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Posted to commits@milagro.apache.org by br...@apache.org on 2019/01/15 15:19:07 UTC
[02/51] [partial] incubator-milagro-crypto git commit: update code
http://git-wip-us.apache.org/repos/asf/incubator-milagro-crypto/blob/1add7560/version3/cpp/ecp4.cpp
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diff --git a/version3/cpp/ecp4.cpp b/version3/cpp/ecp4.cpp
deleted file mode 100644
index 33c60d1..0000000
--- a/version3/cpp/ecp4.cpp
+++ /dev/null
@@ -1,1074 +0,0 @@
-/*
-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)
-{
-// if (P->inf) return 1;
- return (FP4_iszilch(&(P->x)) & FP4_iszilch(&(P->z)));
-}
-
-/* Set P=Q */
-void ZZZ::ECP4_copy(ECP4 *P,ECP4 *Q)
-{
-// P->inf=Q->inf;
- 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)
-{
-// P->inf=1;
- 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);
-// d=~(d-1);
-// P->inf^=(P->inf^Q->inf)&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;
- // if (ECP4_isinf(P) && ECP4_isinf(Q)) return 1;
- // if (ECP4_isinf(P) || ECP4_isinf(Q)) return 0;
-
- 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;
- //ECP4_affine(P);
- 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);
-
-//cout << "y2= ";
-//FP4_output(&y2);
-//cout << endl;
-//cout << "rhs= ";
-//FP4_output(&rhs);
-//cout << endl;
-
- if (!FP4_equals(&y2,&rhs))
- {
- ECP4_inf(P);
- //P->inf=1;
- return 0;
- }
-
- //P->inf=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);
- // P->inf=1;
- return 0;
- }
-
- //P->inf=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)
-{
-// if (ECP4_isinf(P)) return;
- 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;
-// if (P->inf) return -1;
-
- FP4_copy(&iy,&(P->y)); //FP4 iy=new FP4(y);
-#if SEXTIC_TWIST_ZZZ==D_TYPE
- FP4_times_i(&iy); //iy.mul_ip();
- //FP4_norm(&iy); //iy.norm();
-#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);
- //FP4_norm(&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;
-/* if (Q->inf) return 0;
- if (P->inf)
- {
- ECP4_copy(P,Q);
- return 0;
- }
-*/
- 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();
- //FP4_norm(&t3); //t3.norm(); //t3=(X1+Y1)(X2+Y2)-(X1.X2+Y1.Y2) = X1.Y2+X2.Y1
-#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();
- //FP4_norm(&t4); //t4.norm(); //t4=(Y1+Z1)(Y2+Z2) - (Y1.Y2+Z1.Z2) = Y1.Z2+Y2.Z1
-#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_norm(&t0); //t0.norm(); // x.Q.x
- FP4_times_i(&t1); //t1.mul_ip();
- //FP4_norm(&t1); //t1.norm(); // y.Q.y
-#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);
- //FP4_norm(&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_neg(Q);
- ECP4_add(P,&NQ);
- //ECP4_neg(Q);
-}
-
-
-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;
- //ECP4_affine(P);
-
- /* 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;
-// if (P->inf) return;
-
- //ECP4_get(&X,&Y,P); // F=(1+i)^(p-7)/12
-
- 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++)
- {
- //ECP4_affine(&Q[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);
-}
-/*
-void ZZZ::ECP4_mul8(ECP4 *P,ECP4 Q[8],BIG u[8])
-{
- int i,j,a[4],nb,pb;
- ECP4 W[8],Z[8],T,C;
- BIG mt,t[8];
- sign8 w[NLEN_XXX*BASEBITS_XXX+1];
- sign8 z[NLEN_XXX*BASEBITS_XXX+1];
- FP fx,fy;
- FP2 X;
-
- FP_rcopy(&fx,Fra);
- FP_rcopy(&fy,Frb);
- FP2_from_FPs(&X,&fx,&fy);
-
- for (i=0; i<8; i++)
- BIG_copy(t[i],u[i]);
-
- // precompute tables
-
-// 12 add/subs
-
- ECP4_copy(&W[0],&Q[0]);
- ECP4_sub(&W[0],&Q[1]); // P-Q
- ECP4_copy(&W[1],&W[0]);
- ECP4_copy(&W[2],&W[0]);
- ECP4_copy(&W[3],&W[0]);
- ECP4_copy(&W[4],&Q[0]);
- ECP4_add(&W[4],&Q[1]); // P+Q
- ECP4_copy(&W[5],&W[4]);
- ECP4_copy(&W[6],&W[4]);
- ECP4_copy(&W[7],&W[4]);
-
- ECP4_copy(&T,&Q[2]);
- ECP4_sub(&T,&Q[3]); // R-S
- ECP4_sub(&W[1],&T);
- ECP4_add(&W[2],&T);
- ECP4_sub(&W[5],&T);
- ECP4_add(&W[6],&T);
- ECP4_copy(&T,&Q[2]);
- ECP4_add(&T,&Q[3]); // R+S
- ECP4_sub(&W[0],&T);
- ECP4_add(&W[3],&T);
- ECP4_sub(&W[4],&T);
- ECP4_add(&W[7],&T);
-
-
-// Use Frobenius
-
- for (i=0;i<8;i++)
- {
- ECP4_copy(&Z[i],&W[i]);
- ECP4_frob(&Z[i],&X,4);
- }
-
- // if multiplier is even add 1 to multiplier, and add P to correction
- ECP4_inf(&C);
-
- BIG_zero(mt);
- for (i=0; i<8; i++)
- {
- pb=BIG_parity(t[i]);
- BIG_inc(t[i],1-pb);
- BIG_norm(t[i]);
- ECP4_copy(&T,&C);
- ECP4_add(&T,&Q[i]);
- ECP4_cmove(&C,&T,1-pb);
-
-
- BIG_add(mt,mt,t[i]);
- BIG_norm(mt);
- }
-
- nb=1+BIG_nbits(mt);
-
- // convert exponents to signed 1-bit windows
- for (j=0; j<nb; j++)
- {
- for (i=0; i<4; i++)
- {
- a[i]=BIG_lastbits(t[i],2)-2;
- BIG_dec(t[i],a[i]);
- BIG_norm(t[i]);
- BIG_fshr(t[i],1);
- }
- w[j]=8*a[0]+4*a[1]+2*a[2]+a[3];
- }
- w[nb]=8*BIG_lastbits(t[0],2)+4*BIG_lastbits(t[1],2)+2*BIG_lastbits(t[2],2)+BIG_lastbits(t[3],2);
-
-
- for (j=0; j<nb; j++)
- {
- for (i=0; i<4; i++)
- {
- a[i]=BIG_lastbits(t[i+4],2)-2;
- BIG_dec(t[i+4],a[i]);
- BIG_norm(t[i+4]);
- BIG_fshr(t[i+4],1);
- }
- z[j]=8*a[0]+4*a[1]+2*a[2]+a[3];
- }
- z[nb]=8*BIG_lastbits(t[4],2)+4*BIG_lastbits(t[5],2)+2*BIG_lastbits(t[6],2)+BIG_lastbits(t[7],2);
-
-
- ECP4_copy(P,&W[(w[nb]-1)/2]);
- ECP4_add(P,&Z[(z[nb]-1)/2]);
- for (i=nb-1; i>=0; i--)
- {
- ECP4_dbl(P);
- ECP4_select(&T,W,w[i]);
- ECP4_add(P,&T);
- ECP4_select(&T,Z,z[i]);
- ECP4_add(P,&T);
- }
- ECP4_sub(P,&C); // apply correction
- ECP4_reduce(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);
-}
-
-
-// g++ -O2 ecp4_BLS24.cpp fp4_BLS24.cpp fp2_BLS24.cpp fp_BLS24.cpp big_XXX.cpp rand.cpp hash.cpp rom_field_BLS24.cpp rom_curve_BLS24.cpp oct.cpp -o ecp4_BLS24.exe
-/*
-int main()
-{
- int i;
- ECP4 G,P;
- FP2 Aa,Bb,f;
- FP4 X,Y;
- BIG a,b,r,p;
- char w[100];
- octet W= {0,sizeof(w),w};
-
- ECP4_ggg(&G);
-
- BIG_rcopy(a,Fra);
- BIG_rcopy(b,Frb);
- FP2_from_BIGs(&f,a,b);
-
-
- if (G.inf) cout << "Failed to set - point not on curve" << endl;
- else cout << "set success" << endl;
-
- ECP4_output(&G);
- ECP4_copy(&P,&G);
-
- //ECP4_reduce(&G);
- //ECP4_reduce(&P);
-
- BIG_rcopy(r,CURVE_Order);
- BIG_rcopy(p,Modulus);
-
- BIG_output(r);
- cout << endl;
-
- ECP4_mul(&G,r);
- ECP4_output(&G);
- cout << endl;
-
- ECP4_copy(&G,&P);
-
- cout << "pG = ";
- ECP4_mul(&G,p);
- ECP4_output(&G);
- cout << endl;
-
- cout << "G^p= ";
- ECP4_frob(&P,&f,1);
- ECP4_output(&P);
- cout << endl;
-
-
- for (i=0;i<MODBYTES_XXX;i++)
- {
- W.val[i]=i+11;
- }
- W.len=MODBYTES_XXX;
-
- printf("W= ");
- OCT_output(&W);
- printf("\n");
-
- ECP4_mapit(&P,&W);
-
- cout << "Hash to P= ";
- ECP4_output(&P);
- cout << endl;
-
- ECP4_mul(&P,r);
-
- cout << "rP= ";
- ECP4_output(&P);
- cout << endl;
-
-
-
-// ECP4_dbl(&G);
-// ECP4_output(&G);
-// ECP4_reduce(&G);
-// cout << endl;
-// ECP4_add(&G,&P);
-// ECP4_output(&G);
-// cout << endl;
-
-
- return 0;
-}
-*/
-
http://git-wip-us.apache.org/repos/asf/incubator-milagro-crypto/blob/1add7560/version3/cpp/ecp4.h
----------------------------------------------------------------------
diff --git a/version3/cpp/ecp4.h b/version3/cpp/ecp4.h
deleted file mode 100644
index 98b383b..0000000
--- a/version3/cpp/ecp4.h
+++ /dev/null
@@ -1,243 +0,0 @@
-#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/1add7560/version3/cpp/ecp8.cpp
----------------------------------------------------------------------
diff --git a/version3/cpp/ecp8.cpp b/version3/cpp/ecp8.cpp
deleted file mode 100644
index 48a76c8..0000000
--- a/version3/cpp/ecp8.cpp
+++ /dev/null
@@ -1,1318 +0,0 @@
-/*
-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)
-{
-// if (P->inf) return 1;
- return (FP8_iszilch(&(P->x)) & FP8_iszilch(&(P->z)));
-}
-
-/* Set P=Q */
-void ZZZ::ECP8_copy(ECP8 *P,ECP8 *Q)
-{
-// P->inf=Q->inf;
- 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)
-{
-// P->inf=1;
- 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);
-// d=~(d-1);
-// P->inf^=(P->inf^Q->inf)&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;
-// if (ECP8_isinf(P) && ECP8_isinf(Q)) return 1;
-// if (ECP8_isinf(P) || ECP8_isinf(Q)) return 0;
-
- 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;
- //ECP8_affine(P);
- 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);
- //P->inf=1;
- return 0;
- }
-
- // P->inf=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);
- // P->inf=1;
- return 0;
- }
-
-// P->inf=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)
-{
-// if (ECP8_isinf(P)) return;
- 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;
-// if (P->inf) return -1;
-
- FP8_copy(&iy,&(P->y)); //FP8 iy=new FP8(y);
-#if SEXTIC_TWIST_ZZZ==D_TYPE
- FP8_times_i(&iy); //iy.mul_ip();
- //FP8_norm(&iy); //iy.norm();
-#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);
- //FP8_norm(&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;
-/* if (Q->inf) return 0;
- if (P->inf)
- {
- ECP8_copy(P,Q);
- return 0;
- }*/
-
- 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();
- //FP8_norm(&t3); //t3.norm(); //t3=(X1+Y1)(X2+Y2)-(X1.X2+Y1.Y2) = X1.Y2+X2.Y1
-#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();
- //FP8_norm(&t4); //t4.norm(); //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_norm(&t0); //t0.norm(); // x.Q.x
- FP8_times_i(&t1); //t1.mul_ip();
- //FP8_norm(&t1); //t1.norm(); // y.Q.y
-#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);
- //FP8_norm(&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_neg(Q);
- ECP8_add(P,&NQ);
- //ECP8_neg(Q);
-}
-
-
-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;
- //ECP8_affine(P);
-
- /* 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;
-
- //if (P->inf) return;
-
- //ECP8_get(&X,&Y,P); // 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);
-
-
-// ECP8_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::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++)
- {
- //ECP8_affine(&Q[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);
-}
-
-/*
-void ZZZ::ECP8_mul16(ECP8 *P,ECP8 Q[16],BIG u[16])
-{
- int i,j,a[4],nb,pb;
- ECP8 W[8],Z[8],WW[8],ZZ[8],T,C;
- BIG mt,t[16];
- sign8 w[NLEN_XXX*BASEBITS_XXX+1];
- sign8 z[NLEN_XXX*BASEBITS_XXX+1];
- sign8 ww[NLEN_XXX*BASEBITS_XXX+1];
- sign8 zz[NLEN_XXX*BASEBITS_XXX+1];
-
- FP fx,fy;
- FP2 X;
-
- FP_rcopy(&fx,Fra);
- FP_rcopy(&fy,Frb);
- FP2_from_FPs(&X,&fx,&fy);
-
-
- for (i=0; i<16; i++)
- BIG_copy(t[i],u[i]);
-
- // precompute tables
-
-// 12 add/subs
-
- ECP8_copy(&W[0],&Q[0]);
- ECP8_sub(&W[0],&Q[1]); // P-Q
- ECP8_copy(&W[1],&W[0]);
- ECP8_copy(&W[2],&W[0]);
- ECP8_copy(&W[3],&W[0]);
- ECP8_copy(&W[4],&Q[0]);
- ECP8_add(&W[4],&Q[1]); // P+Q
- ECP8_copy(&W[5],&W[4]);
- ECP8_copy(&W[6],&W[4]);
- ECP8_copy(&W[7],&W[4]);
-
- ECP8_copy(&T,&Q[2]);
- ECP8_sub(&T,&Q[3]); // R-S
- ECP8_sub(&W[1],&T);
- ECP8_add(&W[2],&T);
- ECP8_sub(&W[5],&T);
- ECP8_add(&W[6],&T);
- ECP8_copy(&T,&Q[2]);
- ECP8_add(&T,&Q[3]); // R+S
- ECP8_sub(&W[0],&T);
- ECP8_add(&W[3],&T);
- ECP8_sub(&W[4],&T);
- ECP8_add(&W[7],&T);
-
-
-// Use Frobenius
-
- for (i=0;i<8;i++)
- {
- ECP8_copy(&Z[i],&W[i]);
- ECP8_frob(&Z[i],&X,4);
- }
-
- for (i=0;i<8;i++)
- {
- ECP8_copy(&WW[i],&Z[i]);
- ECP8_frob(&WW[i],&X,4);
- }
-
- for (i=0;i<8;i++)
- {
- ECP8_copy(&ZZ[i],&WW[i]);
- ECP8_frob(&ZZ[i],&X,4);
- }
-
- // if multiplier is even add 1 to multiplier, and add P to correction
- ECP8_inf(&C);
-
- BIG_zero(mt);
- for (i=0; i<16; i++)
- {
- pb=BIG_parity(t[i]);
- BIG_inc(t[i],1-pb);
- BIG_norm(t[i]);
- ECP8_copy(&T,&C);
- ECP8_add(&T,&Q[i]);
- ECP8_cmove(&C,&T,1-pb);
-
-
- BIG_add(mt,mt,t[i]);
- BIG_norm(mt);
- }
-
- nb=1+BIG_nbits(mt);
-
- // convert exponents to signed 1-bit windows
- for (j=0; j<nb; j++)
- {
- for (i=0; i<4; i++)
- {
- a[i]=BIG_lastbits(t[i],2)-2;
- BIG_dec(t[i],a[i]);
- BIG_norm(t[i]);
- BIG_fshr(t[i],1);
- }
- w[j]=8*a[0]+4*a[1]+2*a[2]+a[3];
- }
- w[nb]=8*BIG_lastbits(t[0],2)+4*BIG_lastbits(t[1],2)+2*BIG_lastbits(t[2],2)+BIG_lastbits(t[3],2);
-
-
- for (j=0; j<nb; j++)
- {
- for (i=0; i<4; i++)
- {
- a[i]=BIG_lastbits(t[i+4],2)-2;
- BIG_dec(t[i+4],a[i]);
- BIG_norm(t[i+4]);
- BIG_fshr(t[i+4],1);
- }
- z[j]=8*a[0]+4*a[1]+2*a[2]+a[3];
- }
- z[nb]=8*BIG_lastbits(t[4],2)+4*BIG_lastbits(t[5],2)+2*BIG_lastbits(t[6],2)+BIG_lastbits(t[7],2);
-
-
- for (j=0; j<nb; j++)
- {
- for (i=0; i<4; i++)
- {
- a[i]=BIG_lastbits(t[i+8],2)-2;
- BIG_dec(t[i+8],a[i]);
- BIG_norm(t[i+8]);
- BIG_fshr(t[i+8],1);
- }
- ww[j]=8*a[0]+4*a[1]+2*a[2]+a[3];
- }
- ww[nb]=8*BIG_lastbits(t[8],2)+4*BIG_lastbits(t[9],2)+2*BIG_lastbits(t[10],2)+BIG_lastbits(t[11],2);
-
- for (j=0; j<nb; j++)
- {
- for (i=0; i<4; i++)
- {
- a[i]=BIG_lastbits(t[i+12],2)-2;
- BIG_dec(t[i+12],a[i]);
- BIG_norm(t[i+12]);
- BIG_fshr(t[i+12],1);
- }
- zz[j]=8*a[0]+4*a[1]+2*a[2]+a[3];
- }
- zz[nb]=8*BIG_lastbits(t[12],2)+4*BIG_lastbits(t[13],2)+2*BIG_lastbits(t[14],2)+BIG_lastbits(t[15],2);
-
- ECP8_copy(P,&W[(w[nb]-1)/2]);
- ECP8_add(P,&Z[(z[nb]-1)/2]);
- ECP8_add(P,&WW[(ww[nb]-1)/2]);
- ECP8_add(P,&ZZ[(zz[nb]-1)/2]);
- for (i=nb-1; i>=0; i--)
- {
- ECP8_dbl(P);
- ECP8_select(&T,W,w[i]);
- ECP8_add(P,&T);
- ECP8_select(&T,Z,z[i]);
- ECP8_add(P,&T);
- ECP8_select(&T,WW,ww[i]);
- ECP8_add(P,&T);
- ECP8_select(&T,ZZ,zz[i]);
- ECP8_add(P,&T);
-
- }
- ECP8_sub(P,&C); // apply correction
- ECP8_reduce(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);
-}
-
-
-// g++ -O2 ecp8_BLS48.cpp fp8_BLS48.cpp fp4_BLS48.cpp fp2_BLS48.cpp fp_BLS48.cpp big_B560_29.cpp rand.cpp hash.cpp rom_field_BLS48.cpp rom_curve_BLS48.cpp oct.cpp -o ecp8_BLS48.exe
-/*
-int main()
-{
- int i;
- ECP8 G,P;
- FP2 Aa,Bb,f;
- FP8 X,Y;
- BIG a,b,r,p;
- char w[100];
- octet W= {0,sizeof(w),w};
-
- ECP8_generator(&G);
-
- BIG_rcopy(a,Fra);
- BIG_rcopy(b,Frb);
- FP2_from_BIGs(&f,a,b);
-
- if (G.inf) cout << "Failed to set - point not on curve" << endl;
- else cout << "set success" << endl;
-
- ECP8_output(&G);
- ECP8_copy(&P,&G);
-
- BIG_rcopy(r,CURVE_Order);
- BIG_rcopy(p,Modulus);
-
- BIG_output(r);
- cout << endl;
-
- ECP8_mul(&G,r);
- ECP8_output(&G);
- cout << endl;
-
- ECP8_copy(&G,&P);
-
- cout << "pG = ";
- ECP8_mul(&G,p);
- ECP8_output(&G);
- cout << endl;
-
- cout << "G^p= ";
- ECP8_frob(&P,&f,1);
- ECP8_output(&P);
- cout << endl;
-
-
- for (i=0;i<MODBYTES_XXX;i++)
- {
- W.val[i]=i+11;
- }
- W.len=MODBYTES_XXX;
-
- printf("W= ");
- OCT_output(&W);
- printf("\n");
-
- ECP8_mapit(&P,&W);
-
- cout << "Hash to P= ";
- ECP8_output(&P);
- cout << endl;
-
- ECP8_mul(&P,r);
-
- cout << "rP= ";
- ECP8_output(&P);
- cout << endl;
-
-
-
-// ECP8_dbl(&G);
-// ECP8_output(&G);
-// ECP8_reduce(&G);
-// cout << endl;
-// ECP8_add(&G,&P);
-// ECP8_output(&G);
-// cout << endl;
-
-
- return 0;
-}
-*/
-
http://git-wip-us.apache.org/repos/asf/incubator-milagro-crypto/blob/1add7560/version3/cpp/ecp8.h
----------------------------------------------------------------------
diff --git a/version3/cpp/ecp8.h b/version3/cpp/ecp8.h
deleted file mode 100644
index 681f199..0000000
--- a/version3/cpp/ecp8.h
+++ /dev/null
@@ -1,253 +0,0 @@
-#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