| /* |
| 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. |
| */ |
| |
| use super::rom; |
| use super::big; |
| use super::ecp; |
| use super::fp2::FP2; |
| use super::big::BIG; |
| use types::{SexticTwist, CurvePairingType, SignOfX}; |
| use std::str::SplitWhitespace; |
| use std::fmt; |
| |
| #[derive(Copy, Clone)] |
| pub struct ECP2 { |
| x: FP2, |
| y: FP2, |
| z: FP2, |
| } |
| |
| impl PartialEq for ECP2 { |
| fn eq(&self, other: &ECP2) -> bool { |
| self.equals(other) |
| } |
| } |
| |
| impl fmt::Display for ECP2 { |
| fn fmt(&self, f: &mut fmt::Formatter) -> fmt::Result { |
| write!(f, "ECP2: [ {}, {}, {} ]", self.x, self.y, self.z) |
| } |
| } |
| |
| impl fmt::Debug for ECP2 { |
| fn fmt(&self, f: &mut fmt::Formatter) -> fmt::Result { |
| write!(f, "ECP2: [ {}, {}, {} ]", self.x, self.y, self.z) |
| } |
| } |
| |
| #[allow(non_snake_case)] |
| impl ECP2 { |
| pub fn new() -> ECP2 { |
| ECP2 { |
| x: FP2::new(), |
| y: FP2::new_int(1), |
| z: FP2::new(), |
| } |
| } |
| #[allow(non_snake_case)] |
| /* construct this from (x,y) - but set to O if not on curve */ |
| pub fn new_fp2s(ix: &FP2, iy: &FP2) -> ECP2 { |
| let mut E = ECP2::new(); |
| E.x.copy(&ix); |
| E.y.copy(&iy); |
| E.z.one(); |
| E.x.norm(); |
| |
| let mut rhs = ECP2::rhs(&E.x); |
| let mut y2 = FP2::new_copy(&E.y); |
| y2.sqr(); |
| if !y2.equals(&mut rhs) { |
| E.inf(); |
| } |
| return E; |
| } |
| |
| /* construct this from x - but set to O if not on curve */ |
| pub fn new_fp2(ix: &FP2) -> ECP2 { |
| let mut E = ECP2::new(); |
| E.x.copy(&ix); |
| E.y.one(); |
| E.z.one(); |
| E.x.norm(); |
| let mut rhs = ECP2::rhs(&E.x); |
| if rhs.sqrt() { |
| E.y.copy(&rhs); |
| } else { |
| E.inf(); |
| } |
| return E; |
| } |
| |
| /* Test this=O? */ |
| pub fn is_infinity(&self) -> bool { |
| self.x.iszilch() && self.z.iszilch() |
| } |
| |
| /* copy self=P */ |
| pub fn copy(&mut self, P: &ECP2) { |
| self.x.copy(&P.x); |
| self.y.copy(&P.y); |
| self.z.copy(&P.z); |
| } |
| |
| /* set self=O */ |
| pub fn inf(&mut self) { |
| self.x.zero(); |
| self.y.one(); |
| self.z.zero(); |
| } |
| |
| /* set self=-self */ |
| pub fn neg(&mut self) { |
| self.y.norm(); |
| self.y.neg(); |
| self.y.norm(); |
| } |
| |
| /* Conditional move of Q to self dependant on d */ |
| pub fn cmove(&mut self, Q: &ECP2, d: isize) { |
| self.x.cmove(&Q.x, d); |
| self.y.cmove(&Q.y, d); |
| self.z.cmove(&Q.z, d); |
| } |
| |
| /* return 1 if b==c, no branching */ |
| fn teq(b: i32, c: i32) -> isize { |
| let mut x = b ^ c; |
| x -= 1; // if x=0, x now -1 |
| return ((x >> 31) & 1) as isize; |
| } |
| |
| /* Constant time select from pre-computed table */ |
| pub fn selector(&mut self, W: &[ECP2], b: i32) { |
| let mut MP = ECP2::new(); |
| let m = b >> 31; |
| let mut babs = (b ^ m) - m; |
| |
| babs = (babs - 1) / 2; |
| |
| self.cmove(&W[0], ECP2::teq(babs, 0)); // conditional move |
| self.cmove(&W[1], ECP2::teq(babs, 1)); |
| self.cmove(&W[2], ECP2::teq(babs, 2)); |
| self.cmove(&W[3], ECP2::teq(babs, 3)); |
| self.cmove(&W[4], ECP2::teq(babs, 4)); |
| self.cmove(&W[5], ECP2::teq(babs, 5)); |
| self.cmove(&W[6], ECP2::teq(babs, 6)); |
| self.cmove(&W[7], ECP2::teq(babs, 7)); |
| |
| MP.copy(self); |
| MP.neg(); |
| self.cmove(&MP, (m & 1) as isize); |
| } |
| |
| /* Test if P == Q */ |
| pub fn equals(&self, Q: &ECP2) -> bool { |
| let mut a = FP2::new_copy(&self.x); |
| let mut b = FP2::new_copy(&Q.x); |
| |
| a.mul(&Q.z); |
| b.mul(&self.z); |
| if !a.equals(&mut b) { |
| return false; |
| } |
| a.copy(&self.y); |
| a.mul(&Q.z); |
| b.copy(&Q.y); |
| b.mul(&self.z); |
| if !a.equals(&mut b) { |
| return false; |
| } |
| |
| return true; |
| } |
| |
| /* set to Affine - (x,y,z) to (x,y) */ |
| pub fn affine(&mut self) { |
| if self.is_infinity() { |
| return; |
| } |
| let mut one = FP2::new_int(1); |
| if self.z.equals(&mut one) { |
| return; |
| } |
| self.z.inverse(); |
| |
| self.x.mul(&self.z); |
| self.x.reduce(); |
| self.y.mul(&self.z); |
| self.y.reduce(); |
| self.z.copy(&one); |
| } |
| |
| /* extract affine x as FP2 */ |
| pub fn getx(&self) -> FP2 { |
| let mut W = ECP2::new(); |
| W.copy(self); |
| W.affine(); |
| return FP2::new_copy(&W.x); |
| } |
| |
| /* extract affine y as FP2 */ |
| pub fn gety(&self) -> FP2 { |
| let mut W = ECP2::new(); |
| W.copy(self); |
| W.affine(); |
| return FP2::new_copy(&W.y); |
| } |
| |
| /* extract projective x */ |
| pub fn getpx(&self) -> FP2 { |
| return FP2::new_copy(&self.x); |
| } |
| /* extract projective y */ |
| pub fn getpy(&self) -> FP2 { |
| return FP2::new_copy(&self.y); |
| } |
| /* extract projective z */ |
| pub fn getpz(&self) -> FP2 { |
| return FP2::new_copy(&self.z); |
| } |
| |
| /* convert to byte array */ |
| pub fn tobytes(&self, b: &mut [u8]) { |
| let mut t: [u8; big::MODBYTES as usize] = [0; big::MODBYTES as usize]; |
| let mb = big::MODBYTES as usize; |
| let mut W = ECP2::new(); |
| W.copy(self); |
| |
| W.affine(); |
| W.x.geta().tobytes(&mut t); |
| for i in 0..mb { |
| b[i] = t[i] |
| } |
| W.x.getb().tobytes(&mut t); |
| for i in 0..mb { |
| b[i + mb] = t[i] |
| } |
| |
| W.y.geta().tobytes(&mut t); |
| for i in 0..mb { |
| b[i + 2 * mb] = t[i] |
| } |
| W.y.getb().tobytes(&mut t); |
| for i in 0..mb { |
| b[i + 3 * mb] = t[i] |
| } |
| } |
| |
| /* convert from byte array to point */ |
| pub fn frombytes(b: &[u8]) -> ECP2 { |
| let mut t: [u8; big::MODBYTES as usize] = [0; big::MODBYTES as usize]; |
| let mb = big::MODBYTES as usize; |
| |
| for i in 0..mb { |
| t[i] = b[i] |
| } |
| let mut ra = BIG::frombytes(&t); |
| for i in 0..mb { |
| t[i] = b[i + mb] |
| } |
| let mut rb = BIG::frombytes(&t); |
| let rx = FP2::new_bigs(&ra, &rb); |
| |
| for i in 0..mb { |
| t[i] = b[i + 2 * mb] |
| } |
| ra.copy(&BIG::frombytes(&t)); |
| for i in 0..mb { |
| t[i] = b[i + 3 * mb] |
| } |
| rb.copy(&BIG::frombytes(&t)); |
| let ry = FP2::new_bigs(&ra, &rb); |
| |
| return ECP2::new_fp2s(&rx, &ry); |
| } |
| |
| /* convert this to hex string */ |
| pub fn tostring(&self) -> String { |
| let mut W = ECP2::new(); |
| W.copy(self); |
| W.affine(); |
| if W.is_infinity() { |
| return String::from("infinity"); |
| } |
| return format!("({},{})", W.x.tostring(), W.y.tostring()); |
| } |
| |
| pub fn to_hex(&self) -> String { |
| format!("{} {} {}", self.x.to_hex(), self.y.to_hex(), self.z.to_hex()) |
| } |
| |
| pub fn from_hex_iter(iter: &mut SplitWhitespace) -> ECP2 { |
| ECP2 { |
| x: FP2::from_hex_iter(iter), |
| y: FP2::from_hex_iter(iter), |
| z: FP2::from_hex_iter(iter) |
| } |
| } |
| |
| pub fn from_hex(val: String) -> ECP2 { |
| let mut iter = val.split_whitespace(); |
| return ECP2::from_hex_iter(&mut iter); |
| } |
| |
| /* Calculate RHS of twisted curve equation x^3+B/i */ |
| pub fn rhs(x: &FP2) -> FP2 { |
| let mut r = FP2::new_copy(x); |
| r.sqr(); |
| let mut b = FP2::new_big(&BIG::new_ints(&rom::CURVE_B)); |
| if ecp::SEXTIC_TWIST == SexticTwist::D_TYPE { |
| b.div_ip(); |
| } |
| if ecp::SEXTIC_TWIST == SexticTwist::M_TYPE { |
| b.norm(); |
| b.mul_ip(); |
| b.norm(); |
| } |
| |
| r.mul(x); |
| r.add(&b); |
| |
| r.reduce(); |
| return r; |
| } |
| |
| /* self+=self */ |
| pub fn dbl(&mut self) -> isize { |
| let mut iy = FP2::new_copy(&self.y); |
| if ecp::SEXTIC_TWIST == SexticTwist::D_TYPE { |
| iy.mul_ip(); |
| iy.norm(); |
| } |
| |
| let mut t0 = FP2::new_copy(&self.y); //***** Change |
| t0.sqr(); |
| if ecp::SEXTIC_TWIST == SexticTwist::D_TYPE { |
| t0.mul_ip(); |
| } |
| let mut t1 = FP2::new_copy(&iy); |
| t1.mul(&self.z); |
| let mut t2 = FP2::new_copy(&self.z); |
| t2.sqr(); |
| |
| self.z.copy(&t0); |
| self.z.add(&t0); |
| self.z.norm(); |
| self.z.dbl(); |
| self.z.dbl(); |
| self.z.norm(); |
| |
| t2.imul(3 * rom::CURVE_B_I); |
| if ecp::SEXTIC_TWIST == SexticTwist::M_TYPE { |
| t2.mul_ip(); |
| t2.norm(); |
| } |
| let mut x3 = FP2::new_copy(&t2); |
| x3.mul(&self.z); |
| |
| let mut y3 = FP2::new_copy(&t0); |
| |
| y3.add(&t2); |
| y3.norm(); |
| self.z.mul(&t1); |
| t1.copy(&t2); |
| t1.add(&t2); |
| t2.add(&t1); |
| t2.norm(); |
| t0.sub(&t2); |
| t0.norm(); //y^2-9bz^2 |
| y3.mul(&t0); |
| y3.add(&x3); //(y^2+3z*2)(y^2-9z^2)+3b.z^2.8y^2 |
| t1.copy(&self.x); |
| t1.mul(&iy); // |
| self.x.copy(&t0); |
| self.x.norm(); |
| self.x.mul(&t1); |
| self.x.dbl(); //(y^2-9bz^2)xy2 |
| |
| self.x.norm(); |
| self.y.copy(&y3); |
| self.y.norm(); |
| |
| return 1; |
| } |
| |
| /* self+=Q - return 0 for add, 1 for double, -1 for O */ |
| pub fn add(&mut self, Q: &ECP2) -> isize { |
| let b = 3 * rom::CURVE_B_I; |
| let mut t0 = FP2::new_copy(&self.x); |
| t0.mul(&Q.x); // x.Q.x |
| let mut t1 = FP2::new_copy(&self.y); |
| t1.mul(&Q.y); // y.Q.y |
| |
| let mut t2 = FP2::new_copy(&self.z); |
| t2.mul(&Q.z); |
| let mut t3 = FP2::new_copy(&self.x); |
| t3.add(&self.y); |
| t3.norm(); //t3=X1+Y1 |
| let mut t4 = FP2::new_copy(&Q.x); |
| t4.add(&Q.y); |
| t4.norm(); //t4=X2+Y2 |
| t3.mul(&t4); //t3=(X1+Y1)(X2+Y2) |
| t4.copy(&t0); |
| t4.add(&t1); //t4=X1.X2+Y1.Y2 |
| |
| t3.sub(&t4); |
| t3.norm(); |
| if ecp::SEXTIC_TWIST == SexticTwist::D_TYPE { |
| t3.mul_ip(); |
| t3.norm(); //t3=(X1+Y1)(X2+Y2)-(X1.X2+Y1.Y2) = X1.Y2+X2.Y1 |
| } |
| t4.copy(&self.y); |
| t4.add(&self.z); |
| t4.norm(); //t4=Y1+Z1 |
| let mut x3 = FP2::new_copy(&Q.y); |
| x3.add(&Q.z); |
| x3.norm(); //x3=Y2+Z2 |
| |
| t4.mul(&x3); //t4=(Y1+Z1)(Y2+Z2) |
| x3.copy(&t1); // |
| x3.add(&t2); //X3=Y1.Y2+Z1.Z2 |
| |
| t4.sub(&x3); |
| t4.norm(); |
| if ecp::SEXTIC_TWIST == SexticTwist::D_TYPE { |
| t4.mul_ip(); |
| t4.norm(); //t4=(Y1+Z1)(Y2+Z2) - (Y1.Y2+Z1.Z2) = Y1.Z2+Y2.Z1 |
| } |
| x3.copy(&self.x); |
| x3.add(&self.z); |
| x3.norm(); // x3=X1+Z1 |
| let mut y3 = FP2::new_copy(&Q.x); |
| y3.add(&Q.z); |
| y3.norm(); // y3=X2+Z2 |
| x3.mul(&y3); // x3=(X1+Z1)(X2+Z2) |
| y3.copy(&t0); |
| y3.add(&t2); // y3=X1.X2+Z1+Z2 |
| y3.rsub(&x3); |
| y3.norm(); // y3=(X1+Z1)(X2+Z2) - (X1.X2+Z1.Z2) = X1.Z2+X2.Z1 |
| |
| if ecp::SEXTIC_TWIST == SexticTwist::D_TYPE { |
| t0.mul_ip(); |
| t0.norm(); // x.Q.x |
| t1.mul_ip(); |
| t1.norm(); // y.Q.y |
| } |
| x3.copy(&t0); |
| x3.add(&t0); |
| t0.add(&x3); |
| t0.norm(); |
| t2.imul(b); |
| if ecp::SEXTIC_TWIST == SexticTwist::M_TYPE { |
| t2.mul_ip(); |
| t2.norm(); |
| } |
| let mut z3 = FP2::new_copy(&t1); |
| z3.add(&t2); |
| z3.norm(); |
| t1.sub(&t2); |
| t1.norm(); |
| y3.imul(b); |
| if ecp::SEXTIC_TWIST == SexticTwist::M_TYPE { |
| y3.mul_ip(); |
| y3.norm(); |
| } |
| 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); |
| |
| self.x.copy(&x3); |
| self.x.norm(); |
| self.y.copy(&y3); |
| self.y.norm(); |
| self.z.copy(&z3); |
| self.z.norm(); |
| |
| return 0; |
| } |
| |
| /* set this-=Q */ |
| pub fn sub(&mut self, Q: &ECP2) -> isize { |
| let mut NQ = ECP2::new(); |
| NQ.copy(Q); |
| NQ.neg(); |
| let d = self.add(&NQ); |
| return d; |
| } |
| |
| /* set this*=q, where q is Modulus, using Frobenius */ |
| pub fn frob(&mut self, x: &FP2) { |
| let mut x2 = FP2::new_copy(x); |
| x2.sqr(); |
| self.x.conj(); |
| self.y.conj(); |
| self.z.conj(); |
| self.z.reduce(); |
| self.x.mul(&x2); |
| self.y.mul(&x2); |
| self.y.mul(x); |
| } |
| |
| /* self*=e */ |
| pub fn mul(&self, e: &BIG) -> ECP2 { |
| /* fixed size windows */ |
| let mut mt = BIG::new(); |
| let mut t = BIG::new(); |
| let mut P = ECP2::new(); |
| let mut Q = ECP2::new(); |
| let mut C = ECP2::new(); |
| |
| if self.is_infinity() { |
| return P; |
| } |
| |
| let mut W: [ECP2; 8] = [ |
| ECP2::new(), |
| ECP2::new(), |
| ECP2::new(), |
| ECP2::new(), |
| ECP2::new(), |
| ECP2::new(), |
| ECP2::new(), |
| ECP2::new(), |
| ]; |
| |
| const CT: usize = 1 + (big::NLEN * (big::BASEBITS as usize) + 3) / 4; |
| let mut w: [i8; CT] = [0; CT]; |
| |
| /* precompute table */ |
| Q.copy(&self); |
| Q.dbl(); |
| |
| W[0].copy(&self); |
| |
| for i in 1..8 { |
| C.copy(&W[i - 1]); |
| W[i].copy(&C); |
| W[i].add(&mut Q); |
| } |
| |
| /* 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] = (t.lastbits(5) - 16) as i8; |
| t.dec(w[i] as isize); |
| t.norm(); |
| t.fshr(4); |
| } |
| w[nb] = (t.lastbits(5)) as i8; |
| |
| P.copy(&W[((w[nb] as usize) - 1) / 2]); |
| for i in (0..nb).rev() { |
| Q.selector(&W, w[i] as i32); |
| P.dbl(); |
| P.dbl(); |
| P.dbl(); |
| P.dbl(); |
| P.add(&mut Q); |
| } |
| P.sub(&mut C); |
| P.affine(); |
| return P; |
| } |
| |
| /* P=u0.Q0+u1*Q1+u2*Q2+u3*Q3 */ |
| // Bos & Costello https://eprint.iacr.org/2013/458.pdf |
| // Faz-Hernandez & Longa & Sanchez https://eprint.iacr.org/2013/158.pdf |
| // Side channel attack secure |
| |
| pub fn mul4(Q: &mut [ECP2], u: &[BIG]) -> ECP2 { |
| let mut W = ECP2::new(); |
| let mut P = ECP2::new(); |
| |
| let mut T: [ECP2; 8] = [ |
| ECP2::new(), |
| ECP2::new(), |
| ECP2::new(), |
| ECP2::new(), |
| ECP2::new(), |
| ECP2::new(), |
| ECP2::new(), |
| ECP2::new(), |
| ]; |
| |
| let mut mt = BIG::new(); |
| |
| let mut t: [BIG; 4] = [ |
| BIG::new_copy(&u[0]), |
| BIG::new_copy(&u[1]), |
| BIG::new_copy(&u[2]), |
| BIG::new_copy(&u[3]), |
| ]; |
| |
| const CT: usize = 1 + big::NLEN * (big::BASEBITS as usize); |
| let mut w: [i8; CT] = [0; CT]; |
| let mut s: [i8; CT] = [0; CT]; |
| |
| for i in 0..4 { |
| t[i].norm(); |
| } |
| |
| T[0].copy(&Q[0]); |
| W.copy(&T[0]); |
| T[1].copy(&W); |
| T[1].add(&mut Q[1]); // Q[0]+Q[1] |
| T[2].copy(&W); |
| T[2].add(&mut Q[2]); |
| W.copy(&T[1]); // Q[0]+Q[2] |
| T[3].copy(&W); |
| T[3].add(&mut Q[2]); |
| W.copy(&T[0]); // Q[0]+Q[1]+Q[2] |
| T[4].copy(&W); |
| T[4].add(&mut Q[3]); |
| W.copy(&T[1]); // Q[0]+Q[3] |
| T[5].copy(&W); |
| T[5].add(&mut Q[3]); |
| W.copy(&T[2]); // Q[0]+Q[1]+Q[3] |
| T[6].copy(&W); |
| T[6].add(&mut Q[3]); |
| W.copy(&T[3]); // Q[0]+Q[2]+Q[3] |
| T[7].copy(&W); |
| T[7].add(&mut Q[3]); // Q[0]+Q[1]+Q[2]+Q[3] |
| |
| // Make it odd |
| let pb = 1 - t[0].parity(); |
| t[0].inc(pb); |
| t[0].norm(); |
| |
| // Number of bits |
| mt.zero(); |
| for i in 0..4 { |
| mt.or(&t[i]); |
| } |
| |
| let nb = 1 + mt.nbits(); |
| |
| // Sign pivot |
| |
| s[nb - 1] = 1; |
| for i in 0..nb - 1 { |
| t[0].fshr(1); |
| s[i] = (2 * t[0].parity() - 1) as i8; |
| } |
| |
| // Recoded exponent |
| for i in 0..nb { |
| w[i] = 0; |
| let mut k = 1; |
| for j in 1..4 { |
| let bt = s[i] * (t[j].parity() as i8); |
| t[j].fshr(1); |
| t[j].dec((bt >> 1) as isize); |
| t[j].norm(); |
| w[i] += bt * (k as i8); |
| k = 2 * k; |
| } |
| } |
| |
| // Main loop |
| P.selector(&T, (2 * w[nb - 1] + 1) as i32); |
| for i in (0..nb - 1).rev() { |
| P.dbl(); |
| W.selector(&T, (2 * w[i] + s[i]) as i32); |
| P.add(&mut W); |
| } |
| |
| // apply correction |
| W.copy(&P); |
| W.sub(&mut Q[0]); |
| P.cmove(&W, pb); |
| P.affine(); |
| |
| return P; |
| } |
| |
| #[allow(non_snake_case)] |
| pub fn mapit(h: &[u8]) -> ECP2 { |
| let mut q = BIG::new_ints(&rom::MODULUS); |
| let mut x = BIG::frombytes(h); |
| x.rmod(&mut q); |
| let mut Q: ECP2; |
| let one = BIG::new_int(1); |
| |
| loop { |
| let X = FP2::new_bigs(&one, &x); |
| Q = ECP2::new_fp2(&X); |
| if !Q.is_infinity() { |
| break; |
| } |
| x.inc(1); |
| x.norm(); |
| } |
| let mut X = FP2::new_bigs(&BIG::new_ints(&rom::FRA), &BIG::new_ints(&rom::FRB)); |
| if ecp::SEXTIC_TWIST == SexticTwist::M_TYPE { |
| X.inverse(); |
| X.norm(); |
| } |
| x = BIG::new_ints(&rom::CURVE_BNX); |
| |
| if ecp::CURVE_PAIRING_TYPE == CurvePairingType::BN { |
| let mut T = Q.mul(&mut x); |
| if ecp::SIGN_OF_X == SignOfX::NEGATIVEX { |
| T.neg(); |
| } |
| let mut K = ECP2::new(); |
| K.copy(&T); |
| K.dbl(); |
| K.add(&T); |
| |
| K.frob(&X); |
| Q.frob(&X); |
| Q.frob(&X); |
| Q.frob(&X); |
| Q.add(&T); |
| Q.add(&K); |
| T.frob(&X); |
| T.frob(&X); |
| Q.add(&T); |
| } |
| if ecp::CURVE_PAIRING_TYPE == CurvePairingType::BLS { |
| let mut xQ = Q.mul(&mut x); |
| let mut x2Q = xQ.mul(&mut x); |
| |
| if ecp::SIGN_OF_X == SignOfX::NEGATIVEX { |
| xQ.neg(); |
| } |
| x2Q.sub(&xQ); |
| x2Q.sub(&Q); |
| |
| xQ.sub(&Q); |
| xQ.frob(&X); |
| |
| Q.dbl(); |
| Q.frob(&X); |
| Q.frob(&X); |
| |
| Q.add(&x2Q); |
| Q.add(&xQ); |
| } |
| |
| Q.affine(); |
| return Q; |
| } |
| |
| pub fn generator() -> ECP2 { |
| return ECP2::new_fp2s( |
| &FP2::new_bigs( |
| &BIG::new_ints(&rom::CURVE_PXA), |
| &BIG::new_ints(&rom::CURVE_PXB), |
| ), |
| &FP2::new_bigs( |
| &BIG::new_ints(&rom::CURVE_PYA), |
| &BIG::new_ints(&rom::CURVE_PYB), |
| ), |
| ); |
| } |
| } |
