public override ECFieldElement Sqrt() { uint[] y = this.x; if (Nat160.IsZero(y) || Nat160.IsOne(y)) { return(this); } uint[] array = Nat160.Create(); SecP160R2Field.Square(y, array); SecP160R2Field.Multiply(array, y, array); uint[] array2 = Nat160.Create(); SecP160R2Field.Square(array, array2); SecP160R2Field.Multiply(array2, y, array2); uint[] array3 = Nat160.Create(); SecP160R2Field.Square(array2, array3); SecP160R2Field.Multiply(array3, y, array3); uint[] array4 = Nat160.Create(); SecP160R2Field.SquareN(array3, 3, array4); SecP160R2Field.Multiply(array4, array2, array4); uint[] array5 = array3; SecP160R2Field.SquareN(array4, 7, array5); SecP160R2Field.Multiply(array5, array4, array5); uint[] array6 = array4; SecP160R2Field.SquareN(array5, 3, array6); SecP160R2Field.Multiply(array6, array2, array6); uint[] array7 = Nat160.Create(); SecP160R2Field.SquareN(array6, 14, array7); SecP160R2Field.Multiply(array7, array5, array7); uint[] array8 = array5; SecP160R2Field.SquareN(array7, 31, array8); SecP160R2Field.Multiply(array8, array7, array8); uint[] z = array7; SecP160R2Field.SquareN(array8, 62, z); SecP160R2Field.Multiply(z, array8, z); uint[] array9 = array8; SecP160R2Field.SquareN(z, 3, array9); SecP160R2Field.Multiply(array9, array2, array9); uint[] z2 = array9; SecP160R2Field.SquareN(z2, 18, z2); SecP160R2Field.Multiply(z2, array6, z2); SecP160R2Field.SquareN(z2, 2, z2); SecP160R2Field.Multiply(z2, y, z2); SecP160R2Field.SquareN(z2, 3, z2); SecP160R2Field.Multiply(z2, array, z2); SecP160R2Field.SquareN(z2, 6, z2); SecP160R2Field.Multiply(z2, array2, z2); SecP160R2Field.SquareN(z2, 2, z2); SecP160R2Field.Multiply(z2, y, z2); uint[] array10 = array; SecP160R2Field.Square(z2, array10); if (!Nat160.Eq(y, array10)) { return(null); } return(new SecP160R2FieldElement(z2)); }
public override ECFieldElement Sqrt() { uint[] x = this.x; if (Nat160.IsZero(x) || Nat160.IsOne(x)) { return(this); } uint[] z = Nat160.Create(); SecP160R2Field.Square(x, z); SecP160R2Field.Multiply(z, x, z); uint[] numArray3 = Nat160.Create(); SecP160R2Field.Square(z, numArray3); SecP160R2Field.Multiply(numArray3, x, numArray3); uint[] numArray4 = Nat160.Create(); SecP160R2Field.Square(numArray3, numArray4); SecP160R2Field.Multiply(numArray4, x, numArray4); uint[] numArray5 = Nat160.Create(); SecP160R2Field.SquareN(numArray4, 3, numArray5); SecP160R2Field.Multiply(numArray5, numArray3, numArray5); uint[] numArray6 = numArray4; SecP160R2Field.SquareN(numArray5, 7, numArray6); SecP160R2Field.Multiply(numArray6, numArray5, numArray6); uint[] numArray7 = numArray5; SecP160R2Field.SquareN(numArray6, 3, numArray7); SecP160R2Field.Multiply(numArray7, numArray3, numArray7); uint[] numArray8 = Nat160.Create(); SecP160R2Field.SquareN(numArray7, 14, numArray8); SecP160R2Field.Multiply(numArray8, numArray6, numArray8); uint[] numArray9 = numArray6; SecP160R2Field.SquareN(numArray8, 0x1f, numArray9); SecP160R2Field.Multiply(numArray9, numArray8, numArray9); uint[] numArray10 = numArray8; SecP160R2Field.SquareN(numArray9, 0x3e, numArray10); SecP160R2Field.Multiply(numArray10, numArray9, numArray10); uint[] numArray11 = numArray9; SecP160R2Field.SquareN(numArray10, 3, numArray11); SecP160R2Field.Multiply(numArray11, numArray3, numArray11); uint[] numArray12 = numArray11; SecP160R2Field.SquareN(numArray12, 0x12, numArray12); SecP160R2Field.Multiply(numArray12, numArray7, numArray12); SecP160R2Field.SquareN(numArray12, 2, numArray12); SecP160R2Field.Multiply(numArray12, x, numArray12); SecP160R2Field.SquareN(numArray12, 3, numArray12); SecP160R2Field.Multiply(numArray12, z, numArray12); SecP160R2Field.SquareN(numArray12, 6, numArray12); SecP160R2Field.Multiply(numArray12, numArray3, numArray12); SecP160R2Field.SquareN(numArray12, 2, numArray12); SecP160R2Field.Multiply(numArray12, x, numArray12); uint[] numArray13 = z; SecP160R2Field.Square(numArray12, numArray13); return(!Nat160.Eq(x, numArray13) ? null : new SecP160R2FieldElement(numArray12)); }
// D.1.4 91 /** * return a sqrt root - the routine verifies that the calculation returns the right value - if * none exists it returns null. */ public override ECFieldElement Sqrt() { /* * Raise this element to the exponent 2^158 - 2^29 * * Breaking up the exponent's binary representation into "repunits", we get: * { 129 1s } { 29 0s } * * Therefore we need an addition chain containing 129 (the length of the repunit) We use: * 1, 2, 4, 8, 16, 32, 64, 128, [129] */ uint[] x1 = this.x; if (Nat160.IsZero(x1) || Nat160.IsOne(x1)) { return(this); } uint[] x2 = Nat160.Create(); SecP160R1Field.Square(x1, x2); SecP160R1Field.Multiply(x2, x1, x2); uint[] x4 = Nat160.Create(); SecP160R1Field.SquareN(x2, 2, x4); SecP160R1Field.Multiply(x4, x2, x4); uint[] x8 = x2; SecP160R1Field.SquareN(x4, 4, x8); SecP160R1Field.Multiply(x8, x4, x8); uint[] x16 = x4; SecP160R1Field.SquareN(x8, 8, x16); SecP160R1Field.Multiply(x16, x8, x16); uint[] x32 = x8; SecP160R1Field.SquareN(x16, 16, x32); SecP160R1Field.Multiply(x32, x16, x32); uint[] x64 = x16; SecP160R1Field.SquareN(x32, 32, x64); SecP160R1Field.Multiply(x64, x32, x64); uint[] x128 = x32; SecP160R1Field.SquareN(x64, 64, x128); SecP160R1Field.Multiply(x128, x64, x128); uint[] x129 = x64; SecP160R1Field.Square(x128, x129); SecP160R1Field.Multiply(x129, x1, x129); uint[] t1 = x129; SecP160R1Field.SquareN(t1, 29, t1); uint[] t2 = x128; SecP160R1Field.Square(t1, t2); return(Nat160.Eq(x1, t2) ? new SecP160R1FieldElement(t1) : null); }
public override ECFieldElement Sqrt() { uint[] y = x; if (Nat160.IsZero(y) || Nat160.IsOne(y)) { return(this); } uint[] array = Nat160.Create(); SecP160R1Field.Square(y, array); SecP160R1Field.Multiply(array, y, array); uint[] array2 = Nat160.Create(); SecP160R1Field.SquareN(array, 2, array2); SecP160R1Field.Multiply(array2, array, array2); uint[] array3 = array; SecP160R1Field.SquareN(array2, 4, array3); SecP160R1Field.Multiply(array3, array2, array3); uint[] array4 = array2; SecP160R1Field.SquareN(array3, 8, array4); SecP160R1Field.Multiply(array4, array3, array4); uint[] array5 = array3; SecP160R1Field.SquareN(array4, 16, array5); SecP160R1Field.Multiply(array5, array4, array5); uint[] array6 = array4; SecP160R1Field.SquareN(array5, 32, array6); SecP160R1Field.Multiply(array6, array5, array6); uint[] array7 = array5; SecP160R1Field.SquareN(array6, 64, array7); SecP160R1Field.Multiply(array7, array6, array7); uint[] array8 = array6; SecP160R1Field.Square(array7, array8); SecP160R1Field.Multiply(array8, y, array8); uint[] z = array8; SecP160R1Field.SquareN(z, 29, z); uint[] array9 = array7; SecP160R1Field.Square(z, array9); if (!Nat160.Eq(y, array9)) { return(null); } return(new SecP160R1FieldElement(z)); }
public override ECFieldElement Sqrt() { uint[] x = this.x; if (Nat160.IsZero(x) || Nat160.IsOne(x)) { return(this); } uint[] z = Nat160.Create(); SecP160R1Field.Square(x, z); SecP160R1Field.Multiply(z, x, z); uint[] numArray3 = Nat160.Create(); SecP160R1Field.SquareN(z, 2, numArray3); SecP160R1Field.Multiply(numArray3, z, numArray3); uint[] numArray4 = z; SecP160R1Field.SquareN(numArray3, 4, numArray4); SecP160R1Field.Multiply(numArray4, numArray3, numArray4); uint[] numArray5 = numArray3; SecP160R1Field.SquareN(numArray4, 8, numArray5); SecP160R1Field.Multiply(numArray5, numArray4, numArray5); uint[] numArray6 = numArray4; SecP160R1Field.SquareN(numArray5, 0x10, numArray6); SecP160R1Field.Multiply(numArray6, numArray5, numArray6); uint[] numArray7 = numArray5; SecP160R1Field.SquareN(numArray6, 0x20, numArray7); SecP160R1Field.Multiply(numArray7, numArray6, numArray7); uint[] numArray8 = numArray6; SecP160R1Field.SquareN(numArray7, 0x40, numArray8); SecP160R1Field.Multiply(numArray8, numArray7, numArray8); uint[] numArray9 = numArray7; SecP160R1Field.Square(numArray8, numArray9); SecP160R1Field.Multiply(numArray9, x, numArray9); uint[] numArray10 = numArray9; SecP160R1Field.SquareN(numArray10, 0x1d, numArray10); uint[] numArray11 = numArray8; SecP160R1Field.Square(numArray10, numArray11); return(!Nat160.Eq(x, numArray11) ? null : new SecP160R1FieldElement(numArray10)); }
// D.1.4 91 /** * return a sqrt root - the routine verifies that the calculation returns the right value - if * none exists it returns null. */ public override ECFieldElement Sqrt() { /* * Raise this element to the exponent 2^158 - 2^30 - 2^12 - 2^10 - 2^7 - 2^6 - 2^5 - 2^1 - 2^0 * * Breaking up the exponent's binary representation into "repunits", we get: { 127 1s } { 1 * 0s } { 17 1s } { 1 0s } { 1 1s } { 1 0s } { 2 1s } { 3 0s } { 3 1s } { 1 0s } { 1 1s } * * Therefore we need an Addition chain containing 1, 2, 3, 17, 127 (the lengths of the repunits) * We use: [1], [2], [3], 4, 7, 14, [17], 31, 62, 124, [127] */ uint[] x1 = this.x; if (Nat160.IsZero(x1) || Nat160.IsOne(x1)) { return(this); } uint[] x2 = Nat160.Create(); SecP160R2Field.Square(x1, x2); SecP160R2Field.Multiply(x2, x1, x2); uint[] x3 = Nat160.Create(); SecP160R2Field.Square(x2, x3); SecP160R2Field.Multiply(x3, x1, x3); uint[] x4 = Nat160.Create(); SecP160R2Field.Square(x3, x4); SecP160R2Field.Multiply(x4, x1, x4); uint[] x7 = Nat160.Create(); SecP160R2Field.SquareN(x4, 3, x7); SecP160R2Field.Multiply(x7, x3, x7); uint[] x14 = x4; SecP160R2Field.SquareN(x7, 7, x14); SecP160R2Field.Multiply(x14, x7, x14); uint[] x17 = x7; SecP160R2Field.SquareN(x14, 3, x17); SecP160R2Field.Multiply(x17, x3, x17); uint[] x31 = Nat160.Create(); SecP160R2Field.SquareN(x17, 14, x31); SecP160R2Field.Multiply(x31, x14, x31); uint[] x62 = x14; SecP160R2Field.SquareN(x31, 31, x62); SecP160R2Field.Multiply(x62, x31, x62); uint[] x124 = x31; SecP160R2Field.SquareN(x62, 62, x124); SecP160R2Field.Multiply(x124, x62, x124); uint[] x127 = x62; SecP160R2Field.SquareN(x124, 3, x127); SecP160R2Field.Multiply(x127, x3, x127); uint[] t1 = x127; SecP160R2Field.SquareN(t1, 18, t1); SecP160R2Field.Multiply(t1, x17, t1); SecP160R2Field.SquareN(t1, 2, t1); SecP160R2Field.Multiply(t1, x1, t1); SecP160R2Field.SquareN(t1, 3, t1); SecP160R2Field.Multiply(t1, x2, t1); SecP160R2Field.SquareN(t1, 6, t1); SecP160R2Field.Multiply(t1, x3, t1); SecP160R2Field.SquareN(t1, 2, t1); SecP160R2Field.Multiply(t1, x1, t1); uint[] t2 = x2; SecP160R2Field.Square(t1, t2); return(Nat160.Eq(x1, t2) ? new SecP160R2FieldElement(t1) : null); }