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ecp_BLS381.c
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ecp_BLS381.c
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/*
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 Elliptic Curve Functions */
/* SU=m, SU is Stack Usage (Weierstrass Curves) */
//#define HAS_MAIN
#include "ecp_BLS381.h"
/* test for P=O point-at-infinity */
int ECP_BLS381_isinf(ECP_BLS381 *P)
{
#if CURVETYPE_BLS381==EDWARDS
return (FP_BLS381_iszilch(&(P->x)) && FP_BLS381_equals(&(P->y),&(P->z)));
#endif
#if CURVETYPE_BLS381==WEIERSTRASS
return (FP_BLS381_iszilch(&(P->x)) && FP_BLS381_iszilch(&(P->z)));
#endif
#if CURVETYPE_BLS381==MONTGOMERY
return FP_BLS381_iszilch(&(P->z));
#endif
}
/* Conditional swap of P and Q dependant on d */
static void ECP_BLS381_cswap(ECP_BLS381 *P,ECP_BLS381 *Q,int d)
{
FP_BLS381_cswap(&(P->x),&(Q->x),d);
#if CURVETYPE_BLS381!=MONTGOMERY
FP_BLS381_cswap(&(P->y),&(Q->y),d);
#endif
FP_BLS381_cswap(&(P->z),&(Q->z),d);
}
#if CURVETYPE_BLS381!=MONTGOMERY
/* Conditional move Q to P dependant on d */
static void ECP_BLS381_cmove(ECP_BLS381 *P,ECP_BLS381 *Q,int d)
{
FP_BLS381_cmove(&(P->x),&(Q->x),d);
#if CURVETYPE_BLS381!=MONTGOMERY
FP_BLS381_cmove(&(P->y),&(Q->y),d);
#endif
FP_BLS381_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);
}
#endif // CURVETYPE_BLS381!=MONTGOMERY
#if CURVETYPE_BLS381!=MONTGOMERY
/* Constant time select from pre-computed table */
static void ECP_BLS381_select(ECP_BLS381 *P,ECP_BLS381 W[],sign32 b)
{
ECP_BLS381 MP;
sign32 m=b>>31;
sign32 babs=(b^m)-m;
babs=(babs-1)/2;
ECP_BLS381_cmove(P,&W[0],teq(babs,0)); // conditional move
ECP_BLS381_cmove(P,&W[1],teq(babs,1));
ECP_BLS381_cmove(P,&W[2],teq(babs,2));
ECP_BLS381_cmove(P,&W[3],teq(babs,3));
ECP_BLS381_cmove(P,&W[4],teq(babs,4));
ECP_BLS381_cmove(P,&W[5],teq(babs,5));
ECP_BLS381_cmove(P,&W[6],teq(babs,6));
ECP_BLS381_cmove(P,&W[7],teq(babs,7));
ECP_BLS381_copy(&MP,P);
ECP_BLS381_neg(&MP); // minus P
ECP_BLS381_cmove(P,&MP,(int)(m&1));
}
#endif
/* Test P == Q */
/* SU=168 */
int ECP_BLS381_equals(ECP_BLS381 *P,ECP_BLS381 *Q)
{
FP_BLS381 a,b;
FP_BLS381_mul(&a,&(P->x),&(Q->z));
FP_BLS381_mul(&b,&(Q->x),&(P->z));
if (!FP_BLS381_equals(&a,&b)) return 0;
#if CURVETYPE_BLS381!=MONTGOMERY
FP_BLS381_mul(&a,&(P->y),&(Q->z));
FP_BLS381_mul(&b,&(Q->y),&(P->z));
if (!FP_BLS381_equals(&a,&b)) return 0;
#endif
return 1;
}
/* Set P=Q */
/* SU=16 */
void ECP_BLS381_copy(ECP_BLS381 *P,ECP_BLS381 *Q)
{
FP_BLS381_copy(&(P->x),&(Q->x));
#if CURVETYPE_BLS381!=MONTGOMERY
FP_BLS381_copy(&(P->y),&(Q->y));
#endif
FP_BLS381_copy(&(P->z),&(Q->z));
}
/* Set P=-Q */
#if CURVETYPE_BLS381!=MONTGOMERY
/* SU=8 */
void ECP_BLS381_neg(ECP_BLS381 *P)
{
#if CURVETYPE_BLS381==WEIERSTRASS
FP_BLS381_neg(&(P->y),&(P->y));
FP_BLS381_norm(&(P->y));
#else
FP_BLS381_neg(&(P->x),&(P->x));
FP_BLS381_norm(&(P->x));
#endif
}
#endif
/* Set P=O */
void ECP_BLS381_inf(ECP_BLS381 *P)
{
FP_BLS381_zero(&(P->x));
#if CURVETYPE_BLS381!=MONTGOMERY
FP_BLS381_one(&(P->y));
#endif
#if CURVETYPE_BLS381!=EDWARDS
FP_BLS381_zero(&(P->z));
#else
FP_BLS381_one(&(P->z));
#endif
}
/* Calculate right Hand Side of curve equation y^2=RHS */
/* SU=56 */
void ECP_BLS381_rhs(FP_BLS381 *v,FP_BLS381 *x)
{
#if CURVETYPE_BLS381==WEIERSTRASS
/* x^3+Ax+B */
FP_BLS381 t;
FP_BLS381_sqr(&t,x);
FP_BLS381_mul(&t,&t,x);
if (CURVE_A_BLS381==-3)
{
FP_BLS381_neg(v,x);
FP_BLS381_norm(v);
FP_BLS381_imul(v,v,-CURVE_A_BLS381);
FP_BLS381_norm(v);
FP_BLS381_add(v,&t,v);
}
else FP_BLS381_copy(v,&t);
FP_BLS381_rcopy(&t,CURVE_B_BLS381);
FP_BLS381_add(v,&t,v);
FP_BLS381_reduce(v);
#endif
#if CURVETYPE_BLS381==EDWARDS
/* (Ax^2-1)/(Bx^2-1) */
FP_BLS381 t,one;
FP_BLS381_sqr(v,x);
FP_BLS381_one(&one);
FP_BLS381_rcopy(&t,CURVE_B_BLS381);
FP_BLS381_mul(&t,v,&t);
FP_BLS381_sub(&t,&t,&one);
FP_BLS381_norm(&t);
if (CURVE_A_BLS381==1) FP_BLS381_sub(v,v,&one);
if (CURVE_A_BLS381==-1)
{
FP_BLS381_add(v,v,&one);
FP_BLS381_norm(v);
FP_BLS381_neg(v,v);
}
FP_BLS381_norm(v);
FP_BLS381_inv(&t,&t);
FP_BLS381_mul(v,v,&t);
FP_BLS381_reduce(v);
#endif
#if CURVETYPE_BLS381==MONTGOMERY
/* x^3+Ax^2+x */
FP_BLS381 x2,x3;
FP_BLS381_sqr(&x2,x);
FP_BLS381_mul(&x3,&x2,x);
FP_BLS381_copy(v,x);
FP_BLS381_imul(&x2,&x2,CURVE_A_BLS381);
FP_BLS381_add(v,v,&x2);
FP_BLS381_add(v,v,&x3);
FP_BLS381_reduce(v);
#endif
}
#if CURVETYPE_BLS381==MONTGOMERY
/* Set P=(x,{y}) */
int ECP_BLS381_set(ECP_BLS381 *P,BIG_384_58 x)
{
BIG_384_58 m,b;
FP_BLS381 rhs;
BIG_384_58_rcopy(m,Modulus_BLS381);
FP_BLS381_nres(&rhs,x);
ECP_BLS381_rhs(&rhs,&rhs);
FP_BLS381_redc(b,&rhs);
if (BIG_384_58_jacobi(b,m)!=1)
{
ECP_BLS381_inf(P);
return 0;
}
FP_BLS381_nres(&(P->x),x);
FP_BLS381_one(&(P->z));
return 1;
}
/* Extract x coordinate as BIG */
int ECP_BLS381_get(BIG_384_58 x,ECP_BLS381 *P)
{
ECP_BLS381 W;
ECP_BLS381_copy(&W,P);
ECP_BLS381_affine(&W);
if (ECP_BLS381_isinf(&W)) return -1;
FP_BLS381_redc(x,&(W.x));
return 0;
}
#else
/* Extract (x,y) and return sign of y. If x and y are the same return only x */
/* SU=16 */
int ECP_BLS381_get(BIG_384_58 x,BIG_384_58 y,ECP_BLS381 *P)
{
ECP_BLS381 W;
int s;
ECP_BLS381_copy(&W,P);
ECP_BLS381_affine(&W);
if (ECP_BLS381_isinf(&W)) return -1;
FP_BLS381_redc(y,&(W.y));
s=BIG_384_58_parity(y);
FP_BLS381_redc(x,&(W.x));
return s;
}
/* Set P=(x,{y}) */
/* SU=96 */
int ECP_BLS381_set(ECP_BLS381 *P,BIG_384_58 x,BIG_384_58 y)
{
FP_BLS381 rhs,y2;
FP_BLS381_nres(&y2,y);
FP_BLS381_sqr(&y2,&y2);
FP_BLS381_reduce(&y2);
FP_BLS381_nres(&rhs,x);
ECP_BLS381_rhs(&rhs,&rhs);
if (!FP_BLS381_equals(&y2,&rhs))
{
ECP_BLS381_inf(P);
return 0;
}
FP_BLS381_nres(&(P->x),x);
FP_BLS381_nres(&(P->y),y);
FP_BLS381_one(&(P->z));
return 1;
}
/* Set P=(x,y), where y is calculated from x with sign s */
/* SU=136 */
int ECP_BLS381_setx(ECP_BLS381 *P,BIG_384_58 x,int s)
{
FP_BLS381 rhs;
BIG_384_58 t,m;
BIG_384_58_rcopy(m,Modulus_BLS381);
FP_BLS381_nres(&rhs,x);
ECP_BLS381_rhs(&rhs,&rhs);
FP_BLS381_redc(t,&rhs);
if (BIG_384_58_jacobi(t,m)!=1)
{
ECP_BLS381_inf(P);
return 0;
}
FP_BLS381_nres(&(P->x),x);
FP_BLS381_sqrt(&(P->y),&rhs);
FP_BLS381_redc(t,&(P->y));
if (BIG_384_58_parity(t)!=s)
FP_BLS381_neg(&(P->y),&(P->y));
FP_BLS381_reduce(&(P->y));
FP_BLS381_one(&(P->z));
return 1;
}
#endif
void ECP_BLS381_cfp(ECP_BLS381 *P)
{
/* multiply point by curves cofactor */
BIG_384_58 c;
int cf=CURVE_Cof_I_BLS381;
if (cf==1) return;
if (cf==4)
{
ECP_BLS381_dbl(P);
ECP_BLS381_dbl(P);
return;
}
if (cf==8)
{
ECP_BLS381_dbl(P);
ECP_BLS381_dbl(P);
ECP_BLS381_dbl(P);
return;
}
BIG_384_58_rcopy(c,CURVE_Cof_BLS381);
ECP_BLS381_mul(P,c);
return;
}
/* map BIG to point on curve of correct order */
/* The BIG should be the output of some hash function */
void ECP_BLS381_mapit(ECP_BLS381 *P,octet *W)
{
BIG_384_58 q,x;
BIG_384_58_fromBytes(x,W->val);
BIG_384_58_rcopy(q,Modulus_BLS381);
BIG_384_58_mod(x,q);
for (;;)
{
for (;;)
{
#if CURVETYPE_BLS381!=MONTGOMERY
ECP_BLS381_setx(P,x,0);
#else
ECP_BLS381_set(P,x);
#endif
BIG_384_58_inc(x,1);
BIG_384_58_norm(x);
if (!ECP_BLS381_isinf(P)) break;
}
ECP_BLS381_cfp(P);
if (!ECP_BLS381_isinf(P)) break;
}
}
/* Convert P to Affine, from (x,y,z) to (x,y) */
/* SU=160 */
void ECP_BLS381_affine(ECP_BLS381 *P)
{
FP_BLS381 one,iz;
if (ECP_BLS381_isinf(P)) return;
FP_BLS381_one(&one);
if (FP_BLS381_equals(&(P->z),&one)) return;
FP_BLS381_inv(&iz,&(P->z));
FP_BLS381_mul(&(P->x),&(P->x),&iz);
#if CURVETYPE_BLS381==EDWARDS || CURVETYPE_BLS381==WEIERSTRASS
FP_BLS381_mul(&(P->y),&(P->y),&iz);
FP_BLS381_reduce(&(P->y));
#endif
FP_BLS381_reduce(&(P->x));
FP_BLS381_copy(&(P->z),&one);
}
/* SU=120 */
void ECP_BLS381_outputxyz(ECP_BLS381 *P)
{
BIG_384_58 x,z;
if (ECP_BLS381_isinf(P))
{
printf("Infinity\n");
return;
}
FP_BLS381_reduce(&(P->x));
FP_BLS381_redc(x,&(P->x));
FP_BLS381_reduce(&(P->z));
FP_BLS381_redc(z,&(P->z));
#if CURVETYPE_BLS381!=MONTGOMERY
BIG_384_58 y;
FP_BLS381_reduce(&(P->y));
FP_BLS381_redc(y,&(P->y));
printf("(");
BIG_384_58_output(x);
printf(",");
BIG_384_58_output(y);
printf(",");
BIG_384_58_output(z);
printf(")\n");
#else
printf("(");
BIG_384_58_output(x);
printf(",");
BIG_384_58_output(z);
printf(")\n");
#endif
}
/* SU=16 */
/* Output point P */
void ECP_BLS381_output(ECP_BLS381 *P)
{
BIG_384_58 x;
if (ECP_BLS381_isinf(P))
{
printf("Infinity\n");
return;
}
ECP_BLS381_affine(P);
#if CURVETYPE_BLS381!=MONTGOMERY
BIG_384_58 y;
FP_BLS381_redc(x,&(P->x));
FP_BLS381_redc(y,&(P->y));
printf("(");
BIG_384_58_output(x);
printf(",");
BIG_384_58_output(y);
printf(")\n");
#else
FP_BLS381_redc(x,&(P->x));
printf("(");
BIG_384_58_output(x);
printf(")\n");
#endif
}
/* SU=16 */
/* Output point P */
void ECP_BLS381_rawoutput(ECP_BLS381 *P)
{
BIG_384_58 x,z;
#if CURVETYPE_BLS381!=MONTGOMERY
BIG_384_58 y;
FP_BLS381_redc(x,&(P->x));
FP_BLS381_redc(y,&(P->y));
FP_BLS381_redc(z,&(P->z));
printf("(");
BIG_384_58_output(x);
printf(",");
BIG_384_58_output(y);
printf(",");
BIG_384_58_output(z);
printf(")\n");
#else
FP_BLS381_redc(x,&(P->x));
FP_BLS381_redc(z,&(P->z));
printf("(");
BIG_384_58_output(x);
printf(",");
BIG_384_58_output(z);
printf(")\n");
#endif
}
/* SU=88 */
/* Convert P to octet string */
void ECP_BLS381_toOctet(octet *W,ECP_BLS381 *P,bool compress)
{
#if CURVETYPE_BLS381==MONTGOMERY
BIG_384_58 x;
ECP_BLS381_get(x,P);
W->len=MODBYTES_384_58+1;
W->val[0]=6;
BIG_384_58_toBytes(&(W->val[1]),x);
#else
BIG_384_58 x,y;
ECP_BLS381_get(x,y,P);
if (compress)
{
W->val[0]=0x02;
if (BIG_384_58_parity(y)==1) W->val[0]=0x03;
W->len=MODBYTES_384_58+1;
BIG_384_58_toBytes(&(W->val[1]),x);
}
else
{
W->val[0]=4;
W->len=2*MODBYTES_384_58+1;
BIG_384_58_toBytes(&(W->val[1]),x);
BIG_384_58_toBytes(&(W->val[MODBYTES_384_58+1]),y);
}
#endif
}
/* SU=88 */
/* Restore P from octet string */
int ECP_BLS381_fromOctet(ECP_BLS381 *P,octet *W)
{
#if CURVETYPE_BLS381==MONTGOMERY
BIG_384_58 x;
BIG_384_58_fromBytes(x,&(W->val[1]));
if (ECP_BLS381_set(P,x)) return 1;
return 0;
#else
BIG_384_58 x,y;
int typ=W->val[0];
BIG_384_58_fromBytes(x,&(W->val[1]));
if (typ==0x04)
{
BIG_384_58_fromBytes(y,&(W->val[MODBYTES_384_58+1]));
if (ECP_BLS381_set(P,x,y)) return 1;
}
if (typ==0x02 || typ==0x03)
{
if (ECP_BLS381_setx(P,x,typ&1)) return 1;
}
return 0;
#endif
}
/* Set P=2P */
/* SU=272 */
void ECP_BLS381_dbl(ECP_BLS381 *P)
{
#if CURVETYPE_BLS381==WEIERSTRASS
FP_BLS381 t0,t1,t2,t3,x3,y3,z3,b;
if (CURVE_A_BLS381==0)
{
FP_BLS381_sqr(&t0,&(P->y)); //t0.sqr();
FP_BLS381_mul(&t1,&(P->y),&(P->z)); //t1.mul(z);
FP_BLS381_sqr(&t2,&(P->z)); //t2.sqr();
FP_BLS381_add(&(P->z),&t0,&t0); //z.add(t0);
FP_BLS381_norm(&(P->z)); //z.norm();
FP_BLS381_add(&(P->z),&(P->z),&(P->z)); //z.add(z);
FP_BLS381_add(&(P->z),&(P->z),&(P->z)); //z.add(z);
FP_BLS381_norm(&(P->z)); //z.norm();
FP_BLS381_imul(&t2,&t2,3*CURVE_B_I_BLS381); //t2.imul(3*ROM.CURVE_B_I);
FP_BLS381_mul(&x3,&t2,&(P->z)); //x3.mul(z);
FP_BLS381_add(&y3,&t0,&t2); //y3.add(t2);
FP_BLS381_norm(&y3); //y3.norm();
FP_BLS381_mul(&(P->z),&(P->z),&t1); //z.mul(t1);
FP_BLS381_add(&t1,&t2,&t2); //t1.add(t2);
FP_BLS381_add(&t2,&t2,&t1); //t2.add(t1);
FP_BLS381_sub(&t0,&t0,&t2); //t0.sub(t2);
FP_BLS381_norm(&t0); //t0.norm();
FP_BLS381_mul(&y3,&y3,&t0); //y3.mul(t0);
FP_BLS381_add(&y3,&y3,&x3); //y3.add(x3);
FP_BLS381_mul(&t1,&(P->x),&(P->y)); //t1.mul(y);
FP_BLS381_norm(&t0); //x.norm();
FP_BLS381_mul(&(P->x),&t0,&t1); //x.mul(t1);
FP_BLS381_add(&(P->x),&(P->x),&(P->x)); //x.add(x);
FP_BLS381_norm(&(P->x)); //x.norm();
FP_BLS381_copy(&(P->y),&y3); //y.copy(y3);
FP_BLS381_norm(&(P->y)); //y.norm();
}
else // its -3
{
if (CURVE_B_I_BLS381==0) //if (ROM.CURVE_B_I==0)
FP_BLS381_rcopy(&b,CURVE_B_BLS381); //b.copy(new FP(new BIG(ROM.CURVE_B)));
FP_BLS381_sqr(&t0,&(P->x)); //t0.sqr(); //1 x^2
FP_BLS381_sqr(&t1,&(P->y)); //t1.sqr(); //2 y^2
FP_BLS381_sqr(&t2,&(P->z)); //t2.sqr(); //3
FP_BLS381_mul(&t3,&(P->x),&(P->y)); //t3.mul(y); //4
FP_BLS381_add(&t3,&t3,&t3); //t3.add(t3);
FP_BLS381_norm(&t3); //t3.norm();//5
FP_BLS381_mul(&z3,&(P->z),&(P->x)); //z3.mul(x); //6
FP_BLS381_add(&z3,&z3,&z3); //z3.add(z3);
FP_BLS381_norm(&z3); //z3.norm();//7
if (CURVE_B_I_BLS381==0) //if (ROM.CURVE_B_I==0)
FP_BLS381_mul(&y3,&t2,&b); //y3.mul(b); //8
else
FP_BLS381_imul(&y3,&t2,CURVE_B_I_BLS381); //y3.imul(ROM.CURVE_B_I);
FP_BLS381_sub(&y3,&y3,&z3); //y3.sub(z3); //y3.norm(); //9 ***
FP_BLS381_add(&x3,&y3,&y3); //x3.add(y3);
FP_BLS381_norm(&x3); //x3.norm();//10
FP_BLS381_add(&y3,&y3,&x3); //y3.add(x3); //y3.norm();//11
FP_BLS381_sub(&x3,&t1,&y3); //x3.sub(y3);
FP_BLS381_norm(&x3); //x3.norm();//12
FP_BLS381_add(&y3,&y3,&t1); //y3.add(t1);
FP_BLS381_norm(&y3); //y3.norm();//13
FP_BLS381_mul(&y3,&y3,&x3); //y3.mul(x3); //14
FP_BLS381_mul(&x3,&x3,&t3); //x3.mul(t3); //15
FP_BLS381_add(&t3,&t2,&t2); //t3.add(t2); //16
FP_BLS381_add(&t2,&t2,&t3); //t2.add(t3); //17
if (CURVE_B_I_BLS381==0) //if (ROM.CURVE_B_I==0)
FP_BLS381_mul(&z3,&z3,&b); //z3.mul(b); //18
else
FP_BLS381_imul(&z3,&z3,CURVE_B_I_BLS381); //z3.imul(ROM.CURVE_B_I);
FP_BLS381_sub(&z3,&z3,&t2); //z3.sub(t2); //z3.norm();//19
FP_BLS381_sub(&z3,&z3,&t0); //z3.sub(t0);
FP_BLS381_norm(&z3); //z3.norm();//20 ***
FP_BLS381_add(&t3,&z3,&z3); //t3.add(z3); //t3.norm();//21
FP_BLS381_add(&z3,&z3,&t3); //z3.add(t3);
FP_BLS381_norm(&z3); //z3.norm(); //22
FP_BLS381_add(&t3,&t0,&t0); //t3.add(t0); //t3.norm(); //23
FP_BLS381_add(&t0,&t0,&t3); //t0.add(t3); //t0.norm();//24
FP_BLS381_sub(&t0,&t0,&t2); //t0.sub(t2);
FP_BLS381_norm(&t0); //t0.norm();//25
FP_BLS381_mul(&t0,&t0,&z3); //t0.mul(z3);//26
FP_BLS381_add(&y3,&y3,&t0); //y3.add(t0); //y3.norm();//27
FP_BLS381_mul(&t0,&(P->y),&(P->z)); //t0.mul(z);//28
FP_BLS381_add(&t0,&t0,&t0); //t0.add(t0);
FP_BLS381_norm(&t0); //t0.norm(); //29
FP_BLS381_mul(&z3,&z3,&t0); //z3.mul(t0);//30
FP_BLS381_sub(&(P->x),&x3,&z3); //x3.sub(z3); //x3.norm();//31
FP_BLS381_add(&t0,&t0,&t0); //t0.add(t0);
FP_BLS381_norm(&t0); //t0.norm();//32
FP_BLS381_add(&t1,&t1,&t1); //t1.add(t1);
FP_BLS381_norm(&t1); //t1.norm();//33
FP_BLS381_mul(&(P->z),&t0,&t1); //z3.mul(t1);//34
FP_BLS381_norm(&(P->x)); //x.norm();
FP_BLS381_copy(&(P->y),&y3); //y.copy(y3);
FP_BLS381_norm(&(P->y)); //y.norm();
FP_BLS381_norm(&(P->z)); //z.norm();
}
#endif
#if CURVETYPE_BLS381==EDWARDS
/* Not using square for multiplication swap, as (1) it needs more adds, and (2) it triggers more reductions */
FP_BLS381 C,D,H,J;
FP_BLS381_sqr(&C,&(P->x)); //C.sqr();
FP_BLS381_mul(&(P->x),&(P->x),&(P->y)); //x.mul(y);
FP_BLS381_add(&(P->x),&(P->x),&(P->x)); //x.add(x);
FP_BLS381_norm(&(P->x)); //x.norm();
FP_BLS381_sqr(&D,&(P->y)); //D.sqr();
if (CURVE_A_BLS381==-1) //if (ROM.CURVE_A==-1)
FP_BLS381_neg(&C,&C); // C.neg();
FP_BLS381_add(&(P->y),&C,&D); //y.add(D);
FP_BLS381_norm(&(P->y)); //y.norm();
FP_BLS381_sqr(&H,&(P->z)); //H.sqr();
FP_BLS381_add(&H,&H,&H); //H.add(H);
FP_BLS381_sub(&J,&(P->y),&H); //J.sub(H);
FP_BLS381_norm(&J); //J.norm();
FP_BLS381_mul(&(P->x),&(P->x),&J); //x.mul(J);
FP_BLS381_sub(&C,&C,&D); //C.sub(D);
FP_BLS381_norm(&C); //C.norm();
FP_BLS381_mul(&(P->z),&(P->y),&J); //z.mul(J);
FP_BLS381_mul(&(P->y),&(P->y),&C); //y.mul(C);
#endif
#if CURVETYPE_BLS381==MONTGOMERY
FP_BLS381 A,B,AA,BB,C;
FP_BLS381_add(&A,&(P->x),&(P->z)); //A.add(z);
FP_BLS381_norm(&A); //A.norm();
FP_BLS381_sqr(&AA,&A); //AA.sqr();
FP_BLS381_sub(&B,&(P->x),&(P->z)); //B.sub(z);
FP_BLS381_norm(&B); //B.norm();
FP_BLS381_sqr(&BB,&B); //BB.sqr();
FP_BLS381_sub(&C,&AA,&BB); //C.sub(BB);
FP_BLS381_norm(&C); //C.norm();
FP_BLS381_mul(&(P->x),&AA,&BB); //x.mul(BB);
FP_BLS381_imul(&A,&C,(CURVE_A_BLS381+2)/4); //A.imul((ROM.CURVE_A+2)/4);
FP_BLS381_add(&BB,&BB,&A); //BB.add(A);
FP_BLS381_norm(&BB); //BB.norm();
FP_BLS381_mul(&(P->z),&BB,&C); //z.mul(C);
#endif
}
#if CURVETYPE_BLS381==MONTGOMERY
/* Set P+=Q. W is difference between P and Q and is affine */
void ECP_BLS381_add(ECP_BLS381 *P,ECP_BLS381 *Q,ECP_BLS381 *W)
{
FP_BLS381 A,B,C,D,DA,CB;
FP_BLS381_add(&A,&(P->x),&(P->z)); //A.add(z);
FP_BLS381_sub(&B,&(P->x),&(P->z)); //B.sub(z);
FP_BLS381_add(&C,&(Q->x),&(Q->z)); //C.add(Q.z);
FP_BLS381_sub(&D,&(Q->x),&(Q->z)); //D.sub(Q.z);
FP_BLS381_norm(&A); //A.norm();
FP_BLS381_norm(&D); //D.norm();
FP_BLS381_mul(&DA,&D,&A); //DA.mul(A);
FP_BLS381_norm(&C); //C.norm();
FP_BLS381_norm(&B); //B.norm();
FP_BLS381_mul(&CB,&C,&B); //CB.mul(B);
FP_BLS381_add(&A,&DA,&CB); //A.add(CB);
FP_BLS381_norm(&A); //A.norm();
FP_BLS381_sqr(&(P->x),&A); //A.sqr();
FP_BLS381_sub(&B,&DA,&CB); //B.sub(CB);
FP_BLS381_norm(&B); //B.norm();
FP_BLS381_sqr(&B,&B); //B.sqr();
FP_BLS381_mul(&(P->z),&(W->x),&B); //z.mul(B);
}
#else
/* Set P+=Q */
/* SU=248 */
void ECP_BLS381_add(ECP_BLS381 *P,ECP_BLS381 *Q)
{
#if CURVETYPE_BLS381==WEIERSTRASS
int b3;
FP_BLS381 t0,t1,t2,t3,t4,x3,y3,z3,b;
if (CURVE_A_BLS381==0)
{
b3=3*CURVE_B_I_BLS381; //int b=3*ROM.CURVE_B_I;
FP_BLS381_mul(&t0,&(P->x),&(Q->x)); //t0.mul(Q.x);
FP_BLS381_mul(&t1,&(P->y),&(Q->y)); //t1.mul(Q.y);
FP_BLS381_mul(&t2,&(P->z),&(Q->z)); //t2.mul(Q.z);
FP_BLS381_add(&t3,&(P->x),&(P->y)); //t3.add(y);
FP_BLS381_norm(&t3); //t3.norm();
FP_BLS381_add(&t4,&(Q->x),&(Q->y)); //t4.add(Q.y);
FP_BLS381_norm(&t4); //t4.norm();
FP_BLS381_mul(&t3,&t3,&t4); //t3.mul(t4);
FP_BLS381_add(&t4,&t0,&t1); //t4.add(t1);
FP_BLS381_sub(&t3,&t3,&t4); //t3.sub(t4);
FP_BLS381_norm(&t3); //t3.norm();
FP_BLS381_add(&t4,&(P->y),&(P->z)); //t4.add(z);
FP_BLS381_norm(&t4); //t4.norm();
FP_BLS381_add(&x3,&(Q->y),&(Q->z)); //x3.add(Q.z);
FP_BLS381_norm(&x3); //x3.norm();
FP_BLS381_mul(&t4,&t4,&x3); //t4.mul(x3);
FP_BLS381_add(&x3,&t1,&t2); //x3.add(t2);
FP_BLS381_sub(&t4,&t4,&x3); //t4.sub(x3);
FP_BLS381_norm(&t4); //t4.norm();
FP_BLS381_add(&x3,&(P->x),&(P->z)); //x3.add(z);
FP_BLS381_norm(&x3); //x3.norm();
FP_BLS381_add(&y3,&(Q->x),&(Q->z)); //y3.add(Q.z);
FP_BLS381_norm(&y3); //y3.norm();
FP_BLS381_mul(&x3,&x3,&y3); //x3.mul(y3);
FP_BLS381_add(&y3,&t0,&t2); //y3.add(t2);
FP_BLS381_sub(&y3,&x3,&y3); //y3.rsub(x3);
FP_BLS381_norm(&y3); //y3.norm();
FP_BLS381_add(&x3,&t0,&t0); //x3.add(t0);
FP_BLS381_add(&t0,&t0,&x3); //t0.add(x3);
FP_BLS381_norm(&t0); //t0.norm();
FP_BLS381_imul(&t2,&t2,b3); //t2.imul(b);
FP_BLS381_add(&z3,&t1,&t2); //z3.add(t2);
FP_BLS381_norm(&z3); //z3.norm();
FP_BLS381_sub(&t1,&t1,&t2); //t1.sub(t2);
FP_BLS381_norm(&t1); //t1.norm();
FP_BLS381_imul(&y3,&y3,b3); //y3.imul(b);
FP_BLS381_mul(&x3,&y3,&t4); //x3.mul(t4);
FP_BLS381_mul(&t2,&t3,&t1); //t2.mul(t1);
FP_BLS381_sub(&(P->x),&t2,&x3); //x3.rsub(t2);
FP_BLS381_mul(&y3,&y3,&t0); //y3.mul(t0);
FP_BLS381_mul(&t1,&t1,&z3); //t1.mul(z3);
FP_BLS381_add(&(P->y),&y3,&t1); //y3.add(t1);
FP_BLS381_mul(&t0,&t0,&t3); //t0.mul(t3);
FP_BLS381_mul(&z3,&z3,&t4); //z3.mul(t4);
FP_BLS381_add(&(P->z),&z3,&t0); //z3.add(t0);
FP_BLS381_norm(&(P->x)); //x.norm();
FP_BLS381_norm(&(P->y)); //y.norm();
FP_BLS381_norm(&(P->z)); //z.norm();
}
else
{
if (CURVE_B_I_BLS381==0) //if (ROM.CURVE_B_I==0)
FP_BLS381_rcopy(&b,CURVE_B_BLS381); //b.copy(new FP(new BIG(ROM.CURVE_B)));
FP_BLS381_mul(&t0,&(P->x),&(Q->x)); //t0.mul(Q.x); //1
FP_BLS381_mul(&t1,&(P->y),&(Q->y)); //t1.mul(Q.y); //2
FP_BLS381_mul(&t2,&(P->z),&(Q->z)); //t2.mul(Q.z); //3
FP_BLS381_add(&t3,&(P->x),&(P->y)); //t3.add(y);
FP_BLS381_norm(&t3); //t3.norm(); //4
FP_BLS381_add(&t4,&(Q->x),&(Q->y)); //t4.add(Q.y);
FP_BLS381_norm(&t4); //t4.norm();//5
FP_BLS381_mul(&t3,&t3,&t4); //t3.mul(t4);//6
FP_BLS381_add(&t4,&t0,&t1); //t4.add(t1); //t4.norm(); //7
FP_BLS381_sub(&t3,&t3,&t4); //t3.sub(t4);
FP_BLS381_norm(&t3); //t3.norm(); //8
FP_BLS381_add(&t4,&(P->y),&(P->z)); //t4.add(z);
FP_BLS381_norm(&t4); //t4.norm();//9
FP_BLS381_add(&x3,&(Q->y),&(Q->z)); //x3.add(Q.z);
FP_BLS381_norm(&x3); //x3.norm();//10
FP_BLS381_mul(&t4,&t4,&x3); //t4.mul(x3); //11
FP_BLS381_add(&x3,&t1,&t2); //x3.add(t2); //x3.norm();//12
FP_BLS381_sub(&t4,&t4,&x3); //t4.sub(x3);
FP_BLS381_norm(&t4); //t4.norm();//13
FP_BLS381_add(&x3,&(P->x),&(P->z)); //x3.add(z);
FP_BLS381_norm(&x3); //x3.norm(); //14
FP_BLS381_add(&y3,&(Q->x),&(Q->z)); //y3.add(Q.z);
FP_BLS381_norm(&y3); //y3.norm();//15
FP_BLS381_mul(&x3,&x3,&y3); //x3.mul(y3); //16
FP_BLS381_add(&y3,&t0,&t2); //y3.add(t2); //y3.norm();//17
FP_BLS381_sub(&y3,&x3,&y3); //y3.rsub(x3);
FP_BLS381_norm(&y3); //y3.norm(); //18
if (CURVE_B_I_BLS381==0) //if (ROM.CURVE_B_I==0)
FP_BLS381_mul(&z3,&t2,&b); //z3.mul(b); //18
else
FP_BLS381_imul(&z3,&t2,CURVE_B_I_BLS381); //z3.imul(ROM.CURVE_B_I);
FP_BLS381_sub(&x3,&y3,&z3); //x3.sub(z3);
FP_BLS381_norm(&x3); //x3.norm(); //20
FP_BLS381_add(&z3,&x3,&x3); //z3.add(x3); //z3.norm(); //21
FP_BLS381_add(&x3,&x3,&z3); //x3.add(z3); //x3.norm(); //22
FP_BLS381_sub(&z3,&t1,&x3); //z3.sub(x3);
FP_BLS381_norm(&z3); //z3.norm(); //23
FP_BLS381_add(&x3,&x3,&t1); //x3.add(t1);
FP_BLS381_norm(&x3); //x3.norm(); //24
if (CURVE_B_I_BLS381==0) //if (ROM.CURVE_B_I==0)
FP_BLS381_mul(&y3,&y3,&b); //y3.mul(b); //18
else
FP_BLS381_imul(&y3,&y3,CURVE_B_I_BLS381); //y3.imul(ROM.CURVE_B_I);
FP_BLS381_add(&t1,&t2,&t2); //t1.add(t2); //t1.norm();//26
FP_BLS381_add(&t2,&t2,&t1); //t2.add(t1); //t2.norm();//27
FP_BLS381_sub(&y3,&y3,&t2); //y3.sub(t2); //y3.norm(); //28
FP_BLS381_sub(&y3,&y3,&t0); //y3.sub(t0);
FP_BLS381_norm(&y3); //y3.norm(); //29
FP_BLS381_add(&t1,&y3,&y3); //t1.add(y3); //t1.norm();//30
FP_BLS381_add(&y3,&y3,&t1); //y3.add(t1);
FP_BLS381_norm(&y3); //y3.norm(); //31
FP_BLS381_add(&t1,&t0,&t0); //t1.add(t0); //t1.norm(); //32
FP_BLS381_add(&t0,&t0,&t1); //t0.add(t1); //t0.norm();//33
FP_BLS381_sub(&t0,&t0,&t2); //t0.sub(t2);
FP_BLS381_norm(&t0); //t0.norm();//34
FP_BLS381_mul(&t1,&t4,&y3); //t1.mul(y3);//35
FP_BLS381_mul(&t2,&t0,&y3); //t2.mul(y3);//36
FP_BLS381_mul(&y3,&x3,&z3); //y3.mul(z3);//37
FP_BLS381_add(&(P->y),&y3,&t2); //y3.add(t2); //y3.norm();//38
FP_BLS381_mul(&x3,&x3,&t3); //x3.mul(t3);//39
FP_BLS381_sub(&(P->x),&x3,&t1); //x3.sub(t1);//40
FP_BLS381_mul(&z3,&z3,&t4); //z3.mul(t4);//41
FP_BLS381_mul(&t1,&t3,&t0); //t1.mul(t0);//42
FP_BLS381_add(&(P->z),&z3,&t1); //z3.add(t1);
FP_BLS381_norm(&(P->x)); //x.norm();
FP_BLS381_norm(&(P->y)); //y.norm();
FP_BLS381_norm(&(P->z)); //z.norm();
}
#else
FP_BLS381 A,B,C,D,E,F,G,b;
FP_BLS381_mul(&A,&(P->z),&(Q->z)); //A.mul(Q.z);
FP_BLS381_sqr(&B,&A); //B.sqr();
FP_BLS381_mul(&C,&(P->x),&(Q->x)); //C.mul(Q.x);
FP_BLS381_mul(&D,&(P->y),&(Q->y)); //D.mul(Q.y);
FP_BLS381_mul(&E,&C,&D); //E.mul(D);
if (CURVE_B_I_BLS381==0) //if (ROM.CURVE_B_I==0)
{
FP_BLS381_rcopy(&b,CURVE_B_BLS381); //FP b=new FP(new BIG(ROM.CURVE_B));
FP_BLS381_mul(&E,&E,&b); //E.mul(b);
}
else
FP_BLS381_imul(&E,&E,CURVE_B_I_BLS381); //E.imul(ROM.CURVE_B_I);
FP_BLS381_sub(&F,&B,&E); //F.sub(E);
FP_BLS381_add(&G,&B,&E); //G.add(E);
if (CURVE_A_BLS381==1) //if (ROM.CURVE_A==1)
{
FP_BLS381_sub(&E,&D,&C); //E.sub(C);
}
FP_BLS381_add(&C,&C,&D); //C.add(D);
FP_BLS381_add(&B,&(P->x),&(P->y)); //B.add(y);
FP_BLS381_add(&D,&(Q->x),&(Q->y)); //D.add(Q.y);
FP_BLS381_norm(&B); //B.norm();
FP_BLS381_norm(&D); //D.norm();
FP_BLS381_mul(&B,&B,&D); //B.mul(D);
FP_BLS381_sub(&B,&B,&C); //B.sub(C);
FP_BLS381_norm(&B); //B.norm();
FP_BLS381_norm(&F); //F.norm();
FP_BLS381_mul(&B,&B,&F); //B.mul(F);
FP_BLS381_mul(&(P->x),&A,&B); //x.mul(B);
FP_BLS381_norm(&G); //G.norm();
if (CURVE_A_BLS381==1) //if (ROM.CURVE_A==1)
{
FP_BLS381_norm(&E); //E.norm();
FP_BLS381_mul(&C,&E,&G); //C.mul(G);
}
if (CURVE_A_BLS381==-1) //if (ROM.CURVE_A==-1)
{
FP_BLS381_norm(&C); //C.norm();
FP_BLS381_mul(&C,&C,&G); //C.mul(G);
}
FP_BLS381_mul(&(P->y),&A,&C); //y.mul(C);
FP_BLS381_mul(&(P->z),&F,&G); //z.mul(G);
#endif
}
/* Set P-=Q */
/* SU=16 */
void ECP_BLS381_sub(ECP_BLS381 *P,ECP_BLS381 *Q)
{
ECP_BLS381 NQ;
ECP_BLS381_copy(&NQ,Q);
ECP_BLS381_neg(&NQ);
ECP_BLS381_add(P,&NQ);
}
#endif
#if CURVETYPE_BLS381!=MONTGOMERY
/* constant time multiply by small integer of length bts - use ladder */
void ECP_BLS381_pinmul(ECP_BLS381 *P,int e,int bts)
{
int i,b;
ECP_BLS381 R0,R1;
ECP_BLS381_affine(P);