github.com/intfoundation/intchain@v0.0.0-20220727031208-4316ad31ca73/crypto/bn256/google/constants.go (about)

     1  // Copyright 2012 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  package bn256
     6  
     7  import (
     8  	"math/big"
     9  )
    10  
    11  func bigFromBase10(s string) *big.Int {
    12  	n, _ := new(big.Int).SetString(s, 10)
    13  	return n
    14  }
    15  
    16  // u is the BN parameter that determines the prime: 1868033³.
    17  var u = bigFromBase10("4965661367192848881")
    18  
    19  // p is a prime over which we form a basic field: 36u⁴+36u³+24u²+6u+1.
    20  var P = bigFromBase10("21888242871839275222246405745257275088696311157297823662689037894645226208583")
    21  
    22  // Order is the number of elements in both G₁ and G₂: 36u⁴+36u³+18u²+6u+1.
    23  var Order = bigFromBase10("21888242871839275222246405745257275088548364400416034343698204186575808495617")
    24  
    25  // xiToPMinus1Over6 is ξ^((p-1)/6) where ξ = i+9.
    26  var xiToPMinus1Over6 = &gfP2{bigFromBase10("16469823323077808223889137241176536799009286646108169935659301613961712198316"), bigFromBase10("8376118865763821496583973867626364092589906065868298776909617916018768340080")}
    27  
    28  // xiToPMinus1Over3 is ξ^((p-1)/3) where ξ = i+9.
    29  var xiToPMinus1Over3 = &gfP2{bigFromBase10("10307601595873709700152284273816112264069230130616436755625194854815875713954"), bigFromBase10("21575463638280843010398324269430826099269044274347216827212613867836435027261")}
    30  
    31  // xiToPMinus1Over2 is ξ^((p-1)/2) where ξ = i+9.
    32  var xiToPMinus1Over2 = &gfP2{bigFromBase10("3505843767911556378687030309984248845540243509899259641013678093033130930403"), bigFromBase10("2821565182194536844548159561693502659359617185244120367078079554186484126554")}
    33  
    34  // xiToPSquaredMinus1Over3 is ξ^((p²-1)/3) where ξ = i+9.
    35  var xiToPSquaredMinus1Over3 = bigFromBase10("21888242871839275220042445260109153167277707414472061641714758635765020556616")
    36  
    37  // xiTo2PSquaredMinus2Over3 is ξ^((2p²-2)/3) where ξ = i+9 (a cubic root of unity, mod p).
    38  var xiTo2PSquaredMinus2Over3 = bigFromBase10("2203960485148121921418603742825762020974279258880205651966")
    39  
    40  // xiToPSquaredMinus1Over6 is ξ^((1p²-1)/6) where ξ = i+9 (a cubic root of -1, mod p).
    41  var xiToPSquaredMinus1Over6 = bigFromBase10("21888242871839275220042445260109153167277707414472061641714758635765020556617")
    42  
    43  // xiTo2PMinus2Over3 is ξ^((2p-2)/3) where ξ = i+9.
    44  var xiTo2PMinus2Over3 = &gfP2{bigFromBase10("19937756971775647987995932169929341994314640652964949448313374472400716661030"), bigFromBase10("2581911344467009335267311115468803099551665605076196740867805258568234346338")}