| /* |
| 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:Int) |
| { |
| 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:Int) |
| { |
| 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) -> Int |
| { |
| var x=b^c |
| x-=1 // if x=0, x now -1 |
| return Int((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,Int(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:Int) |
| { |
| 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() -> Int |
| { |
| 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(_ b:inout [UInt8]) |
| { |
| let RM=Int(ROM.MODBYTES) |
| var t=[UInt8](repeating: 0,count: RM) |
| if ROM.CURVETYPE != ROM.MONTGOMERY {b[0]=0x04} |
| else {b[0]=0x02} |
| |
| affine() |
| x.redc().toBytes(&t) |
| for i in 0 ..< RM {b[i+1]=t[i]} |
| if ROM.CURVETYPE != ROM.MONTGOMERY |
| { |
| y.redc().toBytes(&t); |
| for i in 0 ..< RM {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](repeating: 0,count: RM) |
| let p=BIG(ROM.Modulus); |
| |
| for i in 0 ..< RM {t[i]=b[i+1]} |
| let px=BIG.fromBytes(t) |
| if BIG.comp(px,p)>=0 {return ECP()} |
| |
| if (b[0]==0x04) |
| { |
| for i in 0 ..< RM {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) |
| |
| 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.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 _ in 0 ..< m |
| {work.append(FP(0))} |
| |
| work[0].one() |
| work[1].copy(P[0].z) |
| |
| for i in 2 ..< m |
| { |
| 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); |
| var i=m-2; |
| while (true) |
| { |
| 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); |
| i=i-1; |
| } |
| /* now work[] contains inverses of all Z coordinates */ |
| |
| for i in 0 ..< m |
| { |
| 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(Int(e)))} |
| else |
| { |
| let P=ECP() |
| let R0=ECP() |
| let R1=ECP(); R1.copy(self) |
| |
| for i in (0...bts-1).reversed() |
| { |
| let b=Int(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 i in (0...nb-2).reversed() |
| { |
| let b=e.bit(UInt(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](repeating: 0,count: n) |
| |
| affine(); |
| |
| // precompute table |
| Q.copy(self) |
| Q.dbl() |
| W.append(ECP()) |
| |
| W[0].copy(self) |
| |
| for i in 1 ..< 8 |
| { |
| 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 i in 0 ..< nb |
| { |
| 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 in (0...nb-1).reversed() |
| { |
| 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](repeating: 0,count: n); |
| |
| affine(); |
| Q.affine(); |
| |
| te.copy(e); |
| tf.copy(f); |
| |
| // precompute table |
| for _ in 0 ..< 8 {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 i in 0 ..< nb |
| { |
| 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[Int(w[nb]-1)/2]); |
| for i in (0...nb-1).reversed() |
| { |
| T.select(W,Int32(w[i])); |
| S.dbl(); |
| S.dbl(); |
| S.add(T); |
| } |
| S.sub(C); /* apply correction */ |
| S.affine(); |
| return S; |
| } |
| |
| |
| |
| |
| } |