| /* |
| 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. |
| */ |
| |
| package main |
| |
| //import "fmt" |
| |
| /* Elliptic Curve Point Structure */ |
| |
| type ECP struct { |
| x *FP |
| y *FP |
| z *FP |
| INF bool |
| } |
| |
| /* Constructors */ |
| func NewECP() *ECP { |
| E:=new(ECP) |
| E.x=NewFPint(0) |
| E.y=NewFPint(0) |
| E.z=NewFPint(0) |
| E.INF=true |
| return E |
| } |
| |
| /* set (x,y) from two BIGs */ |
| func NewECPbigs(ix *BIG,iy *BIG) *ECP { |
| E:=new(ECP) |
| E.x=NewFPbig(ix) |
| E.y=NewFPbig(iy) |
| E.z=NewFPint(1) |
| rhs:=RHS(E.x) |
| |
| if CURVETYPE==MONTGOMERY { |
| if rhs.jacobi()==1 { |
| E.INF=false |
| } else {E.inf()} |
| } else { |
| y2:=NewFPcopy(E.y) |
| y2.sqr() |
| if y2.equals(rhs) { |
| E.INF=false |
| } else {E.inf()} |
| } |
| return E |
| } |
| |
| /* set (x,y) from BIG and a bit */ |
| func NewECPbigint(ix *BIG,s int) *ECP { |
| E:=new(ECP) |
| E.x=NewFPbig(ix) |
| E.y=NewFPint(0) |
| rhs:=RHS(E.x) |
| E.z=NewFPint(1) |
| if rhs.jacobi()==1 { |
| ny:=rhs.sqrt() |
| if ny.redc().parity()!=s {ny.neg()} |
| E.y.copy(ny) |
| E.INF=false |
| } else {E.inf()} |
| return E; |
| } |
| |
| /* set from x - calculate y from curve equation */ |
| func NewECPbig(ix *BIG) *ECP { |
| E:=new(ECP) |
| E.x=NewFPbig(ix) |
| E.y=NewFPint(0) |
| rhs:=RHS(E.x) |
| E.z=NewFPint(1) |
| if rhs.jacobi()==1 { |
| if CURVETYPE!=MONTGOMERY {E.y.copy(rhs.sqrt())} |
| E.INF=false |
| } else {E.INF=true} |
| return E |
| } |
| |
| /* test for O point-at-infinity */ |
| func (E *ECP) is_infinity() bool { |
| if CURVETYPE==EDWARDS { |
| E.x.reduce(); E.y.reduce(); E.z.reduce() |
| return (E.x.iszilch() && E.y.equals(E.z)) |
| } else {return E.INF} |
| } |
| |
| /* Conditional swap of P and Q dependant on d */ |
| func (E *ECP) cswap(Q *ECP,d int) { |
| E.x.cswap(Q.x,d) |
| if CURVETYPE!=MONTGOMERY {E.y.cswap(Q.y,d)} |
| E.z.cswap(Q.z,d) |
| if CURVETYPE!=EDWARDS { |
| bd:=true |
| if d==0 {bd=false} |
| bd=bd&&(E.INF!=Q.INF) |
| E.INF=(bd!=E.INF) |
| Q.INF=(bd!=Q.INF) |
| } |
| } |
| |
| /* Conditional move of Q to P dependant on d */ |
| func (E *ECP) cmove(Q *ECP,d int) { |
| E.x.cmove(Q.x,d) |
| if CURVETYPE!=MONTGOMERY {E.y.cmove(Q.y,d)} |
| E.z.cmove(Q.z,d); |
| if CURVETYPE!=EDWARDS { |
| bd:=true |
| if d==0 {bd=false} |
| E.INF=(E.INF!=((E.INF!=Q.INF)&&bd)) |
| } |
| } |
| |
| /* return 1 if b==c, no branching */ |
| func teq(b int32,c int32) int { |
| x:=b^c |
| x-=1 // if x=0, x now -1 |
| return int((x>>31)&1) |
| } |
| |
| /* this=P */ |
| func (E *ECP) copy(P *ECP) { |
| E.x.copy(P.x); |
| if CURVETYPE!=MONTGOMERY {E.y.copy(P.y)} |
| E.z.copy(P.z); |
| E.INF=P.INF; |
| } |
| |
| /* this=-this */ |
| func (E *ECP) neg() { |
| if E.is_infinity() {return} |
| if CURVETYPE==WEIERSTRASS { |
| E.y.neg(); E.y.norm() |
| } |
| if CURVETYPE==EDWARDS { |
| E.x.neg(); E.x.norm() |
| } |
| return; |
| } |
| |
| /* Constant time select from pre-computed table */ |
| func (E *ECP) selector(W []*ECP,b int32) { |
| MP:=NewECP() |
| m:=b>>31; |
| babs:=(b^m)-m; |
| |
| babs=(babs-1)/2 |
| |
| E.cmove(W[0],teq(babs,0)) // conditional move |
| E.cmove(W[1],teq(babs,1)) |
| E.cmove(W[2],teq(babs,2)) |
| E.cmove(W[3],teq(babs,3)) |
| E.cmove(W[4],teq(babs,4)) |
| E.cmove(W[5],teq(babs,5)) |
| E.cmove(W[6],teq(babs,6)) |
| E.cmove(W[7],teq(babs,7)) |
| |
| MP.copy(E); |
| MP.neg() |
| E.cmove(MP,int(m&1)); |
| } |
| |
| /* set this=O */ |
| func (E *ECP) inf() { |
| E.INF=true; |
| E.x.zero() |
| E.y.one() |
| E.z.one() |
| } |
| |
| /* Test P == Q */ |
| func( E *ECP) equals(Q *ECP) bool { |
| if E.is_infinity() && Q.is_infinity() {return true} |
| if E.is_infinity() || Q.is_infinity() {return false} |
| if CURVETYPE==WEIERSTRASS { |
| zs2:=NewFPcopy(E.z); zs2.sqr() |
| zo2:=NewFPcopy(Q.z); zo2.sqr() |
| zs3:=NewFPcopy(zs2); zs3.mul(E.z) |
| zo3:=NewFPcopy(zo2); zo3.mul(Q.z) |
| zs2.mul(Q.x) |
| zo2.mul(E.x) |
| if !zs2.equals(zo2) {return false} |
| zs3.mul(Q.y) |
| zo3.mul(E.y) |
| if !zs3.equals(zo3) {return false} |
| } else { |
| a:=NewFPint(0) |
| b:=NewFPint(0) |
| a.copy(E.x); a.mul(Q.z); a.reduce() |
| b.copy(Q.x); b.mul(E.z); b.reduce() |
| if !a.equals(b) {return false} |
| if CURVETYPE==EDWARDS { |
| a.copy(E.y); a.mul(Q.z); a.reduce() |
| b.copy(Q.y); b.mul(E.z); b.reduce() |
| if !a.equals(b) {return false} |
| } |
| } |
| return true |
| } |
| |
| /* Calculate RHS of curve equation */ |
| func RHS(x *FP) *FP { |
| x.norm() |
| r:=NewFPcopy(x) |
| r.sqr(); |
| |
| if CURVETYPE==WEIERSTRASS { // x^3+Ax+B |
| b:=NewFPbig(NewBIGints(CURVE_B)) |
| r.mul(x); |
| if CURVE_A==-3 { |
| cx:=NewFPcopy(x) |
| cx.imul(3) |
| cx.neg(); cx.norm() |
| r.add(cx) |
| } |
| r.add(b) |
| } |
| if CURVETYPE==EDWARDS { // (Ax^2-1)/(Bx^2-1) |
| b:=NewFPbig(NewBIGints(CURVE_B)) |
| |
| one:=NewFPint(1) |
| b.mul(r) |
| b.sub(one) |
| if CURVE_A==-1 {r.neg()} |
| r.sub(one) |
| b.inverse() |
| r.mul(b) |
| } |
| if CURVETYPE==MONTGOMERY { // x^3+Ax^2+x |
| x3:=NewFPint(0) |
| x3.copy(r) |
| x3.mul(x) |
| r.imul(CURVE_A) |
| r.add(x3) |
| r.add(x) |
| } |
| r.reduce() |
| return r |
| } |
| |
| /* set to affine - from (x,y,z) to (x,y) */ |
| func (E *ECP) affine() { |
| if E.is_infinity() {return} |
| one:=NewFPint(1) |
| if E.z.equals(one) {return} |
| E.z.inverse() |
| if CURVETYPE==WEIERSTRASS { |
| z2:=NewFPcopy(E.z) |
| z2.sqr() |
| E.x.mul(z2); E.x.reduce() |
| E.y.mul(z2) |
| E.y.mul(E.z); E.y.reduce() |
| } |
| if CURVETYPE==EDWARDS { |
| E.x.mul(E.z); E.x.reduce() |
| E.y.mul(E.z); E.y.reduce() |
| } |
| if CURVETYPE==MONTGOMERY { |
| E.x.mul(E.z); E.x.reduce() |
| } |
| E.z.one() |
| } |
| |
| /* extract x as a BIG */ |
| func (E *ECP) getX() *BIG { |
| E.affine() |
| return E.x.redc() |
| } |
| /* extract y as a BIG */ |
| func (E *ECP) getY() *BIG { |
| E.affine() |
| return E.y.redc() |
| } |
| |
| /* get sign of Y */ |
| func (E *ECP) getS() int { |
| E.affine() |
| y:=E.getY() |
| return y.parity() |
| } |
| /* extract x as an FP */ |
| func (E *ECP) getx() *FP { |
| return E.x; |
| } |
| /* extract y as an FP */ |
| func (E *ECP) gety() *FP { |
| return E.y |
| } |
| /* extract z as an FP */ |
| func (E *ECP) getz() *FP { |
| return E.z |
| } |
| |
| /* convert to byte array */ |
| func (E *ECP) toBytes(b []byte) { |
| var t [int(MODBYTES)]byte |
| MB:=int(MODBYTES) |
| if CURVETYPE!=MONTGOMERY { |
| b[0]=0x04 |
| } else {b[0]=0x02} |
| |
| E.affine() |
| E.x.redc().toBytes(t[:]) |
| for i:=0;i<MB;i++ {b[i+1]=t[i]} |
| if CURVETYPE!=MONTGOMERY { |
| E.y.redc().toBytes(t[:]) |
| for i:=0;i<MB;i++ {b[i+MB+1]=t[i]} |
| } |
| } |
| |
| /* convert from byte array to point */ |
| func ECP_fromBytes(b []byte) *ECP { |
| var t [int(MODBYTES)]byte |
| MB:=int(MODBYTES) |
| p:=NewBIGints(Modulus) |
| |
| for i:=0;i<MB;i++ {t[i]=b[i+1]} |
| px:=fromBytes(t[:]) |
| if comp(px,p)>=0 {return NewECP()} |
| |
| if (b[0]==0x04) { |
| for i:=0;i<MB;i++ {t[i]=b[i+MB+1]} |
| py:=fromBytes(t[:]) |
| if comp(py,p)>=0 {return NewECP()} |
| return NewECPbigs(px,py) |
| } else {return NewECPbig(px)} |
| } |
| |
| /* convert to hex string */ |
| func (E *ECP) toString() string { |
| if E.is_infinity() {return "infinity"} |
| E.affine(); |
| if CURVETYPE==MONTGOMERY { |
| return "("+E.x.redc().toString()+")" |
| } else {return "("+E.x.redc().toString()+","+E.y.redc().toString()+")"} |
| } |
| |
| /* this*=2 */ |
| func (E *ECP) dbl() { |
| if CURVETYPE==WEIERSTRASS { |
| if E.INF {return} |
| if E.y.iszilch() { |
| E.inf() |
| return |
| } |
| |
| w1:=NewFPcopy(E.x); |
| w6:=NewFPcopy(E.z); |
| w2:=NewFPint(0); |
| w3:=NewFPcopy(E.x) |
| w8:=NewFPcopy(E.x) |
| |
| if CURVE_A==-3 { |
| w6.sqr() |
| w1.copy(w6) |
| w1.neg() |
| w3.add(w1) |
| |
| w8.add(w6) |
| |
| w3.mul(w8) |
| w8.copy(w3) |
| w8.imul(3) |
| } else { |
| w1.sqr() |
| w8.copy(w1) |
| w8.imul(3) |
| } |
| |
| w2.copy(E.y); w2.sqr() |
| w3.copy(E.x); w3.mul(w2) |
| w3.imul(4) |
| w1.copy(w3); w1.neg() |
| // w1.norm(); |
| |
| |
| E.x.copy(w8); E.x.sqr() |
| E.x.add(w1) |
| E.x.add(w1) |
| // x.reduce(); |
| E.x.norm() |
| |
| E.z.mul(E.y) |
| E.z.add(E.z) |
| |
| w2.add(w2) |
| w2.sqr() |
| w2.add(w2) |
| w3.sub(E.x) |
| E.y.copy(w8); E.y.mul(w3); |
| // w2.norm(); |
| E.y.sub(w2) |
| // y.reduce(); |
| // z.reduce(); |
| E.y.norm() |
| E.z.norm() |
| |
| } |
| if CURVETYPE==EDWARDS { |
| C:=NewFPcopy(E.x) |
| D:=NewFPcopy(E.y) |
| H:=NewFPcopy(E.z) |
| J:=NewFPint(0) |
| |
| E.x.mul(E.y); E.x.add(E.x) |
| C.sqr() |
| D.sqr() |
| if CURVE_A==-1 {C.neg()} |
| E.y.copy(C); E.y.add(D) |
| // y.norm(); |
| H.sqr(); H.add(H) |
| E.z.copy(E.y) |
| J.copy(E.y); J.sub(H) |
| E.x.mul(J) |
| C.sub(D) |
| E.y.mul(C) |
| E.z.mul(J) |
| |
| E.x.norm() |
| E.y.norm() |
| E.z.norm() |
| } |
| if CURVETYPE==MONTGOMERY { |
| A:=NewFPcopy(E.x) |
| B:=NewFPcopy(E.x) |
| AA:=NewFPint(0) |
| BB:=NewFPint(0) |
| C:=NewFPint(0) |
| |
| if E.INF {return} |
| |
| A.add(E.z) |
| AA.copy(A); AA.sqr() |
| B.sub(E.z) |
| BB.copy(B); BB.sqr() |
| C.copy(AA); C.sub(BB) |
| // C.norm(); |
| |
| E.x.copy(AA); E.x.mul(BB) |
| |
| A.copy(C); A.imul((CURVE_A+2)/4) |
| |
| BB.add(A) |
| E.z.copy(BB); E.z.mul(C) |
| // x.reduce(); |
| // z.reduce(); |
| E.x.norm() |
| E.z.norm() |
| } |
| return; |
| } |
| |
| /* this+=Q */ |
| func (E *ECP) add(Q *ECP) { |
| if CURVETYPE==WEIERSTRASS { |
| if E.INF { |
| E.copy(Q) |
| return |
| } |
| if Q.INF {return} |
| |
| aff:=false |
| |
| one:=NewFPint(1) |
| if Q.z.equals(one) {aff=true} |
| |
| var A,C *FP |
| B:=NewFPcopy(E.z) |
| D:=NewFPcopy(E.z) |
| if !aff { |
| A=NewFPcopy(Q.z) |
| C=NewFPcopy(Q.z) |
| |
| A.sqr(); B.sqr() |
| C.mul(A); D.mul(B) |
| |
| A.mul(E.x) |
| C.mul(E.y) |
| } else { |
| A=NewFPcopy(E.x) |
| C=NewFPcopy(E.y) |
| |
| B.sqr() |
| D.mul(B) |
| } |
| |
| B.mul(Q.x); B.sub(A) |
| D.mul(Q.y); D.sub(C) |
| |
| if B.iszilch() { |
| if D.iszilch() { |
| E.dbl() |
| return |
| } else { |
| E.INF=true |
| return |
| } |
| } |
| |
| if !aff {E.z.mul(Q.z)} |
| E.z.mul(B) |
| |
| e:=NewFPcopy(B); e.sqr() |
| B.mul(e) |
| A.mul(e) |
| |
| e.copy(A) |
| e.add(A); e.add(B) |
| E.x.copy(D); E.x.sqr(); E.x.sub(e); |
| |
| A.sub(E.x); |
| E.y.copy(A); E.y.mul(D) |
| C.mul(B); E.y.sub(C) |
| |
| // x.reduce(); |
| // y.reduce(); |
| // z.reduce(); |
| E.x.norm() |
| E.y.norm() |
| E.z.norm() |
| } |
| if CURVETYPE==EDWARDS { |
| b:=NewFPbig(NewBIGints(CURVE_B)) |
| A:=NewFPcopy(E.z) |
| B:=NewFPint(0) |
| C:=NewFPcopy(E.x) |
| D:=NewFPcopy(E.y) |
| EE:=NewFPint(0) |
| F:=NewFPint(0) |
| G:=NewFPint(0) |
| //H:=NewFPint(0) |
| //I:=NewFPint(0) |
| |
| A.mul(Q.z); |
| B.copy(A); B.sqr() |
| C.mul(Q.x) |
| D.mul(Q.y) |
| |
| EE.copy(C); EE.mul(D); EE.mul(b) |
| F.copy(B); F.sub(EE) |
| G.copy(B); G.add(EE) |
| |
| if CURVE_A==1 { |
| EE.copy(D); EE.sub(C) |
| } |
| C.add(D) |
| |
| B.copy(E.x); B.add(E.y) |
| D.copy(Q.x); D.add(Q.y) |
| B.mul(D) |
| B.sub(C) |
| B.mul(F) |
| E.x.copy(A); E.x.mul(B) |
| |
| if CURVE_A==1 { |
| C.copy(EE); C.mul(G) |
| } |
| if CURVE_A==-1 { |
| C.mul(G) |
| } |
| E.y.copy(A); E.y.mul(C) |
| E.z.copy(F); E.z.mul(G) |
| // x.reduce(); y.reduce(); z.reduce(); |
| E.x.norm(); E.y.norm(); E.z.norm() |
| } |
| return |
| } |
| |
| /* Differential Add for Montgomery curves. this+=Q where W is this-Q and is affine. */ |
| func (E *ECP) dadd(Q *ECP,W *ECP) { |
| A:=NewFPcopy(E.x) |
| B:=NewFPcopy(E.x) |
| C:=NewFPcopy(Q.x) |
| D:=NewFPcopy(Q.x) |
| DA:=NewFPint(0) |
| CB:=NewFPint(0) |
| |
| A.add(E.z) |
| B.sub(E.z) |
| |
| C.add(Q.z) |
| D.sub(Q.z) |
| |
| DA.copy(D); DA.mul(A) |
| CB.copy(C); CB.mul(B) |
| |
| A.copy(DA); A.add(CB); A.sqr() |
| B.copy(DA); B.sub(CB); B.sqr() |
| |
| E.x.copy(A) |
| E.z.copy(W.x); E.z.mul(B) |
| |
| if E.z.iszilch() { |
| E.inf() |
| } else {E.INF=false;} |
| |
| // x.reduce(); |
| E.x.norm(); |
| } |
| |
| /* this-=Q */ |
| func (E *ECP) sub(Q *ECP) { |
| Q.neg() |
| E.add(Q) |
| Q.neg() |
| } |
| |
| func multiaffine(m int,P []*ECP) { |
| t1:=NewFPint(0) |
| t2:=NewFPint(0) |
| |
| var work []*FP |
| |
| for i:=0;i<m;i++ { |
| work=append(work,NewFPint(0)) |
| } |
| |
| work[0].one() |
| work[1].copy(P[0].z) |
| |
| for i:=2;i<m;i++ { |
| work[i].copy(work[i-1]) |
| work[i].mul(P[i-1].z) |
| } |
| |
| t1.copy(work[m-1]) |
| t1.mul(P[m-1].z) |
| t1.inverse() |
| t2.copy(P[m-1].z) |
| work[m-1].mul(t1) |
| |
| for i:=m-2;;i-- { |
| if i==0 { |
| work[0].copy(t1) |
| work[0].mul(t2) |
| break |
| } |
| work[i].mul(t2) |
| work[i].mul(t1) |
| t2.mul(P[i].z) |
| } |
| /* now work[] contains inverses of all Z coordinates */ |
| |
| for i:=0;i<m;i++ { |
| P[i].z.one() |
| t1.copy(work[i]) |
| t1.sqr() |
| P[i].x.mul(t1) |
| t1.mul(work[i]) |
| P[i].y.mul(t1) |
| } |
| } |
| |
| /* constant time multiply by small integer of length bts - use ladder */ |
| func (E *ECP) pinmul(e int32,bts int32) *ECP { |
| if CURVETYPE==MONTGOMERY { |
| return E.mul(NewBIGint(int(e))) |
| } else { |
| P:=NewECP() |
| R0:=NewECP() |
| R1:=NewECP(); R1.copy(E) |
| |
| for i:=bts-1;i>=0;i-- { |
| b:=int((e>>uint32(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 */ |
| |
| func (E *ECP) mul(e *BIG) *ECP { |
| if (e.iszilch() || E.is_infinity()) {return NewECP()} |
| P:=NewECP() |
| if CURVETYPE==MONTGOMERY { |
| /* use Ladder */ |
| D:=NewECP(); |
| R0:=NewECP(); R0.copy(E) |
| R1:=NewECP(); R1.copy(E) |
| R1.dbl() |
| D.copy(E); D.affine() |
| nb:=e.nbits() |
| for i:=nb-2;i>=0;i-- { |
| b:=int(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 |
| mt:=NewBIG() |
| t:=NewBIG() |
| Q:=NewECP() |
| C:=NewECP() |
| |
| var W []*ECP |
| var w [1+(NLEN*int(BASEBITS)+3)/4]int8 |
| |
| E.affine(); |
| |
| Q.copy(E); |
| Q.dbl(); |
| |
| W=append(W,NewECP()); |
| W[0].copy(E); |
| |
| for i:=1;i<8;i++ { |
| W=append(W,NewECP()) |
| W[i].copy(W[i-1]) |
| W[i].add(Q) |
| } |
| |
| |
| // convert the table to affine |
| if CURVETYPE==WEIERSTRASS { |
| multiaffine(8,W[:]) |
| } |
| |
| |
| // make exponent odd - add 2P if even, P if odd |
| t.copy(e) |
| s:=int(t.parity()) |
| t.inc(1); t.norm(); ns:=int(t.parity()); mt.copy(t); mt.inc(1); mt.norm() |
| t.cmove(mt,s) |
| Q.cmove(E,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]=int8(t.lastbits(5)-16) |
| t.dec(int(w[i])); t.norm() |
| t.fshr(4) |
| } |
| w[nb]=int8(t.lastbits(5)) |
| |
| P.copy(W[(int(w[nb])-1)/2]) |
| for i:=nb-1;i>=0;i-- { |
| Q.selector(W,int32(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 */ |
| |
| func (E *ECP) mul2(e *BIG,Q *ECP,f *BIG) *ECP { |
| te:=NewBIG() |
| tf:=NewBIG() |
| mt:=NewBIG() |
| S:=NewECP() |
| T:=NewECP() |
| C:=NewECP() |
| var W [] *ECP |
| //ECP[] W=new ECP[8]; |
| var w [1+(NLEN*int(BASEBITS)+1)/2]int8 |
| |
| E.affine() |
| Q.affine() |
| |
| te.copy(e) |
| tf.copy(f) |
| |
| // precompute table |
| for i:=0;i<8;i++ { |
| W=append(W,NewECP()) |
| } |
| W[1].copy(E); W[1].sub(Q) |
| W[2].copy(E); W[2].add(Q); |
| S.copy(Q); S.dbl(); |
| W[0].copy(W[1]); W[0].sub(S); |
| W[3].copy(W[2]); W[3].add(S); |
| T.copy(E); T.dbl(); |
| W[5].copy(W[1]); W[5].add(T); |
| W[6].copy(W[2]); W[6].add(T); |
| W[4].copy(W[5]); W[4].sub(S); |
| W[7].copy(W[6]); W[7].add(S); |
| |
| // convert the table to affine |
| if CURVETYPE==WEIERSTRASS { |
| multiaffine(8,W) |
| } |
| |
| // if multiplier is odd, add 2, else add 1 to multiplier, and add 2P or P to correction |
| |
| s:=int(te.parity()); |
| te.inc(1); te.norm(); ns:=int(te.parity()); mt.copy(te); mt.inc(1); mt.norm() |
| te.cmove(mt,s) |
| T.cmove(E,ns) |
| C.copy(T) |
| |
| s=int(tf.parity()) |
| tf.inc(1); tf.norm(); ns=int(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:=(te.lastbits(3)-4) |
| te.dec(int(a)); te.norm() |
| te.fshr(2) |
| b:=(tf.lastbits(3)-4) |
| tf.dec(int(b)); tf.norm() |
| tf.fshr(2) |
| w[i]=int8(4*a+b) |
| } |
| w[nb]=int8(4*te.lastbits(3)+tf.lastbits(3)) |
| S.copy(W[(w[nb]-1)/2]) |
| |
| for i:=nb-1;i>=0;i-- { |
| T.selector(W,int32(w[i])); |
| S.dbl() |
| S.dbl() |
| S.add(T) |
| } |
| S.sub(C) /* apply correction */ |
| S.affine() |
| return S |
| } |
| |
| /* |
| func main() { |
| Gx:=NewBIGints(CURVE_Gx); |
| var Gy *BIG |
| var P *ECP |
| |
| if CURVETYPE!=MONTGOMERY {Gy=NewBIGints(CURVE_Gy)} |
| r:=NewBIGints(CURVE_Order) |
| |
| //r.dec(7); |
| |
| fmt.Printf("Gx= "+Gx.toString()) |
| fmt.Printf("\n") |
| |
| if CURVETYPE!=MONTGOMERY { |
| fmt.Printf("Gy= "+Gy.toString()) |
| fmt.Printf("\n") |
| } |
| |
| if CURVETYPE!=MONTGOMERY { |
| P=NewECPbigs(Gx,Gy) |
| } else {P=NewECPbig(Gx)} |
| |
| fmt.Printf("P= "+P.toString()); |
| fmt.Printf("\n") |
| |
| R:=P.mul(r); |
| //for (int i=0;i<10000;i++) |
| // R=P.mul(r); |
| |
| fmt.Printf("R= "+R.toString()) |
| fmt.Printf("\n") |
| } |
| */ |