// Code generated by go generate; DO NOT EDIT. // This file was generated by robots. package p751 import ( "github.com/henrydcase/nobs/dh/sidh/common" ) // Montgomery multiplication. Input values must be already // in Montgomery domain. func mulP(dest, lhs, rhs *common.Fp) { var ab common.FpX2 mulP751(&ab, lhs, rhs) // = a*b*R*R rdcP751(dest, &ab) // = a*b*R mod p } // Set dest = x^((p-3)/4). If x is square, this is 1/sqrt(x). // Uses variation of sliding-window algorithm from with window size // of 5 and least to most significant bit sliding (left-to-right) // See HAC 14.85 for general description. // // Allowed to overlap x with dest. // All values in Montgomery domains // Set dest = x^(2^k), for k >= 1, by repeated squarings. func p34(dest, x *common.Fp) { var lookup [16]common.Fp // This performs sum(powStrategy) + 1 squarings and len(lookup) + len(mulStrategy) // multiplications. powStrategy := []uint8{5, 7, 6, 2, 10, 4, 6, 9, 8, 5, 9, 4, 7, 5, 5, 4, 8, 3, 9, 5, 5, 4, 10, 4, 6, 6, 6, 5, 8, 9, 3, 4, 9, 4, 5, 6, 6, 2, 9, 4, 5, 5, 5, 7, 7, 9, 4, 6, 4, 8, 5, 8, 6, 6, 2, 9, 7, 4, 8, 8, 8, 4, 6, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 2} mulStrategy := []uint8{15, 11, 10, 0, 15, 3, 3, 3, 4, 4, 9, 7, 11, 11, 5, 3, 12, 2, 10, 8, 5, 2, 8, 3, 5, 4, 11, 4, 0, 9, 2, 1, 12, 7, 5, 14, 15, 0, 14, 5, 6, 4, 5, 13, 6, 9, 7, 15, 1, 14, 11, 15, 12, 5, 0, 10, 9, 7, 7, 10, 14, 6, 11, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 1} initialMul := uint8(13) // Precompute lookup table of odd multiples of x for window // size k=5. var xx common.Fp mulP(&xx, x, x) lookup[0] = *x for i := 1; i < 16; i++ { mulP(&lookup[i], &lookup[i-1], &xx) } // Now lookup = {x, x^3, x^5, ... } // so that lookup[i] = x^{2*i + 1} // so that lookup[k/2] = x^k, for odd k *dest = lookup[initialMul] for i := uint8(0); i < uint8(len(powStrategy)); i++ { mulP(dest, dest, dest) for j := uint8(1); j < powStrategy[i]; j++ { mulP(dest, dest, dest) } mulP(dest, dest, &lookup[mulStrategy[i]]) } } func add(dest, lhs, rhs *common.Fp2) { addP751(&dest.A, &lhs.A, &rhs.A) addP751(&dest.B, &lhs.B, &rhs.B) } func sub(dest, lhs, rhs *common.Fp2) { subP751(&dest.A, &lhs.A, &rhs.A) subP751(&dest.B, &lhs.B, &rhs.B) } func mul(dest, lhs, rhs *common.Fp2) { var bMinA, cMinD common.Fp var ac, bd common.FpX2 var adPlusBc common.FpX2 var acMinBd common.FpX2 // Let (a,b,c,d) = (lhs.a,lhs.b,rhs.a,rhs.b). // // (a + bi)*(c + di) = (a*c - b*d) + (a*d + b*c)i // // Use Karatsuba's trick: note that // // (b - a)*(c - d) = (b*c + a*d) - a*c - b*d // // so (a*d + b*c) = (b-a)*(c-d) + a*c + b*d. mulP751(&ac, &lhs.A, &rhs.A) // = a*c*R*R mulP751(&bd, &lhs.B, &rhs.B) // = b*d*R*R subP751(&bMinA, &lhs.B, &lhs.A) // = (b-a)*R subP751(&cMinD, &rhs.A, &rhs.B) // = (c-d)*R mulP751(&adPlusBc, &bMinA, &cMinD) // = (b-a)*(c-d)*R*R adlP751(&adPlusBc, &adPlusBc, &ac) // = ((b-a)*(c-d) + a*c)*R*R adlP751(&adPlusBc, &adPlusBc, &bd) // = ((b-a)*(c-d) + a*c + b*d)*R*R rdcP751(&dest.B, &adPlusBc) // = (a*d + b*c)*R mod p sulP751(&acMinBd, &ac, &bd) // = (a*c - b*d)*R*R rdcP751(&dest.A, &acMinBd) // = (a*c - b*d)*R mod p } // Set dest = 1/x // // Allowed to overlap dest with x. // // Returns dest to allow chaining operations. func inv(dest, x *common.Fp2) { var e1, e2 common.FpX2 var f1, f2 common.Fp // We want to compute // // 1 1 (a - bi) (a - bi) // -------- = -------- -------- = ----------- // (a + bi) (a + bi) (a - bi) (a^2 + b^2) // // Letting c = 1/(a^2 + b^2), this is // // 1/(a+bi) = a*c - b*ci. mulP751(&e1, &x.A, &x.A) // = a*a*R*R mulP751(&e2, &x.B, &x.B) // = b*b*R*R adlP751(&e1, &e1, &e2) // = (a^2 + b^2)*R*R rdcP751(&f1, &e1) // = (a^2 + b^2)*R mod p // Now f1 = a^2 + b^2 mulP(&f2, &f1, &f1) p34(&f2, &f2) mulP(&f2, &f2, &f2) mulP(&f2, &f2, &f1) mulP751(&e1, &x.A, &f2) rdcP751(&dest.A, &e1) subP751(&f1, &common.Fp{}, &x.B) mulP751(&e1, &f1, &f2) rdcP751(&dest.B, &e1) } func sqr(dest, x *common.Fp2) { var a2, aPlusB, aMinusB common.Fp var a2MinB2, ab2 common.FpX2 a := &x.A b := &x.B // (a + bi)*(a + bi) = (a^2 - b^2) + 2abi. addP751(&a2, a, a) // = a*R + a*R = 2*a*R addP751(&aPlusB, a, b) // = a*R + b*R = (a+b)*R subP751(&aMinusB, a, b) // = a*R - b*R = (a-b)*R mulP751(&a2MinB2, &aPlusB, &aMinusB) // = (a+b)*(a-b)*R*R = (a^2 - b^2)*R*R mulP751(&ab2, &a2, b) // = 2*a*b*R*R rdcP751(&dest.A, &a2MinB2) // = (a^2 - b^2)*R mod p rdcP751(&dest.B, &ab2) // = 2*a*b*R mod p } // In case choice == 1, performs following swap in constant time: // xPx <-> xQx // xPz <-> xQz // Otherwise returns xPx, xPz, xQx, xQz unchanged func cswap(xPx, xPz, xQx, xQz *common.Fp2, choice uint8) { cswapP751(&xPx.A, &xQx.A, choice) cswapP751(&xPx.B, &xQx.B, choice) cswapP751(&xPz.A, &xQz.A, choice) cswapP751(&xPz.B, &xQz.B, choice) } // Converts in.A and in.B to Montgomery domain and stores // in 'out' // out.A = in.A * R mod p // out.B = in.B * R mod p // Performs v = v*R^2*R^(-1) mod p, for both in.A and in.B func ToMontgomery(out, in *common.Fp2) { var aRR common.FpX2 // a*R*R mulP751(&aRR, &in.A, &P751R2) // a*R mod p rdcP751(&out.A, &aRR) mulP751(&aRR, &in.B, &P751R2) rdcP751(&out.B, &aRR) } // Converts in.A and in.B from Montgomery domain and stores // in 'out' // out.A = in.A mod p // out.B = in.B mod p // // After returning from the call 'in' is not modified. func FromMontgomery(out, in *common.Fp2) { var aR common.FpX2 // convert from montgomery domain copy(aR[:], in.A[:]) rdcP751(&out.A, &aR) // = a mod p in [0, 2p) modP751(&out.A) // = a mod p in [0, p) for i := range aR { aR[i] = 0 } copy(aR[:], in.B[:]) rdcP751(&out.B, &aR) modP751(&out.B) }