github.com/emmansun/gmsm@v0.29.1/sm9/bn256/gfp2_g1_generic.go (about)

     1  //go:build purego || plugin || !(amd64 || arm64)
     2  
     3  package bn256
     4  
     5  func gfp2Mul(c, a, b *gfP2) {
     6  	tmp := &gfP2{}
     7  	tx := &tmp.x
     8  	ty := &tmp.y
     9  	v0, v1 := &gfP{}, &gfP{}
    10  
    11  	gfpMul(v0, &a.y, &b.y)
    12  	gfpMul(v1, &a.x, &b.x)
    13  
    14  	gfpAdd(tx, &a.x, &a.y)
    15  	gfpAdd(ty, &b.x, &b.y)
    16  	gfpMul(tx, tx, ty)
    17  	gfpSub(tx, tx, v0)
    18  	gfpSub(tx, tx, v1)
    19  
    20  	gfpSub(ty, v0, v1)
    21  	gfpSub(ty, ty, v1)
    22  
    23  	gfp2Copy(c, tmp)
    24  }
    25  
    26  func gfp2MulU(c, a, b *gfP2) {
    27  	tmp := &gfP2{}
    28  	tx := &tmp.x
    29  	ty := &tmp.y
    30  	v0, v1 := &gfP{}, &gfP{}
    31  
    32  	gfpMul(v0, &a.y, &b.y)
    33  	gfpMul(v1, &a.x, &b.x)
    34  
    35  	gfpAdd(tx, &a.x, &a.y)
    36  	gfpAdd(ty, &b.x, &b.y)
    37  
    38  	gfpMul(ty, tx, ty)
    39  	gfpSub(ty, ty, v0)
    40  	gfpSub(ty, ty, v1)
    41  	gfpDouble(ty, ty)
    42  	gfpNeg(ty, ty)
    43  
    44  	gfpSub(tx, v0, v1)
    45  	gfpSub(tx, tx, v1)
    46  
    47  	gfp2Copy(c, tmp)
    48  }
    49  
    50  func gfp2MulU1(c, a *gfP2) {
    51  	t := &gfP{}
    52  	gfpDouble(t, &a.x)
    53  	gfpNeg(t, t)
    54  
    55  	gfpCopy(&c.x, &a.y)
    56  	gfpCopy(&c.y, t)
    57  }
    58  
    59  func gfp2Square(c, a *gfP2) {
    60  	tmp := &gfP2{}
    61  	tx := &tmp.x
    62  	ty := &tmp.y
    63  
    64  	gfpAdd(ty, &a.x, &a.y)
    65  	gfpDouble(tx, &a.x)
    66  	gfpSub(tx, &a.y, tx)
    67  	gfpMul(ty, tx, ty)
    68  	gfpMul(tx, &a.x, &a.y)
    69  	gfpAdd(ty, tx, ty)
    70  	gfpDouble(tx, tx)
    71  
    72  	gfp2Copy(c, tmp)
    73  }
    74  
    75  func gfp2SquareU(c, a *gfP2) {
    76  	tmp := &gfP2{}
    77  	tx := &tmp.x
    78  	ty := &tmp.y
    79  
    80  	gfpAdd(tx, &a.x, &a.y)
    81  	gfpDouble(ty, &a.x)
    82  	gfpSub(ty, &a.y, ty)
    83  	gfpMul(tx, tx, ty)
    84  	gfpMul(ty, &a.x, &a.y)
    85  	gfpAdd(tx, tx, ty)
    86  	gfpDouble(ty, ty)
    87  	gfpDouble(ty, ty)
    88  	gfpNeg(ty, ty)
    89  
    90  	gfp2Copy(c, tmp)
    91  }
    92  
    93  func curvePointDoubleComplete(c, p *curvePoint) {
    94  	// Complete addition formula for a = 0 from "Complete addition formulas for
    95  	// prime order elliptic curves" (https://eprint.iacr.org/2015/1060), §3.2.
    96  	// Algorithm 9: Exception-free point doubling for prime order j-invariant 0 short Weierstrass curves.
    97  	t0, t1, t2 := new(gfP), new(gfP), new(gfP)
    98  	x3, y3, z3 := new(gfP), new(gfP), new(gfP)
    99  
   100  	gfpSqr(t0, &p.y, 1)         // t0 := Y^2
   101  	gfpDouble(z3, t0)           // Z3 := t0 + t0
   102  	gfpDouble(z3, z3)           // Z3 := Z3 + Z3
   103  	gfpDouble(z3, z3)           // Z3 := Z3 + Z3
   104  	gfpMul(t1, &p.y, &p.z)      // t1 := YZ
   105  	gfpSqr(t2, &p.z, 1)         // t2 := Z^2
   106  	gfpMul(t2, threeCurveB, t2) // t2 := 3b * t2 = 3bZ^2
   107  	gfpMul(x3, t2, z3)          // X3 := t2 * Z3
   108  	gfpAdd(y3, t0, t2)          // Y3 := t0 + t2
   109  	gfpMul(z3, t1, z3)          // Z3 := t1 * Z3
   110  	gfpTriple(t2, t2)           // t2 := t2 + t2 + t2
   111  	gfpSub(t0, t0, t2)          // t0 := t0 - t2
   112  	gfpMul(y3, t0, y3)          // Y3 := t0 * Y3
   113  	gfpAdd(y3, x3, y3)          // Y3 := X3 + Y3
   114  	gfpMul(t1, &p.x, &p.y)      // t1 := XY
   115  	gfpMul(x3, t0, t1)          // X3 := t0 * t1
   116  	gfpDouble(x3, x3)           // X3 := X3 + X3
   117  
   118  	c.x.Set(x3)
   119  	c.y.Set(y3)
   120  	c.z.Set(z3)
   121  }
   122  
   123  func curvePointAddComplete(c, p1, p2 *curvePoint) {
   124  	// Complete addition formula for a = 0 from "Complete addition formulas for
   125  	// prime order elliptic curves" (https://eprint.iacr.org/2015/1060), §3.2.
   126  	// Algorithm 7: Complete, projective point addition for prime order j-invariant 0 short Weierstrass curves.
   127  
   128  	t0, t1, t2, t3, t4 := new(gfP), new(gfP), new(gfP), new(gfP), new(gfP)
   129  	x3, y3, z3 := new(gfP), new(gfP), new(gfP)
   130  	gfpMul(t0, &p1.x, &p2.x)    // t0 := X1X2
   131  	gfpMul(t1, &p1.y, &p2.y)    // t1 := Y1Y2
   132  	gfpMul(t2, &p1.z, &p2.z)    // t2 := Z1Z2
   133  	gfpAdd(t3, &p1.x, &p1.y)    // t3 := X1 + Y1
   134  	gfpAdd(t4, &p2.x, &p2.y)    // t4 := X2 + Y2
   135  	gfpMul(t3, t3, t4)          // t3 := t3 * t4 = (X1 + Y1) * (X2 + Y2)
   136  	gfpAdd(t4, t0, t1)          // t4 := t0 + t1
   137  	gfpSub(t3, t3, t4)          // t3 := t3 - t4 = X1Y2 + X2Y1
   138  	gfpAdd(t4, &p1.y, &p1.z)    // t4 := Y1 + Z1
   139  	gfpAdd(x3, &p2.y, &p2.z)    // X3 := Y2 + Z2
   140  	gfpMul(t4, t4, x3)          // t4 := t4 * X3 = (Y1 + Z1)(Y2 + Z2)
   141  	gfpAdd(x3, t1, t2)          // X3 := t1 + t2
   142  	gfpSub(t4, t4, x3)          // t4 := t4 - X3 = Y1Z2 + Y2Z1
   143  	gfpAdd(x3, &p1.x, &p1.z)    // X3 := X1 + Z1
   144  	gfpAdd(y3, &p2.x, &p2.z)    // Y3 := X2 + Z2
   145  	gfpMul(x3, x3, y3)          // X3 := X3 * Y3
   146  	gfpAdd(y3, t0, t2)          // Y3 := t0 + t2
   147  	gfpSub(y3, x3, y3)          // Y3 := X3 - Y3 = X1Z2 + X2Z1
   148  	gfpTriple(t0, t0)           // t0 := t0 + t0 + t0 = 3X1X2
   149  	gfpMul(t2, threeCurveB, t2) // t2 := 3b * t2 = 3bZ1Z2
   150  	gfpAdd(z3, t1, t2)          // Z3 := t1 + t2 = Y1Y2 + 3bZ1Z2
   151  	gfpSub(t1, t1, t2)          // t1 := t1 - t2 = Y1Y2 - 3bZ1Z2
   152  	gfpMul(y3, threeCurveB, y3) // Y3 = 3b * Y3 = 3b(X1Z2 + X2Z1)
   153  	gfpMul(x3, t4, y3)          // X3 := t4 * Y3 = 3b(X1Z2 + X2Z1)(Y1Z2 + Y2Z1)
   154  	gfpMul(t2, t3, t1)          // t2 := t3 * t1 = (X1Y2 + X2Y1)(Y1Y2 - 3bZ1Z2)
   155  	gfpSub(x3, t2, x3)          // X3 := t2 - X3 = (X1Y2 + X2Y1)(Y1Y2 - 3bZ1Z2) - 3b(Y1Z2 + Y2Z1)(X1Z2 + X2Z1)
   156  	gfpMul(y3, y3, t0)          // Y3 := Y3 * t0 = 9bX1X2(X1Z2 + X2Z1)
   157  	gfpMul(t1, t1, z3)          // t1 := t1 * Z3 = (Y1Y2 + 3bZ1Z2)(Y1Y2 - 3bZ1Z2)
   158  	gfpAdd(y3, t1, y3)          // Y3 := t1 + Y3 = (Y1Y2 + 3bZ1Z2)(Y1Y2 - 3bZ1Z2) + 9bX1X2(X1Z2 + X2Z1)
   159  	gfpMul(t0, t0, t3)          // t0 := t0 * t3 = 3X1X2(X1Y2 + X2Y1)
   160  	gfpMul(z3, z3, t4)          // Z3 := Z3 * t4 = (Y1Z2 + Y2Z1)(Y1Y2 + 3bZ1Z2)
   161  	gfpAdd(z3, z3, t0)          // Z3 := Z3 + t0 = (Y1Z2 + Y2Z1)(Y1Y2 + 3bZ1Z2) + 3X1X2(X1Y2 + X2Y1)
   162  
   163  	c.x.Set(x3)
   164  	c.y.Set(y3)
   165  	c.z.Set(z3)
   166  }