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ECP.java
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ECP.java
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/*
Copyright (C) 2019 MIRACL UK Ltd.
This program is free software: you can redistribute it and/or modify
it under the terms of the GNU Affero General Public License as
published by the Free Software Foundation, either version 3 of the
License, or (at your option) any later version.
This program is distributed in the hope that it will be useful,
but WITHOUT ANY WARRANTY; without even the implied warranty of
MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
GNU Affero General Public License for more details.
https://www.gnu.org/licenses/agpl-3.0.en.html
You should have received a copy of the GNU Affero General Public License
along with this program. If not, see <https://www.gnu.org/licenses/>.
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.
You can be released from the requirements of the license by purchasing
a commercial license. Buying such a license is mandatory as soon as you
develop commercial activities involving the MIRACL Core Crypto SDK
without disclosing the source code of your own applications, or shipping
the MIRACL Core Crypto SDK with a closed source product.
*/
/* Elliptic Curve Point class */
package org.miracl.core.XXX;
public final class ECP {
private FP x;
private FP y;
private FP z;
/* Constructor - set to O */
public ECP() {
x=new FP();
y=new FP(1);
if (CONFIG_CURVE.CURVETYPE==CONFIG_CURVE.EDWARDS)
{
z=new FP(1);
}
else
{
z=new FP();
}
}
public ECP(ECP e) {
this.x = new FP(e.x);
this.y = new FP(e.y);
this.z = new FP(e.z);
}
/* test for O point-at-infinity */
public boolean is_infinity() {
// if (INF) return true; // Edits made
if (CONFIG_CURVE.CURVETYPE==CONFIG_CURVE.EDWARDS)
{
return (x.iszilch() && y.equals(z));
}
if (CONFIG_CURVE.CURVETYPE==CONFIG_CURVE.WEIERSTRASS)
{
return (x.iszilch() && z.iszilch());
}
if (CONFIG_CURVE.CURVETYPE==CONFIG_CURVE.MONTGOMERY)
{
return z.iszilch();
}
return true;
}
/* Conditional swap of P and Q dependant on d */
private void cswap(ECP Q,int d)
{
x.cswap(Q.x,d);
if (CONFIG_CURVE.CURVETYPE!=CONFIG_CURVE.MONTGOMERY) y.cswap(Q.y,d);
z.cswap(Q.z,d);
}
/* Conditional move of Q to P dependant on d */
private void cmove(ECP Q,int d)
{
x.cmove(Q.x,d);
if (CONFIG_CURVE.CURVETYPE!=CONFIG_CURVE.MONTGOMERY) y.cmove(Q.y,d);
z.cmove(Q.z,d);
}
/* return 1 if b==c, no branching */
private static int teq(int b,int c)
{
int x=b^c;
x-=1; // if x=0, x now -1
return ((x>>31)&1);
}
/* Constant time select from pre-computed table */
private void select(ECP W[],int b)
{
ECP MP=new ECP();
int m=b>>31;
int babs=(b^m)-m;
babs=(babs-1)/2;
cmove(W[0],teq(babs,0)); // conditional move
cmove(W[1],teq(babs,1));
cmove(W[2],teq(babs,2));
cmove(W[3],teq(babs,3));
cmove(W[4],teq(babs,4));
cmove(W[5],teq(babs,5));
cmove(W[6],teq(babs,6));
cmove(W[7],teq(babs,7));
MP.copy(this);
MP.neg();
cmove(MP,(int)(m&1));
}
/* Test P == Q */
public boolean equals(ECP Q) {
FP a=new FP(); // Edits made
FP b=new FP();
a.copy(x); a.mul(Q.z);
b.copy(Q.x); b.mul(z);
if (!a.equals(b)) return false;
if (CONFIG_CURVE.CURVETYPE!=CONFIG_CURVE.MONTGOMERY)
{
a.copy(y); a.mul(Q.z);
b.copy(Q.y); b.mul(z);
if (!a.equals(b)) return false;
}
return true;
}
/* this=P */
public void copy(ECP P)
{
x.copy(P.x);
if (CONFIG_CURVE.CURVETYPE!=CONFIG_CURVE.MONTGOMERY) y.copy(P.y);
z.copy(P.z);
}
/* this=-this */
public void neg() {
if (CONFIG_CURVE.CURVETYPE==CONFIG_CURVE.WEIERSTRASS)
{
y.neg(); y.norm();
}
if (CONFIG_CURVE.CURVETYPE==CONFIG_CURVE.EDWARDS)
{
x.neg(); x.norm();
}
return;
}
/* set this=O */
public void inf() {
// INF=true;
x.zero();
if (CONFIG_CURVE.CURVETYPE!=CONFIG_CURVE.MONTGOMERY) y.one();
if (CONFIG_CURVE.CURVETYPE!=CONFIG_CURVE.EDWARDS) z.zero();
else z.one();
}
/* Calculate RHS of curve equation */
public static FP RHS(FP x) {
FP r=new FP(x);
r.sqr();
if (CONFIG_CURVE.CURVETYPE==CONFIG_CURVE.WEIERSTRASS)
{ // x^3+Ax+B
FP b=new FP(new BIG(ROM.CURVE_B));
r.mul(x);
if (ROM.CURVE_A==-3)
{
FP cx=new FP(x);
cx.imul(3);
cx.neg(); cx.norm();
r.add(cx);
}
r.add(b);
}
if (CONFIG_CURVE.CURVETYPE==CONFIG_CURVE.EDWARDS)
{ // (Ax^2-1)/(Bx^2-1)
FP b=new FP(new BIG(ROM.CURVE_B));
FP one=new FP(1);
b.mul(r);
b.sub(one);
b.norm();
if (ROM.CURVE_A==-1) r.neg();
r.sub(one); r.norm();
b.inverse();
r.mul(b);
}
if (CONFIG_CURVE.CURVETYPE==CONFIG_CURVE.MONTGOMERY)
{ // x^3+Ax^2+x
FP x3=new FP();
x3.copy(r);
x3.mul(x);
r.imul(ROM.CURVE_A);
r.add(x3);
r.add(x);
}
r.reduce();
return r;
}
/* set (x,y) from two BIGs */
public ECP(BIG ix,BIG iy) {
x=new FP(ix);
y=new FP(iy);
z=new FP(1);
x.norm();
FP rhs=RHS(x);
if (CONFIG_CURVE.CURVETYPE==CONFIG_CURVE.MONTGOMERY)
{
if (rhs.qr(null)!=1) inf();
}
else
{
FP y2=new FP(y);
y2.sqr();
if (!y2.equals(rhs)) inf();
}
}
/* set (x,y) from BIG and a bit */
public ECP(BIG ix,int s) {
x=new FP(ix);
x.norm();
FP rhs=RHS(x);
FP hint=new FP();
y=new FP();
z=new FP(1);
if (rhs.qr(hint)==1)
{
FP ny=rhs.sqrt(hint);
if (ny.redc().parity()!=s) ny.neg();
y.copy(ny);
}
else inf();
}
/* set from x - calculate y from curve equation */
public ECP(BIG ix) {
x=new FP(ix);
x.norm();
FP rhs=RHS(x);
FP hint=new FP();
y=new FP();
z=new FP(1);
if (rhs.qr(hint)==1)
{
if (CONFIG_CURVE.CURVETYPE!=CONFIG_CURVE.MONTGOMERY) y.copy(rhs.sqrt(hint));
}
else inf(); //INF=true;
}
/* set to affine - from (x,y,z) to (x,y) */
public void affine() {
if (is_infinity()) return; //
FP one=new FP(1);
if (z.equals(one)) return;
z.inverse();
x.mul(z); x.reduce();
if (CONFIG_CURVE.CURVETYPE!=CONFIG_CURVE.MONTGOMERY) // Edits made
{
y.mul(z); y.reduce();
}
z.copy(one);
}
/* extract x as a BIG */
public BIG getX()
{
ECP W=new ECP(this);
W.affine();
return W.x.redc();
}
/* extract y as a BIG */
public BIG getY()
{
ECP W=new ECP(this);
W.affine();
return W.y.redc();
}
/* get sign of Y */
public int getS()
{
BIG y=getY();
return y.parity();
}
/* extract x as an FP */
public FP getx()
{
return x;
}
/* extract y as an FP */
public FP gety()
{
return y;
}
/* extract z as an FP */
public FP getz()
{
return z;
}
/* convert to byte array */
public void toBytes(byte[] b,boolean compress)
{
byte[] t=new byte[CONFIG_BIG.MODBYTES];
ECP W=new ECP(this);
W.affine();
W.x.redc().toBytes(t);
for (int i=0;i<CONFIG_BIG.MODBYTES;i++) b[i+1]=t[i];
if (CONFIG_CURVE.CURVETYPE==CONFIG_CURVE.MONTGOMERY)
{
b[0]=0x06;
return;
}
if (compress)
{
b[0]=0x02;
if (y.redc().parity()==1) b[0]=0x03;
return;
}
b[0]=0x04;
W.y.redc().toBytes(t);
for (int i=0;i<CONFIG_BIG.MODBYTES;i++) b[i+CONFIG_BIG.MODBYTES+1]=t[i];
}
/* convert from byte array to point */
public static ECP fromBytes(byte[] b)
{
byte[] t=new byte[CONFIG_BIG.MODBYTES];
BIG p=new BIG(ROM.Modulus);
for (int i=0;i<CONFIG_BIG.MODBYTES;i++) t[i]=b[i+1];
BIG px=BIG.fromBytes(t);
if (BIG.comp(px,p)>=0) return new ECP();
if (CONFIG_CURVE.CURVETYPE==CONFIG_CURVE.MONTGOMERY)
{
return new ECP(px);
}
if (b[0]==0x04)
{
for (int i=0;i<CONFIG_BIG.MODBYTES;i++) t[i]=b[i+CONFIG_BIG.MODBYTES+1];
BIG py=BIG.fromBytes(t);
if (BIG.comp(py,p)>=0) return new ECP();
return new ECP(px,py);
}
if (b[0]==0x02 || b[0]==0x03)
{
return new ECP(px,(int)(b[0]&1));
}
return new ECP();
}
/* convert to hex string */
public String toString() {
ECP W=new ECP(this);
W.affine();
if (W.is_infinity()) return "infinity";
if (CONFIG_CURVE.CURVETYPE==CONFIG_CURVE.MONTGOMERY) return "("+W.x.redc().toString()+")";
else return "("+W.x.redc().toString()+","+W.y.redc().toString()+")";
}
/* convert to hex string */
public String toRawString() {
ECP W=new ECP(this);
if (CONFIG_CURVE.CURVETYPE==CONFIG_CURVE.MONTGOMERY) return "("+W.x.redc().toString()+","+W.z.redc().toString()+")";
else return "("+W.x.redc().toString()+","+W.y.redc().toString()+","+W.z.redc().toString()+")";
}
/* this*=2 */
public void dbl() {
if (CONFIG_CURVE.CURVETYPE==CONFIG_CURVE.WEIERSTRASS)
{
if (ROM.CURVE_A==0)
{
FP t0=new FP(y); /*** Change ***/ // Edits made
t0.sqr();
FP t1=new FP(y);
t1.mul(z);
FP t2=new FP(z);
t2.sqr();
z.copy(t0);
z.add(t0); z.norm();
z.add(z); z.add(z); z.norm();
t2.imul(3*ROM.CURVE_B_I);
FP x3=new FP(t2);
x3.mul(z);
FP y3=new FP(t0);
y3.add(t2); y3.norm();
z.mul(t1);
t1.copy(t2); t1.add(t2); t2.add(t1);
t0.sub(t2); t0.norm(); y3.mul(t0); y3.add(x3);
t1.copy(x); t1.mul(y);
x.copy(t0); x.norm(); x.mul(t1); x.add(x);
x.norm();
y.copy(y3); y.norm();
}
else
{
FP t0=new FP(x);
FP t1=new FP(y);
FP t2=new FP(z);
FP t3=new FP(x);
FP z3=new FP(z);
FP y3=new FP();
FP x3=new FP();
FP b=new FP();
if (ROM.CURVE_B_I==0)
b.copy(new FP(new BIG(ROM.CURVE_B)));
t0.sqr(); //1 x^2
t1.sqr(); //2 y^2
t2.sqr(); //3
t3.mul(y); //4
t3.add(t3); t3.norm();//5
z3.mul(x); //6
z3.add(z3); z3.norm();//7
y3.copy(t2);
if (ROM.CURVE_B_I==0)
y3.mul(b); //8
else
y3.imul(ROM.CURVE_B_I);
y3.sub(z3); //y3.norm(); //9 ***
x3.copy(y3); x3.add(y3); x3.norm();//10
y3.add(x3); //y3.norm();//11
x3.copy(t1); x3.sub(y3); x3.norm();//12
y3.add(t1); y3.norm();//13
y3.mul(x3); //14
x3.mul(t3); //15
t3.copy(t2); t3.add(t2); //t3.norm(); //16
t2.add(t3); //t2.norm(); //17
if (ROM.CURVE_B_I==0)
z3.mul(b); //18
else
z3.imul(ROM.CURVE_B_I);
z3.sub(t2); //z3.norm();//19
z3.sub(t0); z3.norm();//20 ***
t3.copy(z3); t3.add(z3); //t3.norm();//21
z3.add(t3); z3.norm(); //22
t3.copy(t0); t3.add(t0); //t3.norm(); //23
t0.add(t3); //t0.norm();//24
t0.sub(t2); t0.norm();//25
t0.mul(z3);//26
y3.add(t0); //y3.norm();//27
t0.copy(y); t0.mul(z);//28
t0.add(t0); t0.norm(); //29
z3.mul(t0);//30
x3.sub(z3); //x3.norm();//31
t0.add(t0); t0.norm();//32
t1.add(t1); t1.norm();//33
z3.copy(t0); z3.mul(t1);//34
x.copy(x3); x.norm();
y.copy(y3); y.norm();
z.copy(z3); z.norm();
}
}
if (CONFIG_CURVE.CURVETYPE==CONFIG_CURVE.EDWARDS)
{
FP C=new FP(x);
FP D=new FP(y);
FP H=new FP(z);
FP J=new FP();
x.mul(y); x.add(x); x.norm();
C.sqr();
D.sqr();
if (ROM.CURVE_A==-1) C.neg();
y.copy(C); y.add(D); y.norm();
H.sqr(); H.add(H);
z.copy(y);
J.copy(y);
J.sub(H); J.norm();
x.mul(J);
C.sub(D); C.norm();
y.mul(C);
z.mul(J);
}
if (CONFIG_CURVE.CURVETYPE==CONFIG_CURVE.MONTGOMERY)
{
FP A=new FP(x);
FP B=new FP(x);
FP AA=new FP();
FP BB=new FP();
FP C=new FP();
A.add(z); A.norm();
AA.copy(A); AA.sqr();
B.sub(z); B.norm();
BB.copy(B); BB.sqr();
C.copy(AA); C.sub(BB); C.norm();
x.copy(AA); x.mul(BB);
A.copy(C); A.imul((ROM.CURVE_A+2)/4);
BB.add(A); BB.norm();
z.copy(BB); z.mul(C);
}
return;
}
/* this+=Q */
public void add(ECP Q) {
if (CONFIG_CURVE.CURVETYPE==CONFIG_CURVE.WEIERSTRASS)
{
if (ROM.CURVE_A==0)
{
int b=3*ROM.CURVE_B_I;
FP t0=new FP(x);
t0.mul(Q.x);
FP t1=new FP(y);
t1.mul(Q.y);
FP t2=new FP(z);
t2.mul(Q.z);
FP t3=new FP(x);
t3.add(y); t3.norm();
FP t4=new FP(Q.x);
t4.add(Q.y); t4.norm();
t3.mul(t4);
t4.copy(t0); t4.add(t1);
t3.sub(t4); t3.norm();
t4.copy(y);
t4.add(z); t4.norm();
FP x3=new FP(Q.y);
x3.add(Q.z); x3.norm();
t4.mul(x3);
x3.copy(t1);
x3.add(t2);
t4.sub(x3); t4.norm();
x3.copy(x); x3.add(z); x3.norm();
FP y3=new FP(Q.x);
y3.add(Q.z); y3.norm();
x3.mul(y3);
y3.copy(t0);
y3.add(t2);
y3.rsub(x3); y3.norm();
x3.copy(t0); x3.add(t0);
t0.add(x3); t0.norm();
t2.imul(b);
FP z3=new FP(t1); z3.add(t2); z3.norm();
t1.sub(t2); t1.norm();
y3.imul(b);
x3.copy(y3); x3.mul(t4); t2.copy(t3); t2.mul(t1); x3.rsub(t2);
y3.mul(t0); t1.mul(z3); y3.add(t1);
t0.mul(t3); z3.mul(t4); z3.add(t0);
x.copy(x3); x.norm();
y.copy(y3); y.norm();
z.copy(z3); z.norm();
}
else
{
FP t0=new FP(x);
FP t1=new FP(y);
FP t2=new FP(z);
FP t3=new FP(x);
FP t4=new FP(Q.x);
FP z3=new FP();
FP y3=new FP(Q.x);
FP x3=new FP(Q.y);
FP b=new FP();
if (ROM.CURVE_B_I==0)
b.copy(new FP(new BIG(ROM.CURVE_B)));
t0.mul(Q.x); //1
t1.mul(Q.y); //2
t2.mul(Q.z); //3
t3.add(y); t3.norm(); //4
t4.add(Q.y); t4.norm();//5
t3.mul(t4);//6
t4.copy(t0); t4.add(t1); //t4.norm(); //7
t3.sub(t4); t3.norm(); //8
t4.copy(y); t4.add(z); t4.norm();//9
x3.add(Q.z); x3.norm();//10
t4.mul(x3); //11
x3.copy(t1); x3.add(t2); //x3.norm();//12
t4.sub(x3); t4.norm();//13
x3.copy(x); x3.add(z); x3.norm(); //14
y3.add(Q.z); y3.norm();//15
x3.mul(y3); //16
y3.copy(t0); y3.add(t2); //y3.norm();//17
y3.rsub(x3); y3.norm(); //18
z3.copy(t2);
if (ROM.CURVE_B_I==0)
z3.mul(b); //18
else
z3.imul(ROM.CURVE_B_I);
x3.copy(y3); x3.sub(z3); x3.norm(); //20
z3.copy(x3); z3.add(x3); //z3.norm(); //21
x3.add(z3); //x3.norm(); //22
z3.copy(t1); z3.sub(x3); z3.norm(); //23
x3.add(t1); x3.norm(); //24
if (ROM.CURVE_B_I==0)
y3.mul(b); //18
else
y3.imul(ROM.CURVE_B_I);
t1.copy(t2); t1.add(t2); //t1.norm();//26
t2.add(t1); //t2.norm();//27
y3.sub(t2); //y3.norm(); //28
y3.sub(t0); y3.norm(); //29
t1.copy(y3); t1.add(y3); //t1.norm();//30
y3.add(t1); y3.norm(); //31
t1.copy(t0); t1.add(t0); //t1.norm(); //32
t0.add(t1); //t0.norm();//33
t0.sub(t2); t0.norm();//34
t1.copy(t4); t1.mul(y3);//35
t2.copy(t0); t2.mul(y3);//36
y3.copy(x3); y3.mul(z3);//37
y3.add(t2); //y3.norm();//38
x3.mul(t3);//39
x3.sub(t1);//40
z3.mul(t4);//41
t1.copy(t3); t1.mul(t0);//42
z3.add(t1);
x.copy(x3); x.norm();
y.copy(y3); y.norm();
z.copy(z3); z.norm();
}
}
if (CONFIG_CURVE.CURVETYPE==CONFIG_CURVE.EDWARDS)
{
FP A=new FP(z);
FP B=new FP();
FP C=new FP(x);
FP D=new FP(y);
FP E=new FP();
FP F=new FP();
FP G=new FP();
A.mul(Q.z);
B.copy(A); B.sqr();
C.mul(Q.x);
D.mul(Q.y);
E.copy(C); E.mul(D);
if (ROM.CURVE_B_I==0)
{
FP b=new FP(new BIG(ROM.CURVE_B));
E.mul(b);
}
else
E.imul(ROM.CURVE_B_I);
F.copy(B); F.sub(E);
G.copy(B); G.add(E);
if (ROM.CURVE_A==1)
{
E.copy(D); E.sub(C);
}
C.add(D);
B.copy(x); B.add(y);
D.copy(Q.x); D.add(Q.y); B.norm(); D.norm();
B.mul(D);
B.sub(C); B.norm(); F.norm();
B.mul(F);
x.copy(A); x.mul(B); G.norm();
if (ROM.CURVE_A==1)
{
E.norm(); C.copy(E); C.mul(G);
}
if (ROM.CURVE_A==-1)
{
C.norm(); C.mul(G);
}
y.copy(A); y.mul(C);
z.copy(F);
z.mul(G);
}
return;
}
/* Differential Add for CONFIG_CURVE.MONTGOMERY curves. this+=Q where W is this-Q and is affine. */
public void dadd(ECP Q,ECP W) {
FP A=new FP(x);
FP B=new FP(x);
FP C=new FP(Q.x);
FP D=new FP(Q.x);
FP DA=new FP();
FP CB=new FP();
A.add(z);
B.sub(z);
C.add(Q.z);
D.sub(Q.z);
A.norm();
D.norm();
DA.copy(D); DA.mul(A);
C.norm();
B.norm();
CB.copy(C); CB.mul(B);
A.copy(DA); A.add(CB);
A.norm(); A.sqr();
B.copy(DA); B.sub(CB);
B.norm(); B.sqr();
x.copy(A);
z.copy(W.x); z.mul(B);
}
/* this-=Q */
public void sub(ECP Q) {
ECP NQ=new ECP(Q);
NQ.neg();
add(NQ);
}
/* constant time multiply by small integer of length bts - use ladder */
public ECP pinmul(int e,int bts) {
if (CONFIG_CURVE.CURVETYPE==CONFIG_CURVE.MONTGOMERY)
return this.mul(new BIG(e));
else
{
int nb,i,b;
ECP P=new ECP();
ECP R0=new ECP();
ECP R1=new ECP(); R1.copy(this);
for (i=bts-1;i>=0;i--)
{
b=(e>>i)&1;
P.copy(R1);
P.add(R0);
R0.cswap(R1,b);
R1.copy(P);
R0.dbl();
R0.cswap(R1,b);
}
P.copy(R0);
P.affine();
return P;
}
}
/* return e.this */
public ECP mul(BIG e) {
if (e.iszilch() || is_infinity()) return new ECP();
ECP P=new ECP();
if (CONFIG_CURVE.CURVETYPE==CONFIG_CURVE.MONTGOMERY)
{
/* use Ladder */
int nb,i,b;
ECP D=new ECP();
ECP R0=new ECP(); R0.copy(this);
ECP R1=new ECP(); R1.copy(this);
R1.dbl();
D.copy(this); D.affine();
nb=e.nbits();
for (i=nb-2;i>=0;i--)
{
b=e.bit(i);
P.copy(R1);
P.dadd(R0,D);
R0.cswap(R1,b);
R1.copy(P);
R0.dbl();
R0.cswap(R1,b);
}
P.copy(R0);
}
else
{
// fixed size windows
int i,b,nb,m,s,ns;
BIG mt=new BIG();
BIG t=new BIG();
ECP Q=new ECP();
ECP C=new ECP();
ECP[] W=new ECP[8];
byte[] w=new byte[1+(BIG.NLEN*CONFIG_BIG.BASEBITS+3)/4];
// precompute table
Q.copy(this);
Q.dbl();
W[0]=new ECP();
W[0].copy(this);
for (i=1;i<8;i++)
{
W[i]=new ECP();
W[i].copy(W[i-1]);
W[i].add(Q);
}
// make exponent odd - add 2P if even, P if odd
t.copy(e);
s=t.parity();
t.inc(1); t.norm(); ns=t.parity(); mt.copy(t); mt.inc(1); mt.norm();
t.cmove(mt,s);
Q.cmove(this,ns);
C.copy(Q);
nb=1+(t.nbits()+3)/4;
// convert exponent to signed 4-bit window
for (i=0;i<nb;i++)
{
w[i]=(byte)(t.lastbits(5)-16);
t.dec(w[i]); t.norm();
t.fshr(4);
}
w[nb]=(byte)t.lastbits(5);
P.copy(W[(w[nb]-1)/2]);
for (i=nb-1;i>=0;i--)
{
Q.select(W,w[i]);
P.dbl();
P.dbl();
P.dbl();
P.dbl();
P.add(Q);
}
P.sub(C); /* apply correction */
}
P.affine();
return P;
}
/* Return e.this+f.Q */
public ECP mul2(BIG e,ECP Q,BIG f) {
BIG te=new BIG();
BIG tf=new BIG();
BIG mt=new BIG();
ECP S=new ECP();
ECP T=new ECP();
ECP C=new ECP();
ECP[] W=new ECP[8];
byte[] w=new byte[1+(BIG.NLEN*CONFIG_BIG.BASEBITS+1)/2];
int i,s,ns,nb;
byte a,b;
te.copy(e);
tf.copy(f);
// precompute table
W[1]=new ECP(); W[1].copy(this); W[1].sub(Q);
W[2]=new ECP(); W[2].copy(this); W[2].add(Q);
S.copy(Q); S.dbl();
W[0]=new ECP(); W[0].copy(W[1]); W[0].sub(S);
W[3]=new ECP(); W[3].copy(W[2]); W[3].add(S);
T.copy(this); T.dbl();
W[5]=new ECP(); W[5].copy(W[1]); W[5].add(T);
W[6]=new ECP(); W[6].copy(W[2]); W[6].add(T);
W[4]=new ECP(); W[4].copy(W[5]); W[4].sub(S);
W[7]=new ECP(); W[7].copy(W[6]); W[7].add(S);
// if multiplier is odd, add 2, else add 1 to multiplier, and add 2P or P to correction
s=te.parity();
te.inc(1); te.norm(); ns=te.parity(); mt.copy(te); mt.inc(1); mt.norm();
te.cmove(mt,s);
T.cmove(this,ns);
C.copy(T);
s=tf.parity();
tf.inc(1); tf.norm(); ns=tf.parity(); mt.copy(tf); mt.inc(1); mt.norm();
tf.cmove(mt,s);
S.cmove(Q,ns);
C.add(S);
mt.copy(te); mt.add(tf); mt.norm();
nb=1+(mt.nbits()+1)/2;
// convert exponent to signed 2-bit window
for (i=0;i<nb;i++)
{
a=(byte)(te.lastbits(3)-4);
te.dec(a); te.norm();
te.fshr(2);
b=(byte)(tf.lastbits(3)-4);
tf.dec(b); tf.norm();
tf.fshr(2);
w[i]=(byte)(4*a+b);
}
w[nb]=(byte)(4*te.lastbits(3)+tf.lastbits(3));
S.copy(W[(w[nb]-1)/2]);
for (i=nb-1;i>=0;i--)
{
T.select(W,w[i]);
S.dbl();
S.dbl();
S.add(T);
}
S.sub(C); /* apply correction */
S.affine();
return S;
}
// multiply a point by the curves cofactor
public void cfp()
{
int cf=ROM.CURVE_Cof_I;
if (cf==1) return;
if (cf==4)
{
dbl(); dbl();
//affine();
return;
}
if (cf==8)
{
dbl(); dbl(); dbl();
//affine();
return;
}
BIG c=new BIG(ROM.CURVE_Cof);
copy(mul(c));
}
/* Hash random Fp element to point on curve */
public static ECP hashit(BIG h)
{
ECP P;
if (CONFIG_CURVE.CURVETYPE==CONFIG_CURVE.MONTGOMERY)
{ // Elligator 2
FP X1=new FP();
FP X2=new FP();
FP t=new FP(h);
FP one=new FP(1);
FP A=new FP(ROM.CURVE_A);
t.sqr();
if (CONFIG_FIELD.PM1D2 == 2) {
t.add(t);
}
if (CONFIG_FIELD.PM1D2 == 1) {
t.neg();