public override ECFieldElement Sqrt() { uint[] y = x; if (Nat256.IsZero(y) || Nat256.IsOne(y)) { return(this); } uint[] array = Nat256.Create(); Curve25519Field.Square(y, array); Curve25519Field.Multiply(array, y, array); uint[] array2 = array; Curve25519Field.Square(array, array2); Curve25519Field.Multiply(array2, y, array2); uint[] array3 = Nat256.Create(); Curve25519Field.Square(array2, array3); Curve25519Field.Multiply(array3, y, array3); uint[] array4 = Nat256.Create(); Curve25519Field.SquareN(array3, 3, array4); Curve25519Field.Multiply(array4, array2, array4); uint[] array5 = array2; Curve25519Field.SquareN(array4, 4, array5); Curve25519Field.Multiply(array5, array3, array5); uint[] array6 = array4; Curve25519Field.SquareN(array5, 4, array6); Curve25519Field.Multiply(array6, array3, array6); uint[] array7 = array3; Curve25519Field.SquareN(array6, 15, array7); Curve25519Field.Multiply(array7, array6, array7); uint[] array8 = array6; Curve25519Field.SquareN(array7, 30, array8); Curve25519Field.Multiply(array8, array7, array8); uint[] array9 = array7; Curve25519Field.SquareN(array8, 60, array9); Curve25519Field.Multiply(array9, array8, array9); uint[] z = array8; Curve25519Field.SquareN(array9, 11, z); Curve25519Field.Multiply(z, array5, z); uint[] array10 = array5; Curve25519Field.SquareN(z, 120, array10); Curve25519Field.Multiply(array10, array9, array10); uint[] z2 = array10; Curve25519Field.Square(z2, z2); uint[] array11 = array9; Curve25519Field.Square(z2, array11); if (Nat256.Eq(y, array11)) { return(new Curve25519FieldElement(z2)); } Curve25519Field.Multiply(z2, PRECOMP_POW2, z2); Curve25519Field.Square(z2, array11); if (Nat256.Eq(y, array11)) { return(new Curve25519FieldElement(z2)); } return(null); }
public override ECFieldElement Sqrt() { uint[] x = this.x; if (Nat256.IsZero(x) || Nat256.IsOne(x)) { return(this); } uint[] z = Nat256.Create(); Curve25519Field.Square(x, z); Curve25519Field.Multiply(z, x, z); uint[] numArray3 = z; Curve25519Field.Square(z, numArray3); Curve25519Field.Multiply(numArray3, x, numArray3); uint[] numArray4 = Nat256.Create(); Curve25519Field.Square(numArray3, numArray4); Curve25519Field.Multiply(numArray4, x, numArray4); uint[] numArray5 = Nat256.Create(); Curve25519Field.SquareN(numArray4, 3, numArray5); Curve25519Field.Multiply(numArray5, numArray3, numArray5); uint[] numArray6 = numArray3; Curve25519Field.SquareN(numArray5, 4, numArray6); Curve25519Field.Multiply(numArray6, numArray4, numArray6); uint[] numArray7 = numArray5; Curve25519Field.SquareN(numArray6, 4, numArray7); Curve25519Field.Multiply(numArray7, numArray4, numArray7); uint[] numArray8 = numArray4; Curve25519Field.SquareN(numArray7, 15, numArray8); Curve25519Field.Multiply(numArray8, numArray7, numArray8); uint[] numArray9 = numArray7; Curve25519Field.SquareN(numArray8, 30, numArray9); Curve25519Field.Multiply(numArray9, numArray8, numArray9); uint[] numArray10 = numArray8; Curve25519Field.SquareN(numArray9, 60, numArray10); Curve25519Field.Multiply(numArray10, numArray9, numArray10); uint[] numArray11 = numArray9; Curve25519Field.SquareN(numArray10, 11, numArray11); Curve25519Field.Multiply(numArray11, numArray6, numArray11); uint[] numArray12 = numArray6; Curve25519Field.SquareN(numArray11, 120, numArray12); Curve25519Field.Multiply(numArray12, numArray10, numArray12); uint[] numArray13 = numArray12; Curve25519Field.Square(numArray13, numArray13); uint[] numArray14 = numArray10; Curve25519Field.Square(numArray13, numArray14); if (Nat256.Eq(x, numArray14)) { return(new Curve25519FieldElement(numArray13)); } Curve25519Field.Multiply(numArray13, PRECOMP_POW2, numArray13); Curve25519Field.Square(numArray13, numArray14); if (Nat256.Eq(x, numArray14)) { return(new Curve25519FieldElement(numArray13)); } return(null); }
/** * return a sqrt root - the routine verifies that the calculation returns the right value - if * none exists it returns null. */ public override ECFieldElement Sqrt() { /* * Q == 8m + 5, so we use Pocklington's method for this case. * * First, raise this element to the exponent 2^252 - 2^1 (i.e. m + 1) * * Breaking up the exponent's binary representation into "repunits", we get: * { 251 1s } { 1 0s } * * Therefore we need an addition chain containing 251 (the lengths of the repunits) * We use: 1, 2, 3, 4, 7, 11, 15, 30, 60, 120, 131, [251] */ uint[] x1 = this.x; if (Nat256.IsZero(x1) || Nat256.IsOne(x1)) { return(this); } uint[] x2 = Nat256.Create(); Curve25519Field.Square(x1, x2); Curve25519Field.Multiply(x2, x1, x2); uint[] x3 = x2; Curve25519Field.Square(x2, x3); Curve25519Field.Multiply(x3, x1, x3); uint[] x4 = Nat256.Create(); Curve25519Field.Square(x3, x4); Curve25519Field.Multiply(x4, x1, x4); uint[] x7 = Nat256.Create(); Curve25519Field.SquareN(x4, 3, x7); Curve25519Field.Multiply(x7, x3, x7); uint[] x11 = x3; Curve25519Field.SquareN(x7, 4, x11); Curve25519Field.Multiply(x11, x4, x11); uint[] x15 = x7; Curve25519Field.SquareN(x11, 4, x15); Curve25519Field.Multiply(x15, x4, x15); uint[] x30 = x4; Curve25519Field.SquareN(x15, 15, x30); Curve25519Field.Multiply(x30, x15, x30); uint[] x60 = x15; Curve25519Field.SquareN(x30, 30, x60); Curve25519Field.Multiply(x60, x30, x60); uint[] x120 = x30; Curve25519Field.SquareN(x60, 60, x120); Curve25519Field.Multiply(x120, x60, x120); uint[] x131 = x60; Curve25519Field.SquareN(x120, 11, x131); Curve25519Field.Multiply(x131, x11, x131); uint[] x251 = x11; Curve25519Field.SquareN(x131, 120, x251); Curve25519Field.Multiply(x251, x120, x251); uint[] t1 = x251; Curve25519Field.Square(t1, t1); uint[] t2 = x120; Curve25519Field.Square(t1, t2); if (Nat256.Eq(x1, t2)) { return(new Curve25519FieldElement(t1)); } /* * If the first guess is incorrect, we multiply by a precomputed power of 2 to get the second guess, * which is ((4x)^(m + 1))/2 mod Q */ Curve25519Field.Multiply(t1, PRECOMP_POW2, t1); Curve25519Field.Square(t1, t2); if (Nat256.Eq(x1, t2)) { return(new Curve25519FieldElement(t1)); } return(null); }