p256_invert.mx raw

   1  // Copyright 2021 The Go Authors. All rights reserved.
   2  // Use of this source code is governed by a BSD-style
   3  // license that can be found in the LICENSE file.
   4  
   5  // Code generated by addchain. DO NOT EDIT.
   6  
   7  package fiat
   8  
   9  // Invert sets e = 1/x, and returns e.
  10  //
  11  // If x == 0, Invert returns e = 0.
  12  func (e *P256Element) Invert(x *P256Element) *P256Element {
  13  	// Inversion is implemented as exponentiation with exponent p − 2.
  14  	// The sequence of 12 multiplications and 255 squarings is derived from the
  15  	// following addition chain generated with github.com/mmcloughlin/addchain v0.4.0.
  16  	//
  17  	//	_10     = 2*1
  18  	//	_11     = 1 + _10
  19  	//	_110    = 2*_11
  20  	//	_111    = 1 + _110
  21  	//	_111000 = _111 << 3
  22  	//	_111111 = _111 + _111000
  23  	//	x12     = _111111 << 6 + _111111
  24  	//	x15     = x12 << 3 + _111
  25  	//	x16     = 2*x15 + 1
  26  	//	x32     = x16 << 16 + x16
  27  	//	i53     = x32 << 15
  28  	//	x47     = x15 + i53
  29  	//	i263    = ((i53 << 17 + 1) << 143 + x47) << 47
  30  	//	return    (x47 + i263) << 2 + 1
  31  	//
  32  
  33  	var z = (&P256Element{}).Set(e)
  34  	var t0 = &P256Element{}
  35  	var t1 = &P256Element{}
  36  
  37  	z.Square(x)
  38  	z.Mul(x, z)
  39  	z.Square(z)
  40  	z.Mul(x, z)
  41  	t0.Square(z)
  42  	for s := 1; s < 3; s++ {
  43  		t0.Square(t0)
  44  	}
  45  	t0.Mul(z, t0)
  46  	t1.Square(t0)
  47  	for s := 1; s < 6; s++ {
  48  		t1.Square(t1)
  49  	}
  50  	t0.Mul(t0, t1)
  51  	for s := 0; s < 3; s++ {
  52  		t0.Square(t0)
  53  	}
  54  	z.Mul(z, t0)
  55  	t0.Square(z)
  56  	t0.Mul(x, t0)
  57  	t1.Square(t0)
  58  	for s := 1; s < 16; s++ {
  59  		t1.Square(t1)
  60  	}
  61  	t0.Mul(t0, t1)
  62  	for s := 0; s < 15; s++ {
  63  		t0.Square(t0)
  64  	}
  65  	z.Mul(z, t0)
  66  	for s := 0; s < 17; s++ {
  67  		t0.Square(t0)
  68  	}
  69  	t0.Mul(x, t0)
  70  	for s := 0; s < 143; s++ {
  71  		t0.Square(t0)
  72  	}
  73  	t0.Mul(z, t0)
  74  	for s := 0; s < 47; s++ {
  75  		t0.Square(t0)
  76  	}
  77  	z.Mul(z, t0)
  78  	for s := 0; s < 2; s++ {
  79  		z.Square(z)
  80  	}
  81  	z.Mul(x, z)
  82  
  83  	return e.Set(z)
  84  }
  85