github.com/aigarnetwork/aigar@v0.0.0-20191115204914-d59a6eb70f8e/crypto/bn256/cloudflare/gfp12.go (about)

     1  //  Copyright 2018 The go-ethereum Authors
     2  //  Copyright 2019 The go-aigar Authors
     3  //  This file is part of the go-aigar library.
     4  //
     5  //  The go-aigar library is free software: you can redistribute it and/or modify
     6  //  it under the terms of the GNU Lesser General Public License as published by
     7  //  the Free Software Foundation, either version 3 of the License, or
     8  //  (at your option) any later version.
     9  //
    10  //  The go-aigar library is distributed in the hope that it will be useful,
    11  //  but WITHOUT ANY WARRANTY; without even the implied warranty of
    12  //  MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
    13  //  GNU Lesser General Public License for more details.
    14  //
    15  //  You should have received a copy of the GNU Lesser General Public License
    16  //  along with the go-aigar library. If not, see <http://www.gnu.org/licenses/>.
    17  
    18  package bn256
    19  
    20  // For details of the algorithms used, see "Multiplication and Squaring on
    21  // Pairing-Friendly Fields, Devegili et al.
    22  // http://eprint.iacr.org/2006/471.pdf.
    23  
    24  import (
    25  	"math/big"
    26  )
    27  
    28  // gfP12 implements the field of size p¹² as a quadratic extension of gfP6
    29  // where ω²=τ.
    30  type gfP12 struct {
    31  	x, y gfP6 // value is xω + y
    32  }
    33  
    34  func (e *gfP12) String() string {
    35  	return "(" + e.x.String() + "," + e.y.String() + ")"
    36  }
    37  
    38  func (e *gfP12) Set(a *gfP12) *gfP12 {
    39  	e.x.Set(&a.x)
    40  	e.y.Set(&a.y)
    41  	return e
    42  }
    43  
    44  func (e *gfP12) SetZero() *gfP12 {
    45  	e.x.SetZero()
    46  	e.y.SetZero()
    47  	return e
    48  }
    49  
    50  func (e *gfP12) SetOne() *gfP12 {
    51  	e.x.SetZero()
    52  	e.y.SetOne()
    53  	return e
    54  }
    55  
    56  func (e *gfP12) IsZero() bool {
    57  	return e.x.IsZero() && e.y.IsZero()
    58  }
    59  
    60  func (e *gfP12) IsOne() bool {
    61  	return e.x.IsZero() && e.y.IsOne()
    62  }
    63  
    64  func (e *gfP12) Conjugate(a *gfP12) *gfP12 {
    65  	e.x.Neg(&a.x)
    66  	e.y.Set(&a.y)
    67  	return e
    68  }
    69  
    70  func (e *gfP12) Neg(a *gfP12) *gfP12 {
    71  	e.x.Neg(&a.x)
    72  	e.y.Neg(&a.y)
    73  	return e
    74  }
    75  
    76  // Frobenius computes (xω+y)^p = x^p ω·ξ^((p-1)/6) + y^p
    77  func (e *gfP12) Frobenius(a *gfP12) *gfP12 {
    78  	e.x.Frobenius(&a.x)
    79  	e.y.Frobenius(&a.y)
    80  	e.x.MulScalar(&e.x, xiToPMinus1Over6)
    81  	return e
    82  }
    83  
    84  // FrobeniusP2 computes (xω+y)^p² = x^p² ω·ξ^((p²-1)/6) + y^p²
    85  func (e *gfP12) FrobeniusP2(a *gfP12) *gfP12 {
    86  	e.x.FrobeniusP2(&a.x)
    87  	e.x.MulGFP(&e.x, xiToPSquaredMinus1Over6)
    88  	e.y.FrobeniusP2(&a.y)
    89  	return e
    90  }
    91  
    92  func (e *gfP12) FrobeniusP4(a *gfP12) *gfP12 {
    93  	e.x.FrobeniusP4(&a.x)
    94  	e.x.MulGFP(&e.x, xiToPSquaredMinus1Over3)
    95  	e.y.FrobeniusP4(&a.y)
    96  	return e
    97  }
    98  
    99  func (e *gfP12) Add(a, b *gfP12) *gfP12 {
   100  	e.x.Add(&a.x, &b.x)
   101  	e.y.Add(&a.y, &b.y)
   102  	return e
   103  }
   104  
   105  func (e *gfP12) Sub(a, b *gfP12) *gfP12 {
   106  	e.x.Sub(&a.x, &b.x)
   107  	e.y.Sub(&a.y, &b.y)
   108  	return e
   109  }
   110  
   111  func (e *gfP12) Mul(a, b *gfP12) *gfP12 {
   112  	tx := (&gfP6{}).Mul(&a.x, &b.y)
   113  	t := (&gfP6{}).Mul(&b.x, &a.y)
   114  	tx.Add(tx, t)
   115  
   116  	ty := (&gfP6{}).Mul(&a.y, &b.y)
   117  	t.Mul(&a.x, &b.x).MulTau(t)
   118  
   119  	e.x.Set(tx)
   120  	e.y.Add(ty, t)
   121  	return e
   122  }
   123  
   124  func (e *gfP12) MulScalar(a *gfP12, b *gfP6) *gfP12 {
   125  	e.x.Mul(&e.x, b)
   126  	e.y.Mul(&e.y, b)
   127  	return e
   128  }
   129  
   130  func (c *gfP12) Exp(a *gfP12, power *big.Int) *gfP12 {
   131  	sum := (&gfP12{}).SetOne()
   132  	t := &gfP12{}
   133  
   134  	for i := power.BitLen() - 1; i >= 0; i-- {
   135  		t.Square(sum)
   136  		if power.Bit(i) != 0 {
   137  			sum.Mul(t, a)
   138  		} else {
   139  			sum.Set(t)
   140  		}
   141  	}
   142  
   143  	c.Set(sum)
   144  	return c
   145  }
   146  
   147  func (e *gfP12) Square(a *gfP12) *gfP12 {
   148  	// Complex squaring algorithm
   149  	v0 := (&gfP6{}).Mul(&a.x, &a.y)
   150  
   151  	t := (&gfP6{}).MulTau(&a.x)
   152  	t.Add(&a.y, t)
   153  	ty := (&gfP6{}).Add(&a.x, &a.y)
   154  	ty.Mul(ty, t).Sub(ty, v0)
   155  	t.MulTau(v0)
   156  	ty.Sub(ty, t)
   157  
   158  	e.x.Add(v0, v0)
   159  	e.y.Set(ty)
   160  	return e
   161  }
   162  
   163  func (e *gfP12) Invert(a *gfP12) *gfP12 {
   164  	// See "Implementing cryptographic pairings", M. Scott, section 3.2.
   165  	// ftp://136.206.11.249/pub/crypto/pairings.pdf
   166  	t1, t2 := &gfP6{}, &gfP6{}
   167  
   168  	t1.Square(&a.x)
   169  	t2.Square(&a.y)
   170  	t1.MulTau(t1).Sub(t2, t1)
   171  	t2.Invert(t1)
   172  
   173  	e.x.Neg(&a.x)
   174  	e.y.Set(&a.y)
   175  	e.MulScalar(e, t2)
   176  	return e
   177  }