| /* | |
| 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. | |
| */ | |
| // | |
| // ecp.swift | |
| // | |
| // | |
| // Created by Michael Scott on 30/06/2015. | |
| // Copyright (c) 2015 Michael Scott. All rights reserved. | |
| // | |
| final class ECP { | |
| private var x:FP | |
| private var y:FP | |
| private var z:FP | |
| private var INF:Bool | |
| /* Constructor - set to O */ | |
| init() | |
| { | |
| x=FP(0) | |
| y=FP(0) | |
| z=FP(1) | |
| INF=true | |
| } | |
| /* test for O point-at-infinity */ | |
| func is_infinity() -> Bool | |
| { | |
| if (ROM.CURVETYPE==ROM.EDWARDS) | |
| { | |
| x.reduce(); y.reduce(); z.reduce() | |
| return x.iszilch() && y.equals(z) | |
| } | |
| else {return INF} | |
| } | |
| /* Conditional swap of P and Q dependant on d */ | |
| private func cswap(Q: ECP,_ d:Int32) | |
| { | |
| x.cswap(Q.x,d); | |
| if ROM.CURVETYPE != ROM.MONTGOMERY {y.cswap(Q.y,d)} | |
| z.cswap(Q.z,d); | |
| if (ROM.CURVETYPE != ROM.EDWARDS) | |
| { | |
| var bd:Bool | |
| if d==0 {bd=false} | |
| else {bd=true} | |
| bd=bd && (INF != Q.INF) | |
| INF = (INF != bd) | |
| Q.INF = (Q.INF != bd) | |
| } | |
| } | |
| /* Conditional move of Q to P dependant on d */ | |
| private func cmove(Q: ECP,_ d:Int32) | |
| { | |
| x.cmove(Q.x,d); | |
| if ROM.CURVETYPE != ROM.MONTGOMERY {y.cmove(Q.y,d)} | |
| z.cmove(Q.z,d); | |
| if (ROM.CURVETYPE != ROM.EDWARDS) | |
| { | |
| var bd:Bool | |
| if d==0 {bd=false} | |
| else {bd=true} | |
| INF != (INF != Q.INF) && bd; | |
| } | |
| } | |
| /* return 1 if b==c, no branching */ | |
| private static func teq(b: Int32,_ c:Int32) -> Int32 | |
| { | |
| var x=b^c | |
| x-=1 // if x=0, x now -1 | |
| return ((x>>31)&1) | |
| } | |
| /* self=P */ | |
| func copy(P: ECP) | |
| { | |
| x.copy(P.x) | |
| if ROM.CURVETYPE != ROM.MONTGOMERY {y.copy(P.y)} | |
| z.copy(P.z) | |
| INF=P.INF | |
| } | |
| /* self=-self */ | |
| func neg() { | |
| if is_infinity() {return} | |
| if (ROM.CURVETYPE==ROM.WEIERSTRASS) | |
| { | |
| y.neg(); y.norm(); | |
| } | |
| if (ROM.CURVETYPE==ROM.EDWARDS) | |
| { | |
| x.neg(); x.norm(); | |
| } | |
| return; | |
| } | |
| /* Constant time select from pre-computed table */ | |
| private func select(W:[ECP],_ b:Int32) | |
| { | |
| let MP=ECP() | |
| let m=b>>31 | |
| var babs=(b^m)-m | |
| babs=(babs-1)/2 | |
| cmove(W[0],ECP.teq(babs,0)); // conditional move | |
| cmove(W[1],ECP.teq(babs,1)) | |
| cmove(W[2],ECP.teq(babs,2)) | |
| cmove(W[3],ECP.teq(babs,3)) | |
| cmove(W[4],ECP.teq(babs,4)) | |
| cmove(W[5],ECP.teq(babs,5)) | |
| cmove(W[6],ECP.teq(babs,6)) | |
| cmove(W[7],ECP.teq(babs,7)) | |
| MP.copy(self) | |
| MP.neg() | |
| cmove(MP,(m&1)) | |
| } | |
| /* Test P == Q */ | |
| func equals(Q: ECP) -> Bool | |
| { | |
| if (is_infinity() && Q.is_infinity()) {return true} | |
| if (is_infinity() || Q.is_infinity()) {return false} | |
| if (ROM.CURVETYPE==ROM.WEIERSTRASS) | |
| { | |
| let zs2=FP(z); zs2.sqr() | |
| let zo2=FP(Q.z); zo2.sqr() | |
| let zs3=FP(zs2); zs3.mul(z) | |
| let zo3=FP(zo2); zo3.mul(Q.z) | |
| zs2.mul(Q.x) | |
| zo2.mul(x) | |
| if !zs2.equals(zo2) {return false} | |
| zs3.mul(Q.y) | |
| zo3.mul(y) | |
| if !zs3.equals(zo3) {return false} | |
| } | |
| else | |
| { | |
| let a=FP(0) | |
| let b=FP(0) | |
| a.copy(x); a.mul(Q.z); a.reduce() | |
| b.copy(Q.x); b.mul(z); b.reduce() | |
| if !a.equals(b) {return false} | |
| if ROM.CURVETYPE==ROM.EDWARDS | |
| { | |
| a.copy(y); a.mul(Q.z); a.reduce() | |
| b.copy(Q.y); b.mul(z); b.reduce() | |
| if !a.equals(b) {return false} | |
| } | |
| } | |
| return true | |
| } | |
| /* set self=O */ | |
| func inf() | |
| { | |
| INF=true; | |
| x.zero() | |
| y.one() | |
| z.one() | |
| } | |
| /* Calculate RHS of curve equation */ | |
| static func RHS(x: FP) -> FP | |
| { | |
| x.norm(); | |
| let r=FP(x); | |
| r.sqr(); | |
| if ROM.CURVETYPE==ROM.WEIERSTRASS | |
| { // x^3+Ax+B | |
| let b=FP(BIG(ROM.CURVE_B)) | |
| r.mul(x) | |
| if (ROM.CURVE_A == -3) | |
| { | |
| let cx=FP(x) | |
| cx.imul(3) | |
| cx.neg(); cx.norm() | |
| r.add(cx) | |
| } | |
| r.add(b); | |
| } | |
| if (ROM.CURVETYPE==ROM.EDWARDS) | |
| { // (Ax^2-1)/(Bx^2-1) | |
| let b=FP(BIG(ROM.CURVE_B)) | |
| let one=FP(1); | |
| b.mul(r); | |
| b.sub(one); | |
| if ROM.CURVE_A == -1 {r.neg()} | |
| r.sub(one) | |
| b.inverse() | |
| r.mul(b); | |
| } | |
| if ROM.CURVETYPE==ROM.MONTGOMERY | |
| { // x^3+Ax^2+x | |
| let x3=FP(0) | |
| 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 */ | |
| init(_ ix: BIG,_ iy: BIG) | |
| { | |
| x=FP(ix) | |
| y=FP(iy) | |
| z=FP(1) | |
| INF=true | |
| let rhs=ECP.RHS(x); | |
| if ROM.CURVETYPE==ROM.MONTGOMERY | |
| { | |
| if rhs.jacobi()==1 {INF=false} | |
| else {inf()} | |
| } | |
| else | |
| { | |
| let y2=FP(y) | |
| y2.sqr() | |
| if y2.equals(rhs) {INF=false} | |
| else {inf()} | |
| } | |
| } | |
| /* set (x,y) from BIG and a bit */ | |
| init(_ ix: BIG,_ s:Int32) | |
| { | |
| x=FP(ix) | |
| let rhs=ECP.RHS(x) | |
| y=FP(0) | |
| z=FP(1) | |
| INF=true | |
| if rhs.jacobi()==1 | |
| { | |
| let ny=rhs.sqrt() | |
| if (ny.redc().parity() != s) {ny.neg()} | |
| y.copy(ny) | |
| INF=false; | |
| } | |
| else {inf()} | |
| } | |
| /* set from x - calculate y from curve equation */ | |
| init(_ ix:BIG) | |
| { | |
| x=FP(ix) | |
| let rhs=ECP.RHS(x) | |
| y=FP(0) | |
| z=FP(1) | |
| if rhs.jacobi()==1 | |
| { | |
| if ROM.CURVETYPE != ROM.MONTGOMERY {y.copy(rhs.sqrt())} | |
| INF=false; | |
| } | |
| else {INF=true} | |
| } | |
| /* set to affine - from (x,y,z) to (x,y) */ | |
| func affine() | |
| { | |
| if is_infinity() {return} | |
| let one=FP(1) | |
| if (z.equals(one)) {return} | |
| z.inverse() | |
| if ROM.CURVETYPE==ROM.WEIERSTRASS | |
| { | |
| let z2=FP(z) | |
| z2.sqr() | |
| x.mul(z2); x.reduce() | |
| y.mul(z2) | |
| y.mul(z); y.reduce() | |
| } | |
| if ROM.CURVETYPE==ROM.EDWARDS | |
| { | |
| x.mul(z); x.reduce() | |
| y.mul(z); y.reduce() | |
| } | |
| if ROM.CURVETYPE==ROM.MONTGOMERY | |
| { | |
| x.mul(z); x.reduce() | |
| } | |
| z.copy(one) | |
| } | |
| /* extract x as a BIG */ | |
| func getX() -> BIG | |
| { | |
| affine() | |
| return x.redc() | |
| } | |
| /* extract y as a BIG */ | |
| func getY() -> BIG | |
| { | |
| affine(); | |
| return y.redc(); | |
| } | |
| /* get sign of Y */ | |
| func getS() -> Int32 | |
| { | |
| affine() | |
| let y=getY() | |
| return y.parity() | |
| } | |
| /* extract x as an FP */ | |
| func getx() -> FP | |
| { | |
| return x; | |
| } | |
| /* extract y as an FP */ | |
| func gety() -> FP | |
| { | |
| return y; | |
| } | |
| /* extract z as an FP */ | |
| func getz() -> FP | |
| { | |
| return z; | |
| } | |
| /* convert to byte array */ | |
| func toBytes(inout b:[UInt8]) | |
| { | |
| let RM=Int(ROM.MODBYTES) | |
| var t=[UInt8](count:RM,repeatedValue:0) | |
| if ROM.CURVETYPE != ROM.MONTGOMERY {b[0]=0x04} | |
| else {b[0]=0x02} | |
| affine() | |
| x.redc().toBytes(&t) | |
| for var i=0;i<RM;i++ {b[i+1]=t[i]} | |
| if ROM.CURVETYPE != ROM.MONTGOMERY | |
| { | |
| y.redc().toBytes(&t); | |
| for var i=0;i<RM;i++ {b[i+RM+1]=t[i]} | |
| } | |
| } | |
| /* convert from byte array to point */ | |
| static func fromBytes(b: [UInt8]) -> ECP | |
| { | |
| let RM=Int(ROM.MODBYTES) | |
| var t=[UInt8](count:RM,repeatedValue:0) | |
| let p=BIG(ROM.Modulus); | |
| for var i=0;i<RM;i++ {t[i]=b[i+1]} | |
| let px=BIG.fromBytes(t) | |
| if BIG.comp(px,p)>=0 {return ECP()} | |
| if (b[0]==0x04) | |
| { | |
| for var i=0;i<RM;i++ {t[i]=b[i+RM+1]} | |
| let py=BIG.fromBytes(t) | |
| if BIG.comp(py,p)>=0 {return ECP()} | |
| return ECP(px,py) | |
| } | |
| else {return ECP(px)} | |
| } | |
| /* convert to hex string */ | |
| func toString() -> String | |
| { | |
| if is_infinity() {return "infinity"} | |
| affine(); | |
| if ROM.CURVETYPE==ROM.MONTGOMERY {return "("+x.redc().toString()+")"} | |
| else {return "("+x.redc().toString()+","+y.redc().toString()+")"} | |
| } | |
| /* self*=2 */ | |
| func dbl() | |
| { | |
| if (ROM.CURVETYPE==ROM.WEIERSTRASS) | |
| { | |
| if INF {return} | |
| if y.iszilch() | |
| { | |
| inf() | |
| return | |
| } | |
| let w1=FP(x) | |
| let w6=FP(z) | |
| let w2=FP(0) | |
| let w3=FP(x) | |
| let w8=FP(x) | |
| if (ROM.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(y); w2.sqr() | |
| w3.copy(x); w3.mul(w2) | |
| w3.imul(4) | |
| w1.copy(w3); w1.neg() | |
| w1.norm() | |
| x.copy(w8); x.sqr() | |
| x.add(w1) | |
| x.add(w1) | |
| x.norm() | |
| z.mul(y) | |
| z.add(z) | |
| w2.add(w2) | |
| w2.sqr() | |
| w2.add(w2) | |
| w3.sub(x) | |
| y.copy(w8); y.mul(w3) | |
| //w2.norm(); | |
| y.sub(w2) | |
| y.norm() | |
| z.norm() | |
| } | |
| if ROM.CURVETYPE==ROM.EDWARDS | |
| { | |
| let C=FP(x) | |
| let D=FP(y) | |
| let H=FP(z) | |
| let J=FP(0) | |
| x.mul(y); x.add(x) | |
| 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) | |
| x.mul(J) | |
| C.sub(D) | |
| y.mul(C) | |
| z.mul(J) | |
| x.norm(); | |
| y.norm(); | |
| z.norm(); | |
| } | |
| if ROM.CURVETYPE==ROM.MONTGOMERY | |
| { | |
| let A=FP(x) | |
| let B=FP(x); | |
| let AA=FP(0); | |
| let BB=FP(0); | |
| let C=FP(0); | |
| if INF {return} | |
| A.add(z) | |
| AA.copy(A); AA.sqr() | |
| B.sub(z) | |
| 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) | |
| z.copy(BB); z.mul(C) | |
| x.norm() | |
| z.norm() | |
| } | |
| return | |
| } | |
| /* self+=Q */ | |
| func add(Q:ECP) | |
| { | |
| if ROM.CURVETYPE==ROM.WEIERSTRASS | |
| { | |
| if (INF) | |
| { | |
| copy(Q) | |
| return | |
| } | |
| if Q.INF {return} | |
| var aff=false; | |
| let one=FP(1); | |
| if Q.z.equals(one) {aff=true} | |
| var A:FP | |
| var C:FP | |
| let B=FP(z) | |
| let D=FP(z) | |
| if (!aff) | |
| { | |
| A=FP(Q.z) | |
| C=FP(Q.z) | |
| A.sqr(); B.sqr() | |
| C.mul(A); D.mul(B) | |
| A.mul(x) | |
| C.mul(y) | |
| } | |
| else | |
| { | |
| A=FP(x) | |
| C=FP(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()) | |
| { | |
| dbl() | |
| return | |
| } | |
| else | |
| { | |
| INF=true | |
| return | |
| } | |
| } | |
| if !aff {z.mul(Q.z)} | |
| z.mul(B); | |
| let e=FP(B); e.sqr() | |
| B.mul(e) | |
| A.mul(e) | |
| e.copy(A) | |
| e.add(A); e.add(B) | |
| x.copy(D); x.sqr(); x.sub(e) | |
| A.sub(x) | |
| y.copy(A); y.mul(D) | |
| C.mul(B); y.sub(C) | |
| x.norm() | |
| y.norm() | |
| z.norm() | |
| } | |
| if ROM.CURVETYPE==ROM.EDWARDS | |
| { | |
| let b=FP(BIG(ROM.CURVE_B)) | |
| let A=FP(z) | |
| let B=FP(0) | |
| let C=FP(x) | |
| let D=FP(y) | |
| let E=FP(0) | |
| let F=FP(0) | |
| let G=FP(0) | |
| A.mul(Q.z) | |
| B.copy(A); B.sqr() | |
| C.mul(Q.x) | |
| D.mul(Q.y) | |
| E.copy(C); E.mul(D); E.mul(b) | |
| F.copy(B); F.sub(E) | |
| G.copy(B); G.add(E) | |
| C.add(D) | |
| if ROM.CURVE_A==1 | |
| { | |
| E.copy(D); D.sub(C) | |
| } | |
| B.copy(x); B.add(y) | |
| D.copy(Q.x); D.add(Q.y) | |
| B.mul(D) | |
| B.sub(C) | |
| B.mul(F) | |
| x.copy(A); x.mul(B) | |
| if ROM.CURVE_A==1 | |
| { | |
| C.copy(E); C.mul(G) | |
| } | |
| if ROM.CURVE_A == -1 | |
| { | |
| C.mul(G) | |
| } | |
| y.copy(A); y.mul(C) | |
| z.copy(F); z.mul(G) | |
| x.norm(); y.norm(); z.norm() | |
| } | |
| return; | |
| } | |
| /* Differential Add for Montgomery curves. self+=Q where W is self-Q and is affine. */ | |
| func dadd(Q:ECP,_ W:ECP) | |
| { | |
| let A=FP(x) | |
| let B=FP(x) | |
| let C=FP(Q.x) | |
| let D=FP(Q.x) | |
| let DA=FP(0) | |
| let CB=FP(0) | |
| A.add(z) | |
| B.sub(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() | |
| x.copy(A) | |
| z.copy(W.x); z.mul(B) | |
| if z.iszilch() {inf()} | |
| else {INF=false} | |
| x.norm() | |
| } | |
| /* this-=Q */ | |
| func sub(Q:ECP) | |
| { | |
| Q.neg() | |
| add(Q) | |
| Q.neg() | |
| } | |
| static func multiaffine(m: Int,_ P:[ECP]) | |
| { | |
| let t1=FP(0) | |
| let t2=FP(0) | |
| var work=[FP]() | |
| for var i=0;i<m;i++ | |
| {work.append(FP(0))} | |
| work[0].one() | |
| work[1].copy(P[0].z) | |
| for var 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 var 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 var 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 pinmul(e:Int32,_ bts:Int32) -> ECP | |
| { | |
| if ROM.CURVETYPE==ROM.MONTGOMERY | |
| {return self.mul(BIG(e))} | |
| else | |
| { | |
| let P=ECP() | |
| let R0=ECP() | |
| let R1=ECP(); R1.copy(self) | |
| for var i=bts-1;i>=0;i-- | |
| { | |
| let 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.self */ | |
| func mul(e:BIG) -> ECP | |
| { | |
| if (e.iszilch() || is_infinity()) {return ECP()} | |
| let P=ECP() | |
| if ROM.CURVETYPE==ROM.MONTGOMERY | |
| { | |
| /* use Ladder */ | |
| let D=ECP() | |
| let R0=ECP(); R0.copy(self) | |
| let R1=ECP(); R1.copy(self) | |
| R1.dbl(); | |
| D.copy(self); D.affine(); | |
| let nb=e.nbits(); | |
| for var i=nb-2;i>=0;i-- | |
| { | |
| let b=e.bit(i) | |
| //print("\(b)") | |
| 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 | |
| let mt=BIG() | |
| let t=BIG() | |
| let Q=ECP() | |
| let C=ECP() | |
| var W=[ECP]() | |
| let n=1+(ROM.NLEN*Int(ROM.BASEBITS)+3)/4 | |
| var w=[Int8](count:n,repeatedValue:0) | |
| affine(); | |
| // precompute table | |
| Q.copy(self) | |
| Q.dbl() | |
| W.append(ECP()) | |
| W[0].copy(self) | |
| for var i=1;i<8;i++ | |
| { | |
| W.append(ECP()) | |
| W[i].copy(W[i-1]) | |
| W[i].add(Q) | |
| } | |
| // convert the table to affine | |
| if ROM.CURVETYPE==ROM.WEIERSTRASS | |
| {ECP.multiaffine(8,W)} | |
| // make exponent odd - add 2P if even, P if odd | |
| t.copy(e); | |
| let s=t.parity(); | |
| t.inc(1); t.norm(); let ns=t.parity(); | |
| mt.copy(t); mt.inc(1); mt.norm(); | |
| t.cmove(mt,s); | |
| Q.cmove(self,ns); | |
| C.copy(Q); | |
| let nb=1+(t.nbits()+3)/4; | |
| // convert exponent to signed 4-bit window | |
| for var i=0;i<nb;i++ | |
| { | |
| w[i]=Int8(t.lastbits(5)-16); | |
| t.dec(Int32(w[i])); t.norm(); | |
| t.fshr(4); | |
| } | |
| w[nb]=Int8(t.lastbits(5)) | |
| P.copy(W[Int((w[nb])-1)/2]); | |
| for var i=nb-1;i>=0;i-- | |
| { | |
| Q.select(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 mul2(e:BIG,_ Q:ECP,_ f:BIG) -> ECP | |
| { | |
| let te=BIG() | |
| let tf=BIG() | |
| let mt=BIG() | |
| let S=ECP() | |
| let T=ECP() | |
| let C=ECP() | |
| var W=[ECP]() | |
| let n=1+(ROM.NLEN*Int(ROM.BASEBITS)+1)/2 | |
| var w=[Int8](count:n,repeatedValue:0); | |
| affine(); | |
| Q.affine(); | |
| te.copy(e); | |
| tf.copy(f); | |
| // precompute table | |
| for var i=0;i<8;i++ {W.append(ECP())} | |
| W[1].copy(self); W[1].sub(Q) | |
| W[2].copy(self); 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(self); 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 ROM.CURVETYPE==ROM.WEIERSTRASS | |
| {ECP.multiaffine(8,W)} | |
| // if multiplier is odd, add 2, else add 1 to multiplier, and add 2P or P to correction | |
| var s=te.parity() | |
| te.inc(1); te.norm(); var ns=te.parity(); mt.copy(te); mt.inc(1); mt.norm() | |
| te.cmove(mt,s) | |
| T.cmove(self,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() | |
| let nb=1+(mt.nbits()+1)/2 | |
| // convert exponent to signed 2-bit window | |
| for var i=0;i<nb;i++ | |
| { | |
| let a=(te.lastbits(3)-4); | |
| te.dec(a); te.norm(); | |
| te.fshr(2); | |
| let b=(tf.lastbits(3)-4); | |
| tf.dec(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 var i=nb-1;i>=0;i-- | |
| { | |
| T.select(W,Int32(w[i])); | |
| S.dbl(); | |
| S.dbl(); | |
| S.add(T); | |
| } | |
| S.sub(C); /* apply correction */ | |
| S.affine(); | |
| return S; | |
| } | |
| } |