http://git-wip-us.apache.org/repos/asf/incubator-milagro-crypto/blob/c25f9e5c/version3/cpp/ecp2.h ---------------------------------------------------------------------- diff --git a/version3/cpp/ecp2.h b/version3/cpp/ecp2.h new file mode 100644 index 0000000..9cb5739 --- /dev/null +++ b/version3/cpp/ecp2.h @@ -0,0 +1,203 @@ +#ifndef ECP2_ZZZ_H +#define ECP2_ZZZ_H + +#include "fp2_YYY.h" +#include "config_curve_ZZZ.h" + +using namespace amcl; + + +namespace YYY { + +extern const XXX::BIG Fra; /**< real part of BN curve Frobenius Constant */ +extern const XXX::BIG Frb; /**< imaginary part of BN curve Frobenius Constant */ + +} + +namespace ZZZ { + +/** + @brief ECP2 Structure - Elliptic Curve Point over quadratic extension field +*/ + +typedef struct +{ +// int inf; /**< Infinity Flag */ + YYY::FP2 x; /**< x-coordinate of point */ + YYY::FP2 y; /**< y-coordinate of point */ + YYY::FP2 z; /**< z-coordinate of point */ +} ECP2; + + +/* Curve Params - see rom.c */ +extern const int CURVE_A; /**< Elliptic curve A parameter */ +extern const int CURVE_B_I; /**< Elliptic curve B parameter */ +extern const XXX::BIG CURVE_B; /**< Elliptic curve B parameter */ +extern const XXX::BIG CURVE_Order; /**< Elliptic curve group order */ +extern const XXX::BIG CURVE_Cof; /**< Elliptic curve cofactor */ +extern const XXX::BIG CURVE_Bnx; /**< Elliptic curve parameter */ + + +/* Generator point on G1 */ +extern const XXX::BIG CURVE_Gx; /**< x-coordinate of generator point in group G1 */ +extern const XXX::BIG CURVE_Gy; /**< y-coordinate of generator point in group G1 */ + +/* For Pairings only */ + +/* Generator point on G2 */ +extern const XXX::BIG CURVE_Pxa; /**< real part of x-coordinate of generator point in group G2 */ +extern const XXX::BIG CURVE_Pxb; /**< imaginary part of x-coordinate of generator point in group G2 */ +extern const XXX::BIG CURVE_Pya; /**< real part of y-coordinate of generator point in group G2 */ +extern const XXX::BIG CURVE_Pyb; /**< imaginary part of y-coordinate of generator point in group G2 */ + +/* ECP2 E(Fp2) prototypes */ +/** @brief Tests for ECP2 point equal to infinity + * + @param P ECP2 point to be tested + @return 1 if infinity, else returns 0 + */ +extern int ECP2_isinf(ECP2 *P); +/** @brief Copy ECP2 point to another ECP2 point + * + @param P ECP2 instance, on exit = Q + @param Q ECP2 instance to be copied + */ +extern void ECP2_copy(ECP2 *P,ECP2 *Q); +/** @brief Set ECP2 to point-at-infinity + * + @param P ECP2 instance to be set to infinity + */ +extern void ECP2_inf(ECP2 *P); +/** @brief Tests for equality of two ECP2s + * + @param P ECP2 instance to be compared + @param Q ECP2 instance to be compared + @return 1 if P=Q, else returns 0 + */ +extern int ECP2_equals(ECP2 *P,ECP2 *Q); +/** @brief Converts an ECP2 point from Projective (x,y,z) coordinates to affine (x,y) coordinates + * + @param P ECP2 instance to be converted to affine form + */ +extern void ECP2_affine(ECP2 *P); +/** @brief Extract x and y coordinates of an ECP2 point P + * + If x=y, returns only x + @param x FP2 on exit = x coordinate of point + @param y FP2 on exit = y coordinate of point (unless x=y) + @param P ECP2 instance (x,y) + @return -1 if P is point-at-infinity, else 0 + */ +extern int ECP2_get(YYY::FP2 *x,YYY::FP2 *y,ECP2 *P); +/** @brief Formats and outputs an ECP2 point to the console, converted to affine coordinates + * + @param P ECP2 instance to be printed + */ +extern void ECP2_output(ECP2 *P); +/** @brief Formats and outputs an ECP2 point to the console, in projective coordinates + * + @param P ECP2 instance to be printed + */ +extern void ECP2_outputxyz(ECP2 *P); +/** @brief Formats and outputs an ECP2 point to an octet string + * + The octet string is created in the form x|y. + Convert the real and imaginary parts of the x and y coordinates to big-endian base 256 form. + @param S output octet string + @param P ECP2 instance to be converted to an octet string + */ +extern void ECP2_toOctet(octet *S,ECP2 *P); +/** @brief Creates an ECP2 point from an octet string + * + The octet string is in the form x|y + The real and imaginary parts of the x and y coordinates are in big-endian base 256 form. + @param P ECP2 instance to be created from the octet string + @param S input octet string + return 1 if octet string corresponds to a point on the curve, else 0 + */ +extern int ECP2_fromOctet(ECP2 *P,octet *S); +/** @brief Calculate Right Hand Side of curve equation y^2=f(x) + * + Function f(x)=x^3+Ax+B + Used internally. + @param r FP2 value of f(x) + @param x FP2 instance + */ +extern void ECP2_rhs(YYY::FP2 *r,YYY::FP2 *x); +/** @brief Set ECP2 to point(x,y) given x and y + * + Point P set to infinity if no such point on the curve. + @param P ECP2 instance to be set (x,y) + @param x FP2 x coordinate of point + @param y FP2 y coordinate of point + @return 1 if point exists, else 0 + */ +extern int ECP2_set(ECP2 *P,YYY::FP2 *x,YYY::FP2 *y); +/** @brief Set ECP to point(x,[y]) given x + * + Point P set to infinity if no such point on the curve. Otherwise y coordinate is calculated from x. + @param P ECP instance to be set (x,[y]) + @param x BIG x coordinate of point + @return 1 if point exists, else 0 + */ +extern int ECP2_setx(ECP2 *P,YYY::FP2 *x); +/** @brief Negation of an ECP2 point + * + @param P ECP2 instance, on exit = -P + */ +extern void ECP2_neg(ECP2 *P); +/** @brief Doubles an ECP2 instance P + * + @param P ECP2 instance, on exit =2*P + */ +extern int ECP2_dbl(ECP2 *P); +/** @brief Adds ECP2 instance Q to ECP2 instance P + * + @param P ECP2 instance, on exit =P+Q + @param Q ECP2 instance to be added to P + */ +extern int ECP2_add(ECP2 *P,ECP2 *Q); +/** @brief Subtracts ECP instance Q from ECP2 instance P + * + @param P ECP2 instance, on exit =P-Q + @param Q ECP2 instance to be subtracted from P + */ +extern void ECP2_sub(ECP2 *P,ECP2 *Q); +/** @brief Multiplies an ECP2 instance P by a BIG, side-channel resistant + * + Uses fixed sized windows. + @param P ECP2 instance, on exit =b*P + @param b BIG number multiplier + + */ +extern void ECP2_mul(ECP2 *P,XXX::BIG b); +/** @brief Multiplies an ECP2 instance P by the internal modulus p, using precalculated Frobenius constant f + * + Fast point multiplication using Frobenius + @param P ECP2 instance, on exit = p*P + @param f FP2 precalculated Frobenius constant + + */ +extern void ECP2_frob(ECP2 *P,YYY::FP2 *f); +/** @brief Calculates P=b[0]*Q[0]+b[1]*Q[1]+b[2]*Q[2]+b[3]*Q[3] + * + @param P ECP2 instance, on exit = b[0]*Q[0]+b[1]*Q[1]+b[2]*Q[2]+b[3]*Q[3] + @param Q ECP2 array of 4 points + @param b BIG array of 4 multipliers + */ +extern void ECP2_mul4(ECP2 *P,ECP2 *Q,XXX::BIG *b); + +/** @brief Maps random BIG to curve point of correct order + * + @param P ECP2 instance of correct order + @param W OCTET byte array to be mapped + */ +extern void ECP2_mapit(ECP2 *P,octet *w); +/** @brief Get Group Generator from ROM + * + @param G ECP2 instance + */ +extern void ECP2_generator(ECP2 *G); +} + +#endif \ No newline at end of file
http://git-wip-us.apache.org/repos/asf/incubator-milagro-crypto/blob/c25f9e5c/version3/cpp/ecp4.cpp ---------------------------------------------------------------------- diff --git a/version3/cpp/ecp4.cpp b/version3/cpp/ecp4.cpp new file mode 100644 index 0000000..e912d8a --- /dev/null +++ b/version3/cpp/ecp4.cpp @@ -0,0 +1,826 @@ +/* +Licensed to the Apache Software Foundation (ASF) under one +or more contributor license agreements. See the NOTICE file +distributed with this work for additional information +regarding copyright ownership. The ASF licenses this file +to you under the Apache License, Version 2.0 (the +"License"); you may not use this file except in compliance +with the License. You may obtain a copy of the License at + + http://www.apache.org/licenses/LICENSE-2.0 + +Unless required by applicable law or agreed to in writing, +software distributed under the License is distributed on an +"AS IS" BASIS, WITHOUT WARRANTIES OR CONDITIONS OF ANY +KIND, either express or implied. See the License for the +specific language governing permissions and limitations +under the License. +*/ + +/* AMCL Weierstrass elliptic curve functions over FP2 */ + +//#include <iostream> +#include "ecp4_ZZZ.h" + +using namespace std; +using namespace XXX; +using namespace YYY; + +int ZZZ::ECP4_isinf(ECP4 *P) +{ + return (FP4_iszilch(&(P->x)) & FP4_iszilch(&(P->z))); +} + +/* Set P=Q */ +void ZZZ::ECP4_copy(ECP4 *P,ECP4 *Q) +{ + FP4_copy(&(P->x),&(Q->x)); + FP4_copy(&(P->y),&(Q->y)); + FP4_copy(&(P->z),&(Q->z)); +} + +/* set P to Infinity */ +void ZZZ::ECP4_inf(ECP4 *P) +{ + FP4_zero(&(P->x)); + FP4_one(&(P->y)); + FP4_zero(&(P->z)); +} + +/* Conditional move Q to P dependant on d */ +static void ECP4_cmove(ZZZ::ECP4 *P,ZZZ::ECP4 *Q,int d) +{ + FP4_cmove(&(P->x),&(Q->x),d); + FP4_cmove(&(P->y),&(Q->y),d); + FP4_cmove(&(P->z),&(Q->z),d); +} + +/* return 1 if b==c, no branching */ +static int teq(sign32 b,sign32 c) +{ + sign32 x=b^c; + x-=1; // if x=0, x now -1 + return (int)((x>>31)&1); +} + +/* Constant time select from pre-computed table */ +static void ECP4_select(ZZZ::ECP4 *P,ZZZ::ECP4 W[],sign32 b) +{ + ZZZ::ECP4 MP; + sign32 m=b>>31; + sign32 babs=(b^m)-m; + + babs=(babs-1)/2; + + ECP4_cmove(P,&W[0],teq(babs,0)); // conditional move + ECP4_cmove(P,&W[1],teq(babs,1)); + ECP4_cmove(P,&W[2],teq(babs,2)); + ECP4_cmove(P,&W[3],teq(babs,3)); + ECP4_cmove(P,&W[4],teq(babs,4)); + ECP4_cmove(P,&W[5],teq(babs,5)); + ECP4_cmove(P,&W[6],teq(babs,6)); + ECP4_cmove(P,&W[7],teq(babs,7)); + + ECP4_copy(&MP,P); + ECP4_neg(&MP); // minus P + ECP4_cmove(P,&MP,(int)(m&1)); +} + +/* Make P affine (so z=1) */ +void ZZZ::ECP4_affine(ECP4 *P) +{ + FP4 one,iz; + if (ECP4_isinf(P)) return; + + FP4_one(&one); + if (FP4_isunity(&(P->z))) + { + FP4_reduce(&(P->x)); + FP4_reduce(&(P->y)); + return; + } + + FP4_inv(&iz,&(P->z)); + FP4_mul(&(P->x),&(P->x),&iz); + FP4_mul(&(P->y),&(P->y),&iz); + + FP4_reduce(&(P->x)); + FP4_reduce(&(P->y)); + FP4_copy(&(P->z),&one); +} + +/* return 1 if P==Q, else 0 */ +/* SU= 312 */ +int ZZZ::ECP4_equals(ECP4 *P,ECP4 *Q) +{ + FP4 a,b; + + FP4_mul(&a,&(P->x),&(Q->z)); + FP4_mul(&b,&(Q->x),&(P->z)); + if (!FP4_equals(&a,&b)) return 0; + + FP4_mul(&a,&(P->y),&(Q->z)); + FP4_mul(&b,&(Q->y),&(P->z)); + if (!FP4_equals(&a,&b)) return 0; + return 1; + +} + +/* extract x, y from point P */ +int ZZZ::ECP4_get(FP4 *x,FP4 *y,ECP4 *P) +{ + ECP4 W; + ECP4_copy(&W,P); + ECP4_affine(&W); + if (ECP4_isinf(&W)) return -1; + FP4_copy(y,&(W.y)); + FP4_copy(x,&(W.x)); + return 0; +} + +/* Output point P */ +void ZZZ::ECP4_output(ECP4 *P) +{ + FP4 x,y; + if (ECP4_isinf(P)) + { + printf("Infinity\n"); + return; + } + ECP4_get(&x,&y,P); + printf("("); + FP4_output(&x); + printf(","); + FP4_output(&y); + printf(")\n"); +} + +/* Convert Q to octet string */ +void ZZZ::ECP4_toOctet(octet *W,ECP4 *Q) +{ + BIG b; + FP4 qx,qy; + FP2 pa,pb; + + ECP4_get(&qx,&qy,Q); + + FP2_copy(&pa,&(qx.a)); + FP2_copy(&pb,&(qx.b)); + + FP_redc(b,&(pa.a)); + BIG_toBytes(&(W->val[0]),b); + FP_redc(b,&(pa.b)); + BIG_toBytes(&(W->val[MODBYTES_XXX]),b); + FP_redc(b,&(pb.a)); + BIG_toBytes(&(W->val[2*MODBYTES_XXX]),b); + FP_redc(b,&(pb.b)); + BIG_toBytes(&(W->val[3*MODBYTES_XXX]),b); + + FP2_copy(&pa,&(qy.a)); + FP2_copy(&pb,&(qy.b)); + + FP_redc(b,&(pa.a)); + BIG_toBytes(&(W->val[4*MODBYTES_XXX]),b); + FP_redc(b,&(pa.b)); + BIG_toBytes(&(W->val[5*MODBYTES_XXX]),b); + FP_redc(b,&(pb.a)); + BIG_toBytes(&(W->val[6*MODBYTES_XXX]),b); + FP_redc(b,&(pb.b)); + BIG_toBytes(&(W->val[7*MODBYTES_XXX]),b); + + W->len=8*MODBYTES_XXX; +} + +/* restore Q from octet string */ +int ZZZ::ECP4_fromOctet(ECP4 *Q,octet *W) +{ + BIG b; + FP4 qx,qy; + FP2 pa,pb; + + BIG_fromBytes(b,&(W->val[0])); + FP_nres(&(pa.a),b); + BIG_fromBytes(b,&(W->val[MODBYTES_XXX])); + FP_nres(&(pa.b),b); + BIG_fromBytes(b,&(W->val[2*MODBYTES_XXX])); + FP_nres(&(pb.a),b); + BIG_fromBytes(b,&(W->val[3*MODBYTES_XXX])); + FP_nres(&(pb.b),b); + + FP2_copy(&(qx.a),&pa); + FP2_copy(&(qx.b),&pb); + + BIG_fromBytes(b,&(W->val[4*MODBYTES_XXX])); + FP_nres(&(pa.a),b); + BIG_fromBytes(b,&(W->val[5*MODBYTES_XXX])); + FP_nres(&(pa.b),b); + BIG_fromBytes(b,&(W->val[6*MODBYTES_XXX])); + FP_nres(&(pb.a),b); + BIG_fromBytes(b,&(W->val[7*MODBYTES_XXX])); + FP_nres(&(pb.b),b); + + FP2_copy(&(qy.a),&pa); + FP2_copy(&(qy.b),&pb); + + + if (ECP4_set(Q,&qx,&qy)) return 1; + return 0; +} + +/* Calculate RHS of twisted curve equation x^3+B/i or x^3+Bi*/ +void ZZZ::ECP4_rhs(FP4 *rhs,FP4 *x) +{ + /* calculate RHS of elliptic curve equation */ + FP4 t; + FP2 t2; + BIG b; + FP4_sqr(&t,x); + + FP4_mul(rhs,&t,x); + + /* Assuming CURVE_A=0 */ + + BIG_rcopy(b,CURVE_B); + + FP2_from_BIG(&t2,b); + FP4_from_FP2(&t,&t2); + +#if SEXTIC_TWIST_ZZZ == D_TYPE + FP4_div_i(&t); /* IMPORTANT - here we use the correct SEXTIC twist of the curve */ +#endif + +#if SEXTIC_TWIST_ZZZ == M_TYPE + FP4_times_i(&t); /* IMPORTANT - here we use the correct SEXTIC twist of the curve */ +#endif + + FP4_add(rhs,&t,rhs); + FP4_reduce(rhs); +} + +/* Set P=(x,y). Return 1 if (x,y) is on the curve, else return 0*/ +/* SU= 232 */ +int ZZZ::ECP4_set(ECP4 *P,FP4 *x,FP4 *y) +{ + FP4 rhs,y2; + + FP4_sqr(&y2,y); + ECP4_rhs(&rhs,x); + + if (!FP4_equals(&y2,&rhs)) + { + ECP4_inf(P); + return 0; + } + + FP4_copy(&(P->x),x); + FP4_copy(&(P->y),y); + + FP4_one(&(P->z)); + return 1; +} + +/* Set P=(x,y). Return 1 if (x,.) is on the curve, else return 0 */ +/* SU= 232 */ +int ZZZ::ECP4_setx(ECP4 *P,FP4 *x) +{ + FP4 y; + ECP4_rhs(&y,x); + + if (!FP4_sqrt(&y,&y)) + { + ECP4_inf(P); + return 0; + } + + FP4_copy(&(P->x),x); + FP4_copy(&(P->y),&y); + FP4_one(&(P->z)); + return 1; +} + +/* Set P=-P */ +/* SU= 8 */ +void ZZZ::ECP4_neg(ECP4 *P) +{ + FP4_norm(&(P->y)); + FP4_neg(&(P->y),&(P->y)); + FP4_norm(&(P->y)); +} + +/* R+=R */ +/* return -1 for Infinity, 0 for addition, 1 for doubling */ +int ZZZ::ECP4_dbl(ECP4 *P) +{ + FP4 t0,t1,t2,t3,iy,x3,y3; + + FP4_copy(&iy,&(P->y)); //FP4 iy=new FP4(y); +#if SEXTIC_TWIST_ZZZ==D_TYPE + FP4_times_i(&iy); //iy.mul_ip(); +#endif + + FP4_sqr(&t0,&(P->y)); //t0.sqr(); +#if SEXTIC_TWIST_ZZZ==D_TYPE + FP4_times_i(&t0); //t0.mul_ip(); +#endif + + FP4_mul(&t1,&iy,&(P->z)); //t1.mul(z); + FP4_sqr(&t2,&(P->z)); //t2.sqr(); + + FP4_add(&(P->z),&t0,&t0); //z.add(t0); + FP4_norm(&(P->z)); //z.norm(); + FP4_add(&(P->z),&(P->z),&(P->z)); //z.add(z); + FP4_add(&(P->z),&(P->z),&(P->z)); //z.add(z); + FP4_norm(&(P->z)); //z.norm(); + + FP4_imul(&t2,&t2,3*CURVE_B_I); //t2.imul(3*ROM.CURVE_B_I); +#if SEXTIC_TWIST_ZZZ==M_TYPE + FP4_times_i(&t2); +#endif + + FP4_mul(&x3,&t2,&(P->z)); //x3.mul(z); + + FP4_add(&y3,&t0,&t2); //y3.add(t2); + FP4_norm(&y3); //y3.norm(); + FP4_mul(&(P->z),&(P->z),&t1); //z.mul(t1); + + FP4_add(&t1,&t2,&t2); //t1.add(t2); + FP4_add(&t2,&t2,&t1); //t2.add(t1); + FP4_norm(&t2); //t2.norm(); + FP4_sub(&t0,&t0,&t2); //t0.sub(t2); + FP4_norm(&t0); //t0.norm(); //y^2-9bz^2 + FP4_mul(&y3,&y3,&t0); //y3.mul(t0); + FP4_add(&(P->y),&y3,&x3); //y3.add(x3); //(y^2+3z*2)(y^2-9z^2)+3b.z^2.8y^2 + + FP4_mul(&t1,&(P->x),&iy); //t1.mul(iy); // + + FP4_norm(&t0); //x.norm(); + FP4_mul(&(P->x),&t0,&t1); //x.mul(t1); + FP4_add(&(P->x),&(P->x),&(P->x)); //x.add(x); //(y^2-9bz^2)xy2 + + FP4_norm(&(P->x)); //x.norm(); + + FP4_norm(&(P->y)); //y.norm(); + + return 1; +} + +/* Set P+=Q */ + +int ZZZ::ECP4_add(ECP4 *P,ECP4 *Q) +{ + FP4 t0,t1,t2,t3,t4,x3,y3,z3; + int b3=3*CURVE_B_I; + + FP4_mul(&t0,&(P->x),&(Q->x)); //t0.mul(Q.x); // x.Q.x + FP4_mul(&t1,&(P->y),&(Q->y)); //t1.mul(Q.y); // y.Q.y + + FP4_mul(&t2,&(P->z),&(Q->z)); //t2.mul(Q.z); + FP4_add(&t3,&(P->x),&(P->y)); //t3.add(y); + FP4_norm(&t3); //t3.norm(); //t3=X1+Y1 + FP4_add(&t4,&(Q->x),&(Q->y)); //t4.add(Q.y); + FP4_norm(&t4); //t4.norm(); //t4=X2+Y2 + FP4_mul(&t3,&t3,&t4); //t3.mul(t4); //t3=(X1+Y1)(X2+Y2) + FP4_add(&t4,&t0,&t1); //t4.add(t1); //t4=X1.X2+Y1.Y2 + + FP4_sub(&t3,&t3,&t4); //t3.sub(t4); + FP4_norm(&t3); //t3.norm(); +#if SEXTIC_TWIST_ZZZ==D_TYPE + FP4_times_i(&t3); //t3.mul_ip(); +#endif + + FP4_add(&t4,&(P->y),&(P->z)); //t4.add(z); + FP4_norm(&t4); //t4.norm(); //t4=Y1+Z1 + + FP4_add(&x3,&(Q->y),&(Q->z)); //x3.add(Q.z); + FP4_norm(&x3); //x3.norm(); //x3=Y2+Z2 + + FP4_mul(&t4,&t4,&x3); //t4.mul(x3); //t4=(Y1+Z1)(Y2+Z2) + + FP4_add(&x3,&t1,&t2); //x3.add(t2); //X3=Y1.Y2+Z1.Z2 + + FP4_sub(&t4,&t4,&x3); //t4.sub(x3); + FP4_norm(&t4); //t4.norm(); +#if SEXTIC_TWIST_ZZZ==D_TYPE + FP4_times_i(&t4); //t4.mul_ip(); +#endif + + FP4_add(&x3,&(P->x),&(P->z)); //x3.add(z); + FP4_norm(&x3); //x3.norm(); // x3=X1+Z1 + + FP4_add(&y3,&(Q->x),&(Q->z)); //y3.add(Q.z); + FP4_norm(&y3); //y3.norm(); // y3=X2+Z2 + FP4_mul(&x3,&x3,&y3); //x3.mul(y3); // x3=(X1+Z1)(X2+Z2) + + FP4_add(&y3,&t0,&t2); //y3.add(t2); // y3=X1.X2+Z1+Z2 + FP4_sub(&y3,&x3,&y3); //y3.rsub(x3); + FP4_norm(&y3); //y3.norm(); // y3=(X1+Z1)(X2+Z2) - (X1.X2+Z1.Z2) = X1.Z2+X2.Z1 +#if SEXTIC_TWIST_ZZZ==D_TYPE + FP4_times_i(&t0); //t0.mul_ip(); + FP4_times_i(&t1); //t1.mul_ip(); +#endif + + FP4_add(&x3,&t0,&t0); //x3.add(t0); + FP4_add(&t0,&t0,&x3); //t0.add(x3); + FP4_norm(&t0); //t0.norm(); + FP4_imul(&t2,&t2,b3); //t2.imul(b); +#if SEXTIC_TWIST_ZZZ==M_TYPE + FP4_times_i(&t2); +#endif + + FP4_add(&z3,&t1,&t2); //z3.add(t2); + FP4_norm(&z3); //z3.norm(); + FP4_sub(&t1,&t1,&t2); //t1.sub(t2); + FP4_norm(&t1); //t1.norm(); + FP4_imul(&y3,&y3,b3); //y3.imul(b); +#if SEXTIC_TWIST_ZZZ==M_TYPE + FP4_times_i(&y3); +#endif + + FP4_mul(&x3,&y3,&t4); //x3.mul(t4); + + FP4_mul(&t2,&t3,&t1); //t2.mul(t1); + FP4_sub(&(P->x),&t2,&x3); //x3.rsub(t2); + FP4_mul(&y3,&y3,&t0); //y3.mul(t0); + FP4_mul(&t1,&t1,&z3); //t1.mul(z3); + FP4_add(&(P->y),&y3,&t1); //y3.add(t1); + FP4_mul(&t0,&t0,&t3); //t0.mul(t3); + FP4_mul(&z3,&z3,&t4); //z3.mul(t4); + FP4_add(&(P->z),&z3,&t0); //z3.add(t0); + + FP4_norm(&(P->x)); //x.norm(); + FP4_norm(&(P->y)); //y.norm(); + FP4_norm(&(P->z)); //z.norm(); + + return 0; +} + +/* Set P-=Q */ +/* SU= 16 */ +void ZZZ::ECP4_sub(ECP4 *P,ECP4 *Q) +{ + ECP4 NQ; + ECP4_copy(&NQ,Q); + ECP4_neg(&NQ); + ECP4_add(P,&NQ); +} + + +void ZZZ::ECP4_reduce(ECP4 *P) +{ + FP4_reduce(&(P->x)); + FP4_reduce(&(P->y)); + FP4_reduce(&(P->z)); +} + +/* P*=e */ +/* SU= 280 */ +void ZZZ::ECP4_mul(ECP4 *P,BIG e) +{ + /* fixed size windows */ + int i,nb,s,ns; + BIG mt,t; + ECP4 Q,W[8],C; + sign8 w[1+(NLEN_XXX*BASEBITS_XXX+3)/4]; + + if (ECP4_isinf(P)) return; + + /* precompute table */ + + ECP4_copy(&Q,P); + ECP4_dbl(&Q); + ECP4_copy(&W[0],P); + + for (i=1; i<8; i++) + { + ECP4_copy(&W[i],&W[i-1]); + ECP4_add(&W[i],&Q); + } + + /* make exponent odd - add 2P if even, P if odd */ + BIG_copy(t,e); + s=BIG_parity(t); + BIG_inc(t,1); + BIG_norm(t); + ns=BIG_parity(t); + BIG_copy(mt,t); + BIG_inc(mt,1); + BIG_norm(mt); + BIG_cmove(t,mt,s); + ECP4_cmove(&Q,P,ns); + ECP4_copy(&C,&Q); + + nb=1+(BIG_nbits(t)+3)/4; + + /* convert exponent to signed 4-bit window */ + for (i=0; i<nb; i++) + { + w[i]=BIG_lastbits(t,5)-16; + BIG_dec(t,w[i]); + BIG_norm(t); + BIG_fshr(t,4); + } + w[nb]=BIG_lastbits(t,5); + + ECP4_copy(P,&W[(w[nb]-1)/2]); + for (i=nb-1; i>=0; i--) + { + ECP4_select(&Q,W,w[i]); + ECP4_dbl(P); + ECP4_dbl(P); + ECP4_dbl(P); + ECP4_dbl(P); + ECP4_add(P,&Q); + } + ECP4_sub(P,&C); /* apply correction */ + ECP4_affine(P); +} + +// calculate frobenius constants +void ZZZ::ECP4_frob_constants(FP2 F[3]) +{ + FP fx,fy; + FP2 X; + + FP_rcopy(&fx,Fra); + FP_rcopy(&fy,Frb); + FP2_from_FPs(&X,&fx,&fy); + + FP2_sqr(&F[0],&X); // FF=F^2=(1+i)^(p-7)/6 + FP2_copy(&F[2],&F[0]); + FP2_mul_ip(&F[2]); // W=(1+i)^6/6.(1+i)^(p-7)/6 = (1+i)^(p-1)/6 + FP2_norm(&F[2]); + FP2_sqr(&F[1],&F[2]); + FP2_mul(&F[2],&F[2],&F[1]); // W=(1+i)^(p-1)/2 + + FP2_copy(&F[1],&X); + +#if SEXTIC_TWIST_ZZZ == M_TYPE + FP2_mul_ip(&F[1]); // (1+i)^12/12.(1+i)^(p-7)/12 = (1+i)^(p+5)/12 + FP2_inv(&F[1],&F[1]); // (1+i)^-(p+5)/12 + FP2_sqr(&F[0],&F[1]); // (1+i)^-(p+5)/6 +#endif + + FP2_mul_ip(&F[0]); // FF=(1+i)^(p-7)/6.(1+i) = (1+i)^(p-1)/6 // (1+i)^6/6.(1+i)^-(p+5)/6 = (1+i)^-(p-1)/6 + FP2_norm(&F[0]); + FP2_mul(&F[1],&F[1],&F[0]); // FFF = (1+i)^(p-7)/12 . (1+i)^(p-1)/6 = (1+i)^(p-3)/4 // (1+i)^-(p+5)/12 . (1+i)^-(p-1)/6 = (1+i)^-(p+1)/4 + +} + +/* Calculates q^n.P using Frobenius constants */ +void ZZZ::ECP4_frob(ECP4 *P,FP2 F[3],int n) +{ + int i; + FP4 X,Y,Z; + + FP4_copy(&X,&(P->x)); + FP4_copy(&Y,&(P->y)); + FP4_copy(&Z,&(P->z)); + + for (i=0;i<n;i++) + { + FP4_frob(&X,&F[2]); // X^p + FP4_pmul(&X,&X,&F[0]); // X^p.(1+i)^(p-1)/6 // X^p.(1+i)^-(p-1)/6 + + FP4_frob(&Y,&F[2]); // Y^p + FP4_pmul(&Y,&Y,&F[1]); + FP4_times_i(&Y); // Y.p.(1+i)^(p-3)/4.(1+i)^(2/4) = Y^p.(1+i)^(p-1)/4 // (1+i)^-(p+1)/4 .(1+i)^2/4 = Y^p.(1+i)^-(p-1)/4 + + FP4_frob(&Z,&F[2]); + } + + FP4_copy(&(P->x),&X); + FP4_copy(&(P->y),&Y); + FP4_copy(&(P->z),&Z); + + + //ECP4_set(P,&X,&Y); +} + +/* Side channel attack secure */ +// Bos & Costello https://eprint.iacr.org/2013/458.pdf +// Faz-Hernandez & Longa & Sanchez https://eprint.iacr.org/2013/158.pdf + +void ZZZ::ECP4_mul8(ECP4 *P,ECP4 Q[8],BIG u[8]) +{ + int i,j,k,nb,pb1,pb2,bt; + ECP4 T1[8],T2[8],W; + BIG mt,t[8]; + sign8 w1[NLEN_XXX*BASEBITS_XXX+1]; + sign8 s1[NLEN_XXX*BASEBITS_XXX+1]; + sign8 w2[NLEN_XXX*BASEBITS_XXX+1]; + sign8 s2[NLEN_XXX*BASEBITS_XXX+1]; + FP2 X[3]; + + ECP4_frob_constants(X); + + for (i=0; i<8; i++) + { + BIG_copy(t[i],u[i]); + } +// Precomputed table + ECP4_copy(&T1[0],&Q[0]); // Q[0] + ECP4_copy(&T1[1],&T1[0]); + ECP4_add(&T1[1],&Q[1]); // Q[0]+Q[1] + ECP4_copy(&T1[2],&T1[0]); + ECP4_add(&T1[2],&Q[2]); // Q[0]+Q[2] + ECP4_copy(&T1[3],&T1[1]); + ECP4_add(&T1[3],&Q[2]); // Q[0]+Q[1]+Q[2] + ECP4_copy(&T1[4],&T1[0]); + ECP4_add(&T1[4],&Q[3]); // Q[0]+Q[3] + ECP4_copy(&T1[5],&T1[1]); + ECP4_add(&T1[5],&Q[3]); // Q[0]+Q[1]+Q[3] + ECP4_copy(&T1[6],&T1[2]); + ECP4_add(&T1[6],&Q[3]); // Q[0]+Q[2]+Q[3] + ECP4_copy(&T1[7],&T1[3]); + ECP4_add(&T1[7],&Q[3]); // Q[0]+Q[1]+Q[2]+Q[3] + +// Use Frobenius + + for (i=0;i<8;i++) + { + ECP4_copy(&T2[i],&T1[i]); + ECP4_frob(&T2[i],X,4); + } + +// Make them odd + pb1=1-BIG_parity(t[0]); + BIG_inc(t[0],pb1); + BIG_norm(t[0]); + + pb2=1-BIG_parity(t[4]); + BIG_inc(t[4],pb2); + BIG_norm(t[4]); + +// Number of bits + BIG_zero(mt); + for (i=0; i<8; i++) + { + BIG_or(mt,mt,t[i]); + } + nb=1+BIG_nbits(mt); + +// Sign pivot + s1[nb-1]=1; + s2[nb-1]=1; + for (i=0;i<nb-1;i++) + { + BIG_fshr(t[0],1); + s1[i]=2*BIG_parity(t[0])-1; + BIG_fshr(t[4],1); + s2[i]=2*BIG_parity(t[4])-1; + } + + +// Recoded exponents + for (i=0; i<nb; i++) + { + w1[i]=0; + k=1; + for (j=1; j<4; j++) + { + bt=s1[i]*BIG_parity(t[j]); + BIG_fshr(t[j],1); + + BIG_dec(t[j],(bt>>1)); + BIG_norm(t[j]); + w1[i]+=bt*k; + k*=2; + } + + w2[i]=0; + k=1; + for (j=5; j<8; j++) + { + bt=s2[i]*BIG_parity(t[j]); + BIG_fshr(t[j],1); + + BIG_dec(t[j],(bt>>1)); + BIG_norm(t[j]); + w2[i]+=bt*k; + k*=2; + } + } + +// Main loop + ECP4_select(P,T1,2*w1[nb-1]+1); + ECP4_select(&W,T2,2*w2[nb-1]+1); + ECP4_add(P,&W); + for (i=nb-2; i>=0; i--) + { + ECP4_dbl(P); + ECP4_select(&W,T1,2*w1[i]+s1[i]); + ECP4_add(P,&W); + ECP4_select(&W,T2,2*w2[i]+s2[i]); + ECP4_add(P,&W); + } + +// apply corrections + ECP4_copy(&W,P); + ECP4_sub(&W,&Q[0]); + ECP4_cmove(P,&W,pb1); + ECP4_copy(&W,P); + ECP4_sub(&W,&Q[4]); + ECP4_cmove(P,&W,pb2); + + ECP4_affine(P); +} + +/* Map to hash value to point on G2 from random BIG */ + +void ZZZ::ECP4_mapit(ECP4 *Q,octet *W) +{ + BIG q,one,x,hv; + FP2 X[3],T; + FP4 X4,Y4; + + ECP4 xQ, x2Q, x3Q, x4Q; + + BIG_fromBytes(hv,W->val); + BIG_rcopy(q,Modulus); + BIG_one(one); + BIG_mod(hv,q); + + for (;;) + { + FP2_from_BIGs(&T,one,hv); /*******/ + FP4_from_FP2(&X4,&T); + if (ECP4_setx(Q,&X4)) break; + BIG_inc(hv,1); + } + + ECP4_frob_constants(X); + + BIG_rcopy(x,CURVE_Bnx); + + // Efficient hash maps to G2 on BLS24 curves - Budroni, Pintore + // Q -> x4Q -x3Q -Q + F(x3Q-x2Q) + F(F(x2Q-xQ)) + F(F(F(xQ-Q))) +F(F(F(F(2Q)))) + + ECP4_copy(&xQ,Q); + ECP4_mul(&xQ,x); + ECP4_copy(&x2Q,&xQ); + ECP4_mul(&x2Q,x); + ECP4_copy(&x3Q,&x2Q); + ECP4_mul(&x3Q,x); + ECP4_copy(&x4Q,&x3Q); + ECP4_mul(&x4Q,x); + +#if SIGN_OF_X_ZZZ==NEGATIVEX + ECP4_neg(&xQ); + ECP4_neg(&x3Q); +#endif + + ECP4_sub(&x4Q,&x3Q); + ECP4_sub(&x4Q,Q); + + ECP4_sub(&x3Q,&x2Q); + ECP4_frob(&x3Q,X,1); + + ECP4_sub(&x2Q,&xQ); + ECP4_frob(&x2Q,X,2); + + ECP4_sub(&xQ,Q); + ECP4_frob(&xQ,X,3); + + ECP4_dbl(Q); + ECP4_frob(Q,X,4); + + ECP4_add(Q,&x4Q); + ECP4_add(Q,&x3Q); + ECP4_add(Q,&x2Q); + ECP4_add(Q,&xQ); + + ECP4_affine(Q); + +} + +// ECP$ Get Group Generator + +void ZZZ::ECP4_generator(ECP4 *G) +{ + BIG a,b; + FP2 Aa,Bb; + FP4 X,Y; + + BIG_rcopy(a,CURVE_Pxaa); + BIG_rcopy(b,CURVE_Pxab); + FP2_from_BIGs(&Aa,a,b); + + BIG_rcopy(a,CURVE_Pxba); + BIG_rcopy(b,CURVE_Pxbb); + FP2_from_BIGs(&Bb,a,b); + + FP4_from_FP2s(&X,&Aa,&Bb); + + BIG_rcopy(a,CURVE_Pyaa); + BIG_rcopy(b,CURVE_Pyab); + FP2_from_BIGs(&Aa,a,b); + + BIG_rcopy(a,CURVE_Pyba); + BIG_rcopy(b,CURVE_Pybb); + FP2_from_BIGs(&Bb,a,b); + + FP4_from_FP2s(&Y,&Aa,&Bb); + + ECP4_set(G,&X,&Y); +} + http://git-wip-us.apache.org/repos/asf/incubator-milagro-crypto/blob/c25f9e5c/version3/cpp/ecp4.h ---------------------------------------------------------------------- diff --git a/version3/cpp/ecp4.h b/version3/cpp/ecp4.h new file mode 100644 index 0000000..98b383b --- /dev/null +++ b/version3/cpp/ecp4.h @@ -0,0 +1,243 @@ +#ifndef ECP4_ZZZ_H +#define ECP4_ZZZ_H + +#include "fp4_YYY.h" +#include "config_curve_ZZZ.h" + +using namespace amcl; + +namespace YYY { + +extern const XXX::BIG Fra; /**< real part of BN curve Frobenius Constant */ +extern const XXX::BIG Frb; /**< imaginary part of BN curve Frobenius Constant */ + +} + +namespace ZZZ { + +/** + @brief ECP4 Structure - Elliptic Curve Point over quadratic extension field +*/ + +typedef struct +{ +// int inf; /**< Infinity Flag */ + YYY::FP4 x; /**< x-coordinate of point */ + YYY::FP4 y; /**< y-coordinate of point */ + YYY::FP4 z; /**< z-coordinate of point */ +} ECP4; + + +/* Curve Params - see rom.c */ +extern const int CURVE_A; /**< Elliptic curve A parameter */ +extern const int CURVE_B_I; /**< Elliptic curve B parameter */ +extern const XXX::BIG CURVE_B; /**< Elliptic curve B parameter */ +extern const XXX::BIG CURVE_Order; /**< Elliptic curve group order */ +extern const XXX::BIG CURVE_Cof; /**< Elliptic curve cofactor */ +extern const XXX::BIG CURVE_Bnx; /**< Elliptic curve parameter */ + + +/* Generator point on G1 */ +extern const XXX::BIG CURVE_Gx; /**< x-coordinate of generator point in group G1 */ +extern const XXX::BIG CURVE_Gy; /**< y-coordinate of generator point in group G1 */ + +/* For Pairings only */ + +/* Generator point on G2 */ +extern const XXX::BIG CURVE_Pxaa; /**< real part of x-coordinate of generator point in group G2 */ +extern const XXX::BIG CURVE_Pxab; /**< imaginary part of x-coordinate of generator point in group G2 */ +extern const XXX::BIG CURVE_Pxba; /**< real part of x-coordinate of generator point in group G2 */ +extern const XXX::BIG CURVE_Pxbb; /**< imaginary part of x-coordinate of generator point in group G2 */ +extern const XXX::BIG CURVE_Pyaa; /**< real part of y-coordinate of generator point in group G2 */ +extern const XXX::BIG CURVE_Pyab; /**< imaginary part of y-coordinate of generator point in group G2 */ +extern const XXX::BIG CURVE_Pyba; /**< real part of y-coordinate of generator point in group G2 */ +extern const XXX::BIG CURVE_Pybb; /**< imaginary part of y-coordinate of generator point in group G2 */ + +/* ECP4 E(FP4) prototypes */ +/** @brief Tests for ECP4 point equal to infinity + * + @param P ECP4 point to be tested + @return 1 if infinity, else returns 0 + */ +extern int ECP4_isinf(ECP4 *P); +/** @brief Copy ECP4 point to another ECP4 point + * + @param P ECP4 instance, on exit = Q + @param Q ECP4 instance to be copied + */ +extern void ECP4_copy(ECP4 *P,ECP4 *Q); +/** @brief Set ECP4 to point-at-infinity + * + @param P ECP4 instance to be set to infinity + */ +extern void ECP4_inf(ECP4 *P); +/** @brief Tests for equality of two ECP4s + * + @param P ECP4 instance to be compared + @param Q ECP4 instance to be compared + @return 1 if P=Q, else returns 0 + */ +extern int ECP4_equals(ECP4 *P,ECP4 *Q); + +/** @brief Converts an ECP4 point from Projective (x,y,z) coordinates to affine (x,y) coordinates + * + @param P ECP4 instance to be converted to affine form + */ +extern void ECP4_affine(ECP4 *P); + + +/** @brief Extract x and y coordinates of an ECP4 point P + * + If x=y, returns only x + @param x FP4 on exit = x coordinate of point + @param y FP4 on exit = y coordinate of point (unless x=y) + @param P ECP4 instance (x,y) + @return -1 if P is point-at-infinity, else 0 + */ +extern int ECP4_get(YYY::FP4 *x,YYY::FP4 *y,ECP4 *P); +/** @brief Formats and outputs an ECP4 point to the console, converted to affine coordinates + * + @param P ECP4 instance to be printed + */ +extern void ECP4_output(ECP4 *P); + +/** @brief Formats and outputs an ECP4 point to an octet string + * + The octet string is created in the form x|y. + Convert the real and imaginary parts of the x and y coordinates to big-endian base 256 form. + @param S output octet string + @param P ECP4 instance to be converted to an octet string + */ +extern void ECP4_toOctet(octet *S,ECP4 *P); +/** @brief Creates an ECP4 point from an octet string + * + The octet string is in the form x|y + The real and imaginary parts of the x and y coordinates are in big-endian base 256 form. + @param P ECP4 instance to be created from the octet string + @param S input octet string + return 1 if octet string corresponds to a point on the curve, else 0 + */ +extern int ECP4_fromOctet(ECP4 *P,octet *S); +/** @brief Calculate Right Hand Side of curve equation y^2=f(x) + * + Function f(x)=x^3+Ax+B + Used internally. + @param r FP4 value of f(x) + @param x FP4 instance + */ +extern void ECP4_rhs(YYY::FP4 *r,YYY::FP4 *x); +/** @brief Set ECP4 to point(x,y) given x and y + * + Point P set to infinity if no such point on the curve. + @param P ECP4 instance to be set (x,y) + @param x FP4 x coordinate of point + @param y FP4 y coordinate of point + @return 1 if point exists, else 0 + */ +extern int ECP4_set(ECP4 *P,YYY::FP4 *x,YYY::FP4 *y); +/** @brief Set ECP to point(x,[y]) given x + * + Point P set to infinity if no such point on the curve. Otherwise y coordinate is calculated from x. + @param P ECP instance to be set (x,[y]) + @param x BIG x coordinate of point + @return 1 if point exists, else 0 + */ +extern int ECP4_setx(ECP4 *P,YYY::FP4 *x); +/** @brief Negation of an ECP4 point + * + @param P ECP4 instance, on exit = -P + */ +extern void ECP4_neg(ECP4 *P); + +/** @brief Reduction of an ECP4 point + * + @param P ECP4 instance, on exit (x,y) are reduced wrt the modulus + */ +extern void ECP4_reduce(ECP4 *P); + + +/** @brief Doubles an ECP4 instance P and returns slope + * + @param P ECP4 instance, on exit =2*P + @param lam FP4 instance, slope of line + */ +//extern int ECP4_sdbl(ECP4 *P,FP4 *lam); +/** @brief Adds ECP4 instance Q to ECP4 instance P and returns slope + * + @param P ECP4 instance, on exit =P+Q + @param Q ECP4 instance to be added to P + @param lam FP4 instance, slope of line + */ +//extern int ECP4_sadd(ECP4 *P,ECP4 *Q,FP4 *lam); + + +/** @brief Doubles an ECP4 instance P + * + @param P ECP4 instance, on exit =2*P + */ +extern int ECP4_dbl(ECP4 *P); +/** @brief Adds ECP4 instance Q to ECP4 instance P + * + @param P ECP4 instance, on exit =P+Q + @param Q ECP4 instance to be added to P + */ +extern int ECP4_add(ECP4 *P,ECP4 *Q); +/** @brief Subtracts ECP instance Q from ECP4 instance P + * + @param P ECP4 instance, on exit =P-Q + @param Q ECP4 instance to be subtracted from P + */ +extern void ECP4_sub(ECP4 *P,ECP4 *Q); +/** @brief Multiplies an ECP4 instance P by a BIG, side-channel resistant + * + Uses fixed sized windows. + @param P ECP4 instance, on exit =b*P + @param b BIG number multiplier + + */ +extern void ECP4_mul(ECP4 *P,XXX::BIG b); + +/** @brief Calculates required Frobenius constants + * + Calculate Frobenius constants + @param F array of FP2 precalculated constants + + */ +extern void ECP4_frob_constants(YYY::FP2 F[3]); + +/** @brief Multiplies an ECP4 instance P by the internal modulus p^n, using precalculated Frobenius constants + * + Fast point multiplication using Frobenius + @param P ECP4 instance, on exit = p^n*P + @param F array of FP2 precalculated Frobenius constant + @param n power of prime + + */ +extern void ECP4_frob(ECP4 *P,YYY::FP2 F[3],int n); + +/** @brief Calculates P=Sigma b[i]*Q[i] for i=0 to 7 + * + @param P ECP4 instance, on exit = Sigma b[i]*Q[i] for i=0 to 7 + @param Q ECP4 array of 4 points + @param b BIG array of 4 multipliers + */ +extern void ECP4_mul8(ECP4 *P,ECP4 *Q,XXX::BIG *b); + + +/** @brief Maps random BIG to curve point of correct order + * + @param P ECP4 instance of correct order + @param W OCTET byte array to be mapped + */ +extern void ECP4_mapit(ECP4 *P,octet *w); + +/** @brief Get Group Generator from ROM + * + @param G ECP4 instance + */ +extern void ECP4_generator(ECP4 *G); + + +} + +#endif \ No newline at end of file http://git-wip-us.apache.org/repos/asf/incubator-milagro-crypto/blob/c25f9e5c/version3/cpp/ecp8.cpp ---------------------------------------------------------------------- diff --git a/version3/cpp/ecp8.cpp b/version3/cpp/ecp8.cpp new file mode 100644 index 0000000..eed198f --- /dev/null +++ b/version3/cpp/ecp8.cpp @@ -0,0 +1,1029 @@ +/* +Licensed to the Apache Software Foundation (ASF) under one +or more contributor license agreements. See the NOTICE file +distributed with this work for additional information +regarding copyright ownership. The ASF licenses this file +to you under the Apache License, Version 2.0 (the +"License"); you may not use this file except in compliance +with the License. You may obtain a copy of the License at + + http://www.apache.org/licenses/LICENSE-2.0 + +Unless required by applicable law or agreed to in writing, +software distributed under the License is distributed on an +"AS IS" BASIS, WITHOUT WARRANTIES OR CONDITIONS OF ANY +KIND, either express or implied. See the License for the +specific language governing permissions and limitations +under the License. +*/ + +/* AMCL Weierstrass elliptic curve functions over FP2 */ + +//#include <iostream> +#include "ecp8_ZZZ.h" + +using namespace std; +using namespace XXX; +using namespace YYY; + +int ZZZ::ECP8_isinf(ECP8 *P) +{ + return (FP8_iszilch(&(P->x)) & FP8_iszilch(&(P->z))); +} + +/* Set P=Q */ +void ZZZ::ECP8_copy(ECP8 *P,ECP8 *Q) +{ + FP8_copy(&(P->x),&(Q->x)); + FP8_copy(&(P->y),&(Q->y)); + FP8_copy(&(P->z),&(Q->z)); +} + +/* set P to Infinity */ +void ZZZ::ECP8_inf(ECP8 *P) +{ + FP8_zero(&(P->x)); + FP8_one(&(P->y)); + FP8_zero(&(P->z)); +} + +/* Conditional move Q to P dependant on d */ +static void ECP8_cmove(ZZZ::ECP8 *P,ZZZ::ECP8 *Q,int d) +{ + FP8_cmove(&(P->x),&(Q->x),d); + FP8_cmove(&(P->y),&(Q->y),d); + FP8_cmove(&(P->z),&(Q->z),d); +} + +/* return 1 if b==c, no branching */ +static int teq(sign32 b,sign32 c) +{ + sign32 x=b^c; + x-=1; // if x=0, x now -1 + return (int)((x>>31)&1); +} + +/* Constant time select from pre-computed table */ +static void ECP8_select(ZZZ::ECP8 *P,ZZZ::ECP8 W[],sign32 b) +{ + ZZZ::ECP8 MP; + sign32 m=b>>31; + sign32 babs=(b^m)-m; + + babs=(babs-1)/2; + + ECP8_cmove(P,&W[0],teq(babs,0)); // conditional move + ECP8_cmove(P,&W[1],teq(babs,1)); + ECP8_cmove(P,&W[2],teq(babs,2)); + ECP8_cmove(P,&W[3],teq(babs,3)); + ECP8_cmove(P,&W[4],teq(babs,4)); + ECP8_cmove(P,&W[5],teq(babs,5)); + ECP8_cmove(P,&W[6],teq(babs,6)); + ECP8_cmove(P,&W[7],teq(babs,7)); + + ECP8_copy(&MP,P); + ECP8_neg(&MP); // minus P + ECP8_cmove(P,&MP,(int)(m&1)); +} + +/* Make P affine (so z=1) */ +void ZZZ::ECP8_affine(ECP8 *P) +{ + FP8 one,iz; + if (ECP8_isinf(P)) return; + + FP8_one(&one); + if (FP8_isunity(&(P->z))) + { + FP8_reduce(&(P->x)); + FP8_reduce(&(P->y)); + return; + } + + FP8_inv(&iz,&(P->z)); + FP8_mul(&(P->x),&(P->x),&iz); + FP8_mul(&(P->y),&(P->y),&iz); + + FP8_reduce(&(P->x)); + FP8_reduce(&(P->y)); + FP8_copy(&(P->z),&one); +} + +/* return 1 if P==Q, else 0 */ +/* SU= 312 */ +int ZZZ::ECP8_equals(ECP8 *P,ECP8 *Q) +{ + FP8 a,b; + + FP8_mul(&a,&(P->x),&(Q->z)); + FP8_mul(&b,&(Q->x),&(P->z)); + if (!FP8_equals(&a,&b)) return 0; + + FP8_mul(&a,&(P->y),&(Q->z)); + FP8_mul(&b,&(Q->y),&(P->z)); + if (!FP8_equals(&a,&b)) return 0; + return 1; +} + +/* extract x, y from point P */ +int ZZZ::ECP8_get(FP8 *x,FP8 *y,ECP8 *P) +{ + ECP8 W; + ECP8_copy(&W,P); + ECP8_affine(&W); + if (ECP8_isinf(&W)) return -1; + FP8_copy(y,&(W.y)); + FP8_copy(x,&(W.x)); + return 0; +} + +/* Output point P */ +void ZZZ::ECP8_output(ECP8 *P) +{ + FP8 x,y; + if (ECP8_isinf(P)) + { + printf("Infinity\n"); + return; + } + ECP8_get(&x,&y,P); + printf("("); + FP8_output(&x); + printf(","); + FP8_output(&y); + printf(")\n"); +} + +/* Convert Q to octet string */ +void ZZZ::ECP8_toOctet(octet *W,ECP8 *Q) +{ + BIG b; + FP8 qx,qy; + FP4 qa,qb; + FP2 pa,pb; + + ECP8_get(&qx,&qy,Q); + + FP4_copy(&qa,&(qx.a)); + FP4_copy(&qb,&(qx.b)); + + FP2_copy(&pa,&(qa.a)); + FP2_copy(&pb,&(qa.b)); + + FP_redc(b,&(pa.a)); + BIG_toBytes(&(W->val[0]),b); + FP_redc(b,&(pa.b)); + BIG_toBytes(&(W->val[MODBYTES_XXX]),b); + FP_redc(b,&(pb.a)); + BIG_toBytes(&(W->val[2*MODBYTES_XXX]),b); + FP_redc(b,&(pb.b)); + BIG_toBytes(&(W->val[3*MODBYTES_XXX]),b); + + FP2_copy(&pa,&(qb.a)); + FP2_copy(&pb,&(qb.b)); + + FP_redc(b,&(pa.a)); + BIG_toBytes(&(W->val[4*MODBYTES_XXX]),b); + FP_redc(b,&(pa.b)); + BIG_toBytes(&(W->val[5*MODBYTES_XXX]),b); + FP_redc(b,&(pb.a)); + BIG_toBytes(&(W->val[6*MODBYTES_XXX]),b); + FP_redc(b,&(pb.b)); + BIG_toBytes(&(W->val[7*MODBYTES_XXX]),b); + + + FP4_copy(&qa,&(qy.a)); + FP4_copy(&qb,&(qy.b)); + + FP2_copy(&pa,&(qa.a)); + FP2_copy(&pb,&(qa.b)); + + FP_redc(b,&(pa.a)); + BIG_toBytes(&(W->val[8*MODBYTES_XXX]),b); + FP_redc(b,&(pa.b)); + BIG_toBytes(&(W->val[9*MODBYTES_XXX]),b); + FP_redc(b,&(pb.a)); + BIG_toBytes(&(W->val[10*MODBYTES_XXX]),b); + FP_redc(b,&(pb.b)); + BIG_toBytes(&(W->val[11*MODBYTES_XXX]),b); + + FP2_copy(&pa,&(qb.a)); + FP2_copy(&pb,&(qb.b)); + + FP_redc(b,&(pa.a)); + BIG_toBytes(&(W->val[12*MODBYTES_XXX]),b); + FP_redc(b,&(pa.b)); + BIG_toBytes(&(W->val[13*MODBYTES_XXX]),b); + FP_redc(b,&(pb.a)); + BIG_toBytes(&(W->val[14*MODBYTES_XXX]),b); + FP_redc(b,&(pb.b)); + BIG_toBytes(&(W->val[15*MODBYTES_XXX]),b); + + + W->len=16*MODBYTES_XXX; +} + +/* restore Q from octet string */ +int ZZZ::ECP8_fromOctet(ECP8 *Q,octet *W) +{ + BIG b; + FP8 qx,qy; + FP4 qa,qb; + FP2 pa,pb; + + BIG_fromBytes(b,&(W->val[0])); + FP_nres(&(pa.a),b); + BIG_fromBytes(b,&(W->val[MODBYTES_XXX])); + FP_nres(&(pa.b),b); + BIG_fromBytes(b,&(W->val[2*MODBYTES_XXX])); + FP_nres(&(pb.a),b); + BIG_fromBytes(b,&(W->val[3*MODBYTES_XXX])); + FP_nres(&(pb.b),b); + + FP2_copy(&(qa.a),&pa); + FP2_copy(&(qa.b),&pb); + + BIG_fromBytes(b,&(W->val[4*MODBYTES_XXX])); + FP_nres(&(pa.a),b); + BIG_fromBytes(b,&(W->val[5*MODBYTES_XXX])); + FP_nres(&(pa.b),b); + BIG_fromBytes(b,&(W->val[6*MODBYTES_XXX])); + FP_nres(&(pb.a),b); + BIG_fromBytes(b,&(W->val[7*MODBYTES_XXX])); + FP_nres(&(pb.b),b); + + FP2_copy(&(qb.a),&pa); + FP2_copy(&(qb.b),&pb); + + FP4_copy(&(qx.a),&qa); + FP4_copy(&(qx.b),&qb); + + + BIG_fromBytes(b,&(W->val[8*MODBYTES_XXX])); + FP_nres(&(pa.a),b); + BIG_fromBytes(b,&(W->val[9*MODBYTES_XXX])); + FP_nres(&(pa.b),b); + BIG_fromBytes(b,&(W->val[10*MODBYTES_XXX])); + FP_nres(&(pb.a),b); + BIG_fromBytes(b,&(W->val[11*MODBYTES_XXX])); + FP_nres(&(pb.b),b); + + FP2_copy(&(qa.a),&pa); + FP2_copy(&(qa.b),&pb); + + BIG_fromBytes(b,&(W->val[12*MODBYTES_XXX])); + FP_nres(&(pa.a),b); + BIG_fromBytes(b,&(W->val[13*MODBYTES_XXX])); + FP_nres(&(pa.b),b); + BIG_fromBytes(b,&(W->val[14*MODBYTES_XXX])); + FP_nres(&(pb.a),b); + BIG_fromBytes(b,&(W->val[15*MODBYTES_XXX])); + FP_nres(&(pb.b),b); + + FP2_copy(&(qb.a),&pa); + FP2_copy(&(qb.b),&pb); + + FP4_copy(&(qy.a),&qa); + FP4_copy(&(qy.b),&qb); + + + if (ECP8_set(Q,&qx,&qy)) return 1; + return 0; +} + +/* Calculate RHS of twisted curve equation x^3+B/i or x^3+Bi*/ +void ZZZ::ECP8_rhs(FP8 *rhs,FP8 *x) +{ + /* calculate RHS of elliptic curve equation */ + FP8 t; + FP4 t4; + FP2 t2; + BIG b; + FP8_sqr(&t,x); + + FP8_mul(rhs,&t,x); + + /* Assuming CURVE_A=0 */ + + BIG_rcopy(b,CURVE_B); + + FP2_from_BIG(&t2,b); + FP4_from_FP2(&t4,&t2); + FP8_from_FP4(&t,&t4); + +#if SEXTIC_TWIST_ZZZ == D_TYPE + FP8_div_i(&t); /* IMPORTANT - here we use the correct SEXTIC twist of the curve */ +#endif + +#if SEXTIC_TWIST_ZZZ == M_TYPE + FP8_times_i(&t); /* IMPORTANT - here we use the correct SEXTIC twist of the curve */ +#endif + + FP8_add(rhs,&t,rhs); + FP8_reduce(rhs); +} + +/* Set P=(x,y). Return 1 if (x,y) is on the curve, else return 0*/ +/* SU= 232 */ +int ZZZ::ECP8_set(ECP8 *P,FP8 *x,FP8 *y) +{ + FP8 rhs,y2; + + FP8_sqr(&y2,y); + ECP8_rhs(&rhs,x); + + if (!FP8_equals(&y2,&rhs)) + { + ECP8_inf(P); + return 0; + } + + FP8_copy(&(P->x),x); + FP8_copy(&(P->y),y); + FP8_one(&(P->z)); + return 1; +} + +/* Set P=(x,y). Return 1 if (x,.) is on the curve, else return 0 */ +/* SU= 232 */ +int ZZZ::ECP8_setx(ECP8 *P,FP8 *x) +{ + FP8 y; + ECP8_rhs(&y,x); + + if (!FP8_sqrt(&y,&y)) + { + ECP8_inf(P); + return 0; + } + + FP8_copy(&(P->x),x); + FP8_copy(&(P->y),&y); + FP8_one(&(P->z)); + + return 1; +} + +/* Set P=-P */ +/* SU= 8 */ +void ZZZ::ECP8_neg(ECP8 *P) +{ + FP8_norm(&(P->y)); + FP8_neg(&(P->y),&(P->y)); + FP8_norm(&(P->y)); +} + + +/* R+=R */ +/* return -1 for Infinity, 0 for addition, 1 for doubling */ +int ZZZ::ECP8_dbl(ECP8 *P) +{ + FP8 t0,t1,t2,t3,iy,x3,y3; + + FP8_copy(&iy,&(P->y)); //FP8 iy=new FP8(y); +#if SEXTIC_TWIST_ZZZ==D_TYPE + FP8_times_i(&iy); //iy.mul_ip(); +#endif + + FP8_sqr(&t0,&(P->y)); //t0.sqr(); +#if SEXTIC_TWIST_ZZZ==D_TYPE + FP8_times_i(&t0); //t0.mul_ip(); +#endif + + FP8_mul(&t1,&iy,&(P->z)); //t1.mul(z); + FP8_sqr(&t2,&(P->z)); //t2.sqr(); + + FP8_add(&(P->z),&t0,&t0); //z.add(t0); + FP8_norm(&(P->z)); //z.norm(); + FP8_add(&(P->z),&(P->z),&(P->z)); //z.add(z); + FP8_add(&(P->z),&(P->z),&(P->z)); //z.add(z); + FP8_norm(&(P->z)); //z.norm(); + + FP8_imul(&t2,&t2,3*CURVE_B_I); //t2.imul(3*ROM.CURVE_B_I); +#if SEXTIC_TWIST_ZZZ==M_TYPE + FP8_times_i(&t2); +#endif + + FP8_mul(&x3,&t2,&(P->z)); //x3.mul(z); + + FP8_add(&y3,&t0,&t2); //y3.add(t2); + FP8_norm(&y3); //y3.norm(); + FP8_mul(&(P->z),&(P->z),&t1); //z.mul(t1); + + FP8_add(&t1,&t2,&t2); //t1.add(t2); + FP8_add(&t2,&t2,&t1); //t2.add(t1); + FP8_norm(&t2); //t2.norm(); + FP8_sub(&t0,&t0,&t2); //t0.sub(t2); + FP8_norm(&t0); //t0.norm(); //y^2-9bz^2 + FP8_mul(&y3,&y3,&t0); //y3.mul(t0); + FP8_add(&(P->y),&y3,&x3); //y3.add(x3); //(y^2+3z*2)(y^2-9z^2)+3b.z^2.8y^2 + + FP8_mul(&t1,&(P->x),&iy); //t1.mul(iy); // + + FP8_norm(&t0); //x.norm(); + FP8_mul(&(P->x),&t0,&t1); //x.mul(t1); + FP8_add(&(P->x),&(P->x),&(P->x)); //x.add(x); //(y^2-9bz^2)xy2 + + FP8_norm(&(P->x)); //x.norm(); + + FP8_norm(&(P->y)); //y.norm(); + + return 1; +} + +/* Set P+=Q */ + +int ZZZ::ECP8_add(ECP8 *P,ECP8 *Q) +{ + FP8 t0,t1,t2,t3,t4,x3,y3,z3; + int b3=3*CURVE_B_I; + + FP8_mul(&t0,&(P->x),&(Q->x)); //t0.mul(Q.x); // x.Q.x + FP8_mul(&t1,&(P->y),&(Q->y)); //t1.mul(Q.y); // y.Q.y + + FP8_mul(&t2,&(P->z),&(Q->z)); //t2.mul(Q.z); + FP8_add(&t3,&(P->x),&(P->y)); //t3.add(y); + FP8_norm(&t3); //t3.norm(); //t3=X1+Y1 + FP8_add(&t4,&(Q->x),&(Q->y)); //t4.add(Q.y); + FP8_norm(&t4); //t4.norm(); //t4=X2+Y2 + FP8_mul(&t3,&t3,&t4); //t3.mul(t4); //t3=(X1+Y1)(X2+Y2) + FP8_add(&t4,&t0,&t1); //t4.add(t1); //t4=X1.X2+Y1.Y2 + + FP8_sub(&t3,&t3,&t4); //t3.sub(t4); + FP8_norm(&t3); //t3.norm(); +#if SEXTIC_TWIST_ZZZ==D_TYPE + FP8_times_i(&t3); //t3.mul_ip(); +#endif + + FP8_add(&t4,&(P->y),&(P->z)); //t4.add(z); + FP8_norm(&t4); //t4.norm(); //t4=Y1+Z1 + + FP8_add(&x3,&(Q->y),&(Q->z)); //x3.add(Q.z); + FP8_norm(&x3); //x3.norm(); //x3=Y2+Z2 + + FP8_mul(&t4,&t4,&x3); //t4.mul(x3); //t4=(Y1+Z1)(Y2+Z2) + + FP8_add(&x3,&t1,&t2); //x3.add(t2); //X3=Y1.Y2+Z1.Z2 + + FP8_sub(&t4,&t4,&x3); //t4.sub(x3); + FP8_norm(&t4); //t4.norm(); +#if SEXTIC_TWIST_ZZZ==D_TYPE + FP8_times_i(&t4); //t4.mul_ip(); //t4=(Y1+Z1)(Y2+Z2) - (Y1.Y2+Z1.Z2) = Y1.Z2+Y2.Z1 +#endif + + FP8_add(&x3,&(P->x),&(P->z)); //x3.add(z); + FP8_norm(&x3); //x3.norm(); // x3=X1+Z1 + + FP8_add(&y3,&(Q->x),&(Q->z)); //y3.add(Q.z); + FP8_norm(&y3); //y3.norm(); // y3=X2+Z2 + FP8_mul(&x3,&x3,&y3); //x3.mul(y3); // x3=(X1+Z1)(X2+Z2) + + FP8_add(&y3,&t0,&t2); //y3.add(t2); // y3=X1.X2+Z1+Z2 + FP8_sub(&y3,&x3,&y3); //y3.rsub(x3); + FP8_norm(&y3); //y3.norm(); // y3=(X1+Z1)(X2+Z2) - (X1.X2+Z1.Z2) = X1.Z2+X2.Z1 +#if SEXTIC_TWIST_ZZZ==D_TYPE + FP8_times_i(&t0); //t0.mul_ip(); + FP8_times_i(&t1); //t1.mul_ip(); +#endif + + FP8_add(&x3,&t0,&t0); //x3.add(t0); + FP8_add(&t0,&t0,&x3); //t0.add(x3); + FP8_norm(&t0); //t0.norm(); + FP8_imul(&t2,&t2,b3); //t2.imul(b); +#if SEXTIC_TWIST_ZZZ==M_TYPE + FP8_times_i(&t2); +#endif + + FP8_add(&z3,&t1,&t2); //z3.add(t2); + FP8_norm(&z3); //z3.norm(); + FP8_sub(&t1,&t1,&t2); //t1.sub(t2); + FP8_norm(&t1); //t1.norm(); + FP8_imul(&y3,&y3,b3); //y3.imul(b); +#if SEXTIC_TWIST_ZZZ==M_TYPE + FP8_times_i(&y3); +#endif + + FP8_mul(&x3,&y3,&t4); //x3.mul(t4); + + FP8_mul(&t2,&t3,&t1); //t2.mul(t1); + FP8_sub(&(P->x),&t2,&x3); //x3.rsub(t2); + FP8_mul(&y3,&y3,&t0); //y3.mul(t0); + FP8_mul(&t1,&t1,&z3); //t1.mul(z3); + FP8_add(&(P->y),&y3,&t1); //y3.add(t1); + FP8_mul(&t0,&t0,&t3); //t0.mul(t3); + FP8_mul(&z3,&z3,&t4); //z3.mul(t4); + FP8_add(&(P->z),&z3,&t0); //z3.add(t0); + + + FP8_norm(&(P->x)); //x.norm(); + FP8_norm(&(P->y)); //y.norm(); + FP8_norm(&(P->z)); //z.norm(); + + return 0; +} + +/* Set P-=Q */ +/* SU= 16 */ +void ZZZ::ECP8_sub(ECP8 *P,ECP8 *Q) +{ + ECP8 NQ; + ECP8_copy(&NQ,Q); + ECP8_neg(&NQ); + ECP8_add(P,&NQ); +} + + +void ZZZ::ECP8_reduce(ECP8 *P) +{ + FP8_reduce(&(P->x)); + FP8_reduce(&(P->y)); +} + +/* P*=e */ +/* SU= 280 */ +void ZZZ::ECP8_mul(ECP8 *P,BIG e) +{ + /* fixed size windows */ + int i,nb,s,ns; + BIG mt,t; + ECP8 Q,W[8],C; + sign8 w[1+(NLEN_XXX*BASEBITS_XXX+3)/4]; + + if (ECP8_isinf(P)) return; + + /* precompute table */ + + ECP8_copy(&Q,P); + ECP8_dbl(&Q); + ECP8_copy(&W[0],P); + + for (i=1; i<8; i++) + { + ECP8_copy(&W[i],&W[i-1]); + ECP8_add(&W[i],&Q); + } + + /* make exponent odd - add 2P if even, P if odd */ + BIG_copy(t,e); + s=BIG_parity(t); + BIG_inc(t,1); + BIG_norm(t); + ns=BIG_parity(t); + BIG_copy(mt,t); + BIG_inc(mt,1); + BIG_norm(mt); + BIG_cmove(t,mt,s); + ECP8_cmove(&Q,P,ns); + ECP8_copy(&C,&Q); + + nb=1+(BIG_nbits(t)+3)/4; + + /* convert exponent to signed 4-bit window */ + for (i=0; i<nb; i++) + { + w[i]=BIG_lastbits(t,5)-16; + BIG_dec(t,w[i]); + BIG_norm(t); + BIG_fshr(t,4); + } + w[nb]=BIG_lastbits(t,5); + + ECP8_copy(P,&W[(w[nb]-1)/2]); + for (i=nb-1; i>=0; i--) + { + ECP8_select(&Q,W,w[i]); + ECP8_dbl(P); + ECP8_dbl(P); + ECP8_dbl(P); + ECP8_dbl(P); + ECP8_add(P,&Q); + } + ECP8_sub(P,&C); /* apply correction */ + ECP8_affine(P); +} + +void ZZZ::ECP8_frob_constants(FP2 F[3]) +{ + FP fx,fy; + FP2 X; + + FP_rcopy(&fx,Fra); + FP_rcopy(&fy,Frb); + FP2_from_FPs(&X,&fx,&fy); + + + FP2_sqr(&F[0],&X); // FF=F^2=(1+i)^(p-19)/12 + FP2_copy(&F[2],&F[0]); + FP2_mul_ip(&F[2]); // W=(1+i)^12/12.(1+i)^(p-19)/12 = (1+i)^(p-7)/12 + FP2_norm(&F[2]); + FP2_sqr(&F[1],&F[2]); + FP2_mul(&F[2],&F[2],&F[1]); // W=(1+i)^(p-7)/4 + + FP2_mul_ip(&F[2]); // W=(1+i)^4/4.W=(1+i)^(p-7)/4 = (1+i)^(p-3)/4 + FP2_norm(&F[2]); + + FP2_copy(&F[1],&X); + +#if SEXTIC_TWIST_ZZZ == M_TYPE + FP2_mul_ip(&F[1]); // (1+i)^24/24.(1+i)^(p-19)/24 = (1+i)^(p+5)/24 + FP2_inv(&F[1],&F[1]); // (1+i)^-(p+5)/24 + FP2_sqr(&F[0],&F[1]); // (1+i)^-(p+5)/12 +#endif + + + FP2_mul_ip(&F[0]); // FF=(1+i)^(p-19)/12.(1+i)^12/12 = (1+i)^(p-7)/12 // FF=(1+i)^12/12.(1+i)^-(p+5)/12 = (1+i)^-(p-7)/12 + FP2_norm(&F[0]); + + FP2_mul(&F[1],&F[1],&F[0]); // (1+i)^(p-7)/12 . (1+i)^(p-19)/24 = (1+i)^(p-11)/8 // (1+i)^-(p-7)/12 . (1+i)^-(p+5)/24 = (1+i)^-(p-3)/8 + +} + +/* Calculates q^n.P using Frobenius constant X */ +void ZZZ::ECP8_frob(ECP8 *P,FP2 F[3],int n) +{ + int i; + FP8 X,Y,Z; +// F=(1+i)^(p-19)/24 + + FP8_copy(&X,&(P->x)); + FP8_copy(&Y,&(P->y)); + FP8_copy(&Z,&(P->z)); + + for (i=0;i<n;i++) + { + FP8_frob(&X,&F[2]); // X^p + FP8_qmul(&X,&X,&F[0]); +#if SEXTIC_TWIST_ZZZ == M_TYPE + FP8_div_i2(&X); // X^p.(1+i)^-(p-1)/12 +#endif +#if SEXTIC_TWIST_ZZZ == D_TYPE + FP8_times_i2(&X); // X^p.(1+i)^(p-1)/12 +#endif + + FP8_frob(&Y,&F[2]); // Y^p + FP8_qmul(&Y,&Y,&F[1]); +#if SEXTIC_TWIST_ZZZ == M_TYPE + FP8_div_i(&Y); // Y^p.(1+i)^-(p-1)/8 +#endif +#if SEXTIC_TWIST_ZZZ == D_TYPE + FP8_times_i2(&Y); FP8_times_i2(&Y); FP8_times_i(&Y); // Y^p.(1+i)^(p-1)/8 +#endif + FP8_frob(&Z,&F[2]); + } + + FP8_copy(&(P->x),&X); + FP8_copy(&(P->y),&Y); + FP8_copy(&(P->z),&Z); + +} + +/* Side channel attack secure */ +// Bos & Costello https://eprint.iacr.org/2013/458.pdf +// Faz-Hernandez & Longa & Sanchez https://eprint.iacr.org/2013/158.pdf + +void ZZZ::ECP8_mul16(ECP8 *P,ECP8 Q[16],BIG u[16]) +{ + int i,j,k,nb,pb1,pb2,pb3,pb4,bt; + ECP8 T1[8],T2[8],T3[8],T4[8],W; + BIG mt,t[16]; + sign8 w1[NLEN_XXX*BASEBITS_XXX+1]; + sign8 s1[NLEN_XXX*BASEBITS_XXX+1]; + sign8 w2[NLEN_XXX*BASEBITS_XXX+1]; + sign8 s2[NLEN_XXX*BASEBITS_XXX+1]; + sign8 w3[NLEN_XXX*BASEBITS_XXX+1]; + sign8 s3[NLEN_XXX*BASEBITS_XXX+1]; + sign8 w4[NLEN_XXX*BASEBITS_XXX+1]; + sign8 s4[NLEN_XXX*BASEBITS_XXX+1]; + + FP2 X[3]; + ECP8_frob_constants(X); + + for (i=0; i<16; i++) + { + BIG_copy(t[i],u[i]); + } +// Precomputed table + ECP8_copy(&T1[0],&Q[0]); // Q[0] + ECP8_copy(&T1[1],&T1[0]); + ECP8_add(&T1[1],&Q[1]); // Q[0]+Q[1] + ECP8_copy(&T1[2],&T1[0]); + ECP8_add(&T1[2],&Q[2]); // Q[0]+Q[2] + ECP8_copy(&T1[3],&T1[1]); + ECP8_add(&T1[3],&Q[2]); // Q[0]+Q[1]+Q[2] + ECP8_copy(&T1[4],&T1[0]); + ECP8_add(&T1[4],&Q[3]); // Q[0]+Q[3] + ECP8_copy(&T1[5],&T1[1]); + ECP8_add(&T1[5],&Q[3]); // Q[0]+Q[1]+Q[3] + ECP8_copy(&T1[6],&T1[2]); + ECP8_add(&T1[6],&Q[3]); // Q[0]+Q[2]+Q[3] + ECP8_copy(&T1[7],&T1[3]); + ECP8_add(&T1[7],&Q[3]); // Q[0]+Q[1]+Q[2]+Q[3] + +// Use Frobenius + + for (i=0;i<8;i++) + { + ECP8_copy(&T2[i],&T1[i]); + ECP8_frob(&T2[i],X,4); + + ECP8_copy(&T3[i],&T2[i]); + ECP8_frob(&T3[i],X,4); + + ECP8_copy(&T4[i],&T3[i]); + ECP8_frob(&T4[i],X,4); + } + +// Make them odd + pb1=1-BIG_parity(t[0]); + BIG_inc(t[0],pb1); + BIG_norm(t[0]); + + pb2=1-BIG_parity(t[4]); + BIG_inc(t[4],pb2); + BIG_norm(t[4]); + + pb3=1-BIG_parity(t[8]); + BIG_inc(t[8],pb3); + BIG_norm(t[8]); + + pb4=1-BIG_parity(t[12]); + BIG_inc(t[12],pb4); + BIG_norm(t[12]); + +// Number of bits + BIG_zero(mt); + for (i=0; i<16; i++) + { + BIG_or(mt,mt,t[i]); + } + nb=1+BIG_nbits(mt); + +// Sign pivot + s1[nb-1]=1; + s2[nb-1]=1; + s3[nb-1]=1; + s4[nb-1]=1; + for (i=0;i<nb-1;i++) + { + BIG_fshr(t[0],1); + s1[i]=2*BIG_parity(t[0])-1; + BIG_fshr(t[4],1); + s2[i]=2*BIG_parity(t[4])-1; + BIG_fshr(t[8],1); + s3[i]=2*BIG_parity(t[8])-1; + BIG_fshr(t[12],1); + s4[i]=2*BIG_parity(t[12])-1; + } + + +// Recoded exponents + for (i=0; i<nb; i++) + { + w1[i]=0; + k=1; + for (j=1; j<4; j++) + { + bt=s1[i]*BIG_parity(t[j]); + BIG_fshr(t[j],1); + + BIG_dec(t[j],(bt>>1)); + BIG_norm(t[j]); + w1[i]+=bt*k; + k*=2; + } + + w2[i]=0; + k=1; + for (j=5; j<8; j++) + { + bt=s2[i]*BIG_parity(t[j]); + BIG_fshr(t[j],1); + + BIG_dec(t[j],(bt>>1)); + BIG_norm(t[j]); + w2[i]+=bt*k; + k*=2; + } + + w3[i]=0; + k=1; + for (j=9; j<12; j++) + { + bt=s3[i]*BIG_parity(t[j]); + BIG_fshr(t[j],1); + + BIG_dec(t[j],(bt>>1)); + BIG_norm(t[j]); + w3[i]+=bt*k; + k*=2; + } + + w4[i]=0; + k=1; + for (j=13; j<16; j++) + { + bt=s4[i]*BIG_parity(t[j]); + BIG_fshr(t[j],1); + + BIG_dec(t[j],(bt>>1)); + BIG_norm(t[j]); + w4[i]+=bt*k; + k*=2; + } + } + +// Main loop + ECP8_select(P,T1,2*w1[nb-1]+1); + ECP8_select(&W,T2,2*w2[nb-1]+1); + ECP8_add(P,&W); + ECP8_select(&W,T3,2*w3[nb-1]+1); + ECP8_add(P,&W); + ECP8_select(&W,T4,2*w4[nb-1]+1); + ECP8_add(P,&W); + + for (i=nb-2; i>=0; i--) + { + ECP8_dbl(P); + ECP8_select(&W,T1,2*w1[i]+s1[i]); + ECP8_add(P,&W); + ECP8_select(&W,T2,2*w2[i]+s2[i]); + ECP8_add(P,&W); + ECP8_select(&W,T3,2*w3[i]+s3[i]); + ECP8_add(P,&W); + ECP8_select(&W,T4,2*w4[i]+s4[i]); + ECP8_add(P,&W); + } + +// apply corrections + ECP8_copy(&W,P); + ECP8_sub(&W,&Q[0]); + ECP8_cmove(P,&W,pb1); + ECP8_copy(&W,P); + ECP8_sub(&W,&Q[4]); + ECP8_cmove(P,&W,pb2); + + ECP8_copy(&W,P); + ECP8_sub(&W,&Q[8]); + ECP8_cmove(P,&W,pb3); + ECP8_copy(&W,P); + ECP8_sub(&W,&Q[12]); + ECP8_cmove(P,&W,pb4); + + ECP8_affine(P); +} + +/* Map to hash value to point on G2 from random BIG */ + +void ZZZ::ECP8_mapit(ECP8 *Q,octet *W) +{ + BIG q,one,x,hv; + FP Fx,Fy; + FP2 T,X[3]; + FP4 X4; + FP8 X8; + + ECP8 xQ, x2Q, x3Q, x4Q , x5Q, x6Q, x7Q, x8Q; + + BIG_fromBytes(hv,W->val); + BIG_rcopy(q,Modulus); + BIG_one(one); + BIG_mod(hv,q); + + for (;;) + { + FP2_from_BIGs(&T,one,hv); /*******/ + FP4_from_FP2(&X4,&T); + FP8_from_FP4(&X8,&X4); + if (ECP8_setx(Q,&X8)) break; + BIG_inc(hv,1); + } + + ECP8_frob_constants(X); + + BIG_rcopy(x,CURVE_Bnx); + + // Efficient hash maps to G2 on BLS48 curves - Budroni, Pintore + // Q -> x8Q -x7Q -Q + F(x7Q-x6Q) + F(F(x6Q-x5Q)) +F(F(F(x5Q-x4Q))) +F(F(F(F(x4Q-x3Q)))) + F(F(F(F(F(x3Q-x2Q))))) + F(F(F(F(F(F(x2Q-xQ)))))) + F(F(F(F(F(F(F(xQ-Q))))))) +F(F(F(F(F(F(F(F(2Q)))))))) + + ECP8_copy(&xQ,Q); + ECP8_mul(&xQ,x); + ECP8_copy(&x2Q,&xQ); + ECP8_mul(&x2Q,x); + ECP8_copy(&x3Q,&x2Q); + ECP8_mul(&x3Q,x); + ECP8_copy(&x4Q,&x3Q); + + ECP8_mul(&x4Q,x); + ECP8_copy(&x5Q,&x4Q); + ECP8_mul(&x5Q,x); + ECP8_copy(&x6Q,&x5Q); + ECP8_mul(&x6Q,x); + ECP8_copy(&x7Q,&x6Q); + ECP8_mul(&x7Q,x); + ECP8_copy(&x8Q,&x7Q); + ECP8_mul(&x8Q,x); + +#if SIGN_OF_X_ZZZ==NEGATIVEX + ECP8_neg(&xQ); + ECP8_neg(&x3Q); + ECP8_neg(&x5Q); + ECP8_neg(&x7Q); +#endif + + ECP8_sub(&x8Q,&x7Q); + ECP8_sub(&x8Q,Q); + + ECP8_sub(&x7Q,&x6Q); + ECP8_frob(&x7Q,X,1); + + ECP8_sub(&x6Q,&x5Q); + ECP8_frob(&x6Q,X,2); + + ECP8_sub(&x5Q,&x4Q); + ECP8_frob(&x5Q,X,3); + + ECP8_sub(&x4Q,&x3Q); + ECP8_frob(&x4Q,X,4); + + ECP8_sub(&x3Q,&x2Q); + ECP8_frob(&x3Q,X,5); + + ECP8_sub(&x2Q,&xQ); + ECP8_frob(&x2Q,X,6); + + ECP8_sub(&xQ,Q); + ECP8_frob(&xQ,X,7); + + ECP8_dbl(Q); + ECP8_frob(Q,X,8); + + + ECP8_add(Q,&x8Q); + ECP8_add(Q,&x7Q); + ECP8_add(Q,&x6Q); + ECP8_add(Q,&x5Q); + + ECP8_add(Q,&x4Q); + ECP8_add(Q,&x3Q); + ECP8_add(Q,&x2Q); + ECP8_add(Q,&xQ); + + ECP8_affine(Q); + +} + +// ECP$ Get Group Generator + +void ZZZ::ECP8_generator(ECP8 *G) +{ + BIG a,b; + FP2 Aa,Bb; + FP4 A,B; + FP8 X,Y; + + BIG_rcopy(a,CURVE_Pxaaa); + BIG_rcopy(b,CURVE_Pxaab); + FP2_from_BIGs(&Aa,a,b); + + BIG_rcopy(a,CURVE_Pxaba); + BIG_rcopy(b,CURVE_Pxabb); + FP2_from_BIGs(&Bb,a,b); + + FP4_from_FP2s(&A,&Aa,&Bb); + + BIG_rcopy(a,CURVE_Pxbaa); + BIG_rcopy(b,CURVE_Pxbab); + FP2_from_BIGs(&Aa,a,b); + + BIG_rcopy(a,CURVE_Pxbba); + BIG_rcopy(b,CURVE_Pxbbb); + FP2_from_BIGs(&Bb,a,b); + + FP4_from_FP2s(&B,&Aa,&Bb); + + FP8_from_FP4s(&X,&A,&B); + + BIG_rcopy(a,CURVE_Pyaaa); + BIG_rcopy(b,CURVE_Pyaab); + FP2_from_BIGs(&Aa,a,b); + + BIG_rcopy(a,CURVE_Pyaba); + BIG_rcopy(b,CURVE_Pyabb); + FP2_from_BIGs(&Bb,a,b); + + FP4_from_FP2s(&A,&Aa,&Bb); + + BIG_rcopy(a,CURVE_Pybaa); + BIG_rcopy(b,CURVE_Pybab); + FP2_from_BIGs(&Aa,a,b); + + BIG_rcopy(a,CURVE_Pybba); + BIG_rcopy(b,CURVE_Pybbb); + FP2_from_BIGs(&Bb,a,b); + + FP4_from_FP2s(&B,&Aa,&Bb); + + FP8_from_FP4s(&Y,&A,&B); + + ECP8_set(G,&X,&Y); +} http://git-wip-us.apache.org/repos/asf/incubator-milagro-crypto/blob/c25f9e5c/version3/cpp/ecp8.h ---------------------------------------------------------------------- diff --git a/version3/cpp/ecp8.h b/version3/cpp/ecp8.h new file mode 100644 index 0000000..681f199 --- /dev/null +++ b/version3/cpp/ecp8.h @@ -0,0 +1,253 @@ +#ifndef ECP8_ZZZ_H +#define ECP8_ZZZ_H + +#include "fp8_YYY.h" +#include "config_curve_ZZZ.h" + +using namespace amcl; + +namespace YYY { + +extern const XXX::BIG Fra; /**< real part of BN curve Frobenius Constant */ +extern const XXX::BIG Frb; /**< imaginary part of BN curve Frobenius Constant */ + +} + +namespace ZZZ { + +/** + @brief ECP8 Structure - Elliptic Curve Point over quadratic extension field +*/ + +typedef struct +{ +// int inf; /**< Infinity Flag */ + YYY::FP8 x; /**< x-coordinate of point */ + YYY::FP8 y; /**< y-coordinate of point */ + YYY::FP8 z; /**< z-coordinate of point */ +} ECP8; + + +/* Curve Params - see rom.c */ +extern const int CURVE_A; /**< Elliptic curve A parameter */ +extern const int CURVE_B_I; /**< Elliptic curve B parameter */ +extern const XXX::BIG CURVE_B; /**< Elliptic curve B parameter */ +extern const XXX::BIG CURVE_Order; /**< Elliptic curve group order */ +extern const XXX::BIG CURVE_Cof; /**< Elliptic curve cofactor */ +extern const XXX::BIG CURVE_Bnx; /**< Elliptic curve parameter */ + + +/* Generator point on G1 */ +extern const XXX::BIG CURVE_Gx; /**< x-coordinate of generator point in group G1 */ +extern const XXX::BIG CURVE_Gy; /**< y-coordinate of generator point in group G1 */ + +/* For Pairings only */ + +/* Generator point on G2 */ +extern const XXX::BIG CURVE_Pxaaa; /**< real part of x-coordinate of generator point in group G2 */ +extern const XXX::BIG CURVE_Pxaab; /**< imaginary part of x-coordinate of generator point in group G2 */ +extern const XXX::BIG CURVE_Pxaba; /**< real part of x-coordinate of generator point in group G2 */ +extern const XXX::BIG CURVE_Pxabb; /**< imaginary part of x-coordinate of generator point in group G2 */ +extern const XXX::BIG CURVE_Pxbaa; /**< real part of x-coordinate of generator point in group G2 */ +extern const XXX::BIG CURVE_Pxbab; /**< imaginary part of x-coordinate of generator point in group G2 */ +extern const XXX::BIG CURVE_Pxbba; /**< real part of x-coordinate of generator point in group G2 */ +extern const XXX::BIG CURVE_Pxbbb; /**< imaginary part of x-coordinate of generator point in group G2 */ + +extern const XXX::BIG CURVE_Pyaaa; /**< real part of y-coordinate of generator point in group G2 */ +extern const XXX::BIG CURVE_Pyaab; /**< imaginary part of y-coordinate of generator point in group G2 */ +extern const XXX::BIG CURVE_Pyaba; /**< real part of y-coordinate of generator point in group G2 */ +extern const XXX::BIG CURVE_Pyabb; /**< imaginary part of y-coordinate of generator point in group G2 */ +extern const XXX::BIG CURVE_Pybaa; /**< real part of y-coordinate of generator point in group G2 */ +extern const XXX::BIG CURVE_Pybab; /**< imaginary part of y-coordinate of generator point in group G2 */ +extern const XXX::BIG CURVE_Pybba; /**< real part of y-coordinate of generator point in group G2 */ +extern const XXX::BIG CURVE_Pybbb; /**< imaginary part of y-coordinate of generator point in group G2 */ + + +/* ECP8 E(FP8) prototypes */ +/** @brief Tests for ECP8 point equal to infinity + * + @param P ECP8 point to be tested + @return 1 if infinity, else returns 0 + */ +extern int ECP8_isinf(ECP8 *P); +/** @brief Copy ECP8 point to another ECP8 point + * + @param P ECP8 instance, on exit = Q + @param Q ECP8 instance to be copied + */ +extern void ECP8_copy(ECP8 *P,ECP8 *Q); +/** @brief Set ECP8 to point-at-infinity + * + @param P ECP8 instance to be set to infinity + */ +extern void ECP8_inf(ECP8 *P); +/** @brief Tests for equality of two ECP8s + * + @param P ECP8 instance to be compared + @param Q ECP8 instance to be compared + @return 1 if P=Q, else returns 0 + */ +extern int ECP8_equals(ECP8 *P,ECP8 *Q); + +/** @brief Converts an ECP8 point from Projective (x,y,z) coordinates to affine (x,y) coordinates + * + @param P ECP8 instance to be converted to affine form + */ +extern void ECP8_affine(ECP8 *P); + + +/** @brief Extract x and y coordinates of an ECP8 point P + * + If x=y, returns only x + @param x FP8 on exit = x coordinate of point + @param y FP8 on exit = y coordinate of point (unless x=y) + @param P ECP8 instance (x,y) + @return -1 if P is point-at-infinity, else 0 + */ +extern int ECP8_get(YYY::FP8 *x,YYY::FP8 *y,ECP8 *P); +/** @brief Formats and outputs an ECP8 point to the console, converted to affine coordinates + * + @param P ECP8 instance to be printed + */ +extern void ECP8_output(ECP8 *P); + +/** @brief Formats and outputs an ECP8 point to an octet string + * + The octet string is created in the form x|y. + Convert the real and imaginary parts of the x and y coordinates to big-endian base 256 form. + @param S output octet string + @param P ECP8 instance to be converted to an octet string + */ +extern void ECP8_toOctet(octet *S,ECP8 *P); +/** @brief Creates an ECP8 point from an octet string + * + The octet string is in the form x|y + The real and imaginary parts of the x and y coordinates are in big-endian base 256 form. + @param P ECP8 instance to be created from the octet string + @param S input octet string + return 1 if octet string corresponds to a point on the curve, else 0 + */ +extern int ECP8_fromOctet(ECP8 *P,octet *S); +/** @brief Calculate Right Hand Side of curve equation y^2=f(x) + * + Function f(x)=x^3+Ax+B + Used internally. + @param r FP8 value of f(x) + @param x FP8 instance + */ +extern void ECP8_rhs(YYY::FP8 *r,YYY::FP8 *x); +/** @brief Set ECP8 to point(x,y) given x and y + * + Point P set to infinity if no such point on the curve. + @param P ECP8 instance to be set (x,y) + @param x FP8 x coordinate of point + @param y FP8 y coordinate of point + @return 1 if point exists, else 0 + */ +extern int ECP8_set(ECP8 *P,YYY::FP8 *x,YYY::FP8 *y); +/** @brief Set ECP to point(x,[y]) given x + * + Point P set to infinity if no such point on the curve. Otherwise y coordinate is calculated from x. + @param P ECP instance to be set (x,[y]) + @param x BIG x coordinate of point + @return 1 if point exists, else 0 + */ +extern int ECP8_setx(ECP8 *P,YYY::FP8 *x); +/** @brief Negation of an ECP8 point + * + @param P ECP8 instance, on exit = -P + */ +extern void ECP8_neg(ECP8 *P); + +/** @brief Reduction of an ECP8 point + * + @param P ECP8 instance, on exit (x,y) are reduced wrt the modulus + */ +extern void ECP8_reduce(ECP8 *P); + + +/** @brief Doubles an ECP8 instance P and returns slope + * + @param P ECP8 instance, on exit =2*P + @param lam FP8 instance, slope of line + */ +//extern int ECP8_sdbl(ECP8 *P,FP8 *lam); +/** @brief Adds ECP8 instance Q to ECP8 instance P and returns slope + * + @param P ECP8 instance, on exit =P+Q + @param Q ECP8 instance to be added to P + @param lam FP8 instance, slope of line + */ +//extern int ECP8_sadd(ECP8 *P,ECP8 *Q,FP8 *lam); + + +/** @brief Doubles an ECP8 instance P + * + @param P ECP8 instance, on exit =2*P + */ +extern int ECP8_dbl(ECP8 *P); +/** @brief Adds ECP8 instance Q to ECP8 instance P + * + @param P ECP8 instance, on exit =P+Q + @param Q ECP8 instance to be added to P + */ +extern int ECP8_add(ECP8 *P,ECP8 *Q); +/** @brief Subtracts ECP instance Q from ECP8 instance P + * + @param P ECP8 instance, on exit =P-Q + @param Q ECP8 instance to be subtracted from P + */ +extern void ECP8_sub(ECP8 *P,ECP8 *Q); +/** @brief Multiplies an ECP8 instance P by a BIG, side-channel resistant + * + Uses fixed sized windows. + @param P ECP8 instance, on exit =b*P + @param b BIG number multiplier + + */ +extern void ECP8_mul(ECP8 *P,XXX::BIG b); + +/** @brief Calculates required Frobenius constants + * + Calculate Frobenius constants + @param F array of FP2 precalculated constants + + */ +extern void ECP8_frob_constants(YYY::FP2 F[3]); + +/** @brief Multiplies an ECP8 instance P by the internal modulus p^n, using precalculated Frobenius constants + * + Fast point multiplication using Frobenius + @param P ECP8 instance, on exit = p^n*P + @param F array of FP2 precalculated Frobenius constant + @param n power of prime + + */ +extern void ECP8_frob(ECP8 *P,YYY::FP2 F[3],int n); + +/** @brief Calculates P=Sigma b[i]*Q[i] for i=0 to 7 + * + @param P ECP8 instance, on exit = Sigma b[i]*Q[i] for i=0 to 7 + @param Q ECP8 array of 4 points + @param b BIG array of 4 multipliers + */ +extern void ECP8_mul16(ECP8 *P,ECP8 *Q,XXX::BIG *b); + + +/** @brief Maps random BIG to curve point of correct order + * + @param P ECP8 instance of correct order + @param W OCTET byte array to be mapped + */ +extern void ECP8_mapit(ECP8 *P,octet *w); + +/** @brief Get Group Generator from ROM + * + @param G ECP8 instance + */ +extern void ECP8_generator(ECP8 *G); + + +} + +#endif \ No newline at end of file
