1]*Q[1]+b[2]*Q[2]+b[3]*Q[3]
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@param Q ECP2 array of 4 points
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@param b BIG array of 4 multipliers
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*/
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extern void ECP2_mul4(ECP2 *P, ECP2 *Q, B464_60::BIG *b);
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/** @brief Multiplies random point by co-factor
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*
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@param Q ECP2 multiplied by co-factor
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*/
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extern void ECP2_cfp(ECP2 *Q);
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/** @brief Maps random FP2 to curve point in constant time
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*
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@param Q ECP2 instance
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@param x FP2 derived from hash
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*/
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extern void ECP2_map2point(ECP2 *Q, BN462::FP2 *x);
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/** @brief Maps random BIG to curve point using hunt-and-peck
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*
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@param Q ECP2 instance
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@param x Fp derived from hash
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*/
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extern void ECP2_hap2point(ECP2 *Q, B464_60::BIG x);
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/** @brief Maps random octet to curve point of correct order
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*
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@param P ECP2 instance of correct order
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@param W OCTET byte array to be mapped
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*/
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extern void ECP2_mapit(ECP2 *P, octet *w);
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/** @brief Get Group Generator from ROM
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*
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@param G ECP2 instance
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@return 1 if point exists, else 0
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*/
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extern int ECP2_generator(ECP2 *G);
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}
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#endif
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