116 lines
3.2 KiB
Go
116 lines
3.2 KiB
Go
package bn256
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import (
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"math/big"
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)
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var half = new(big.Int).Rsh(Order, 1)
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var curveLattice = &lattice{
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vectors: [][]*big.Int{
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{bigFromBase10("147946756881789319000765030803803410728"), bigFromBase10("147946756881789319010696353538189108491")},
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{bigFromBase10("147946756881789319020627676272574806254"), bigFromBase10("-147946756881789318990833708069417712965")},
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},
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inverse: []*big.Int{
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bigFromBase10("147946756881789318990833708069417712965"),
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bigFromBase10("147946756881789319010696353538189108491"),
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},
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det: bigFromBase10("43776485743678550444492811490514550177096728800832068687396408373151616991234"),
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}
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var targetLattice = &lattice{
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vectors: [][]*big.Int{
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{bigFromBase10("9931322734385697761"), bigFromBase10("9931322734385697761"), bigFromBase10("9931322734385697763"), bigFromBase10("9931322734385697764")},
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{bigFromBase10("4965661367192848881"), bigFromBase10("4965661367192848881"), bigFromBase10("4965661367192848882"), bigFromBase10("-9931322734385697762")},
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{bigFromBase10("-9931322734385697762"), bigFromBase10("-4965661367192848881"), bigFromBase10("4965661367192848881"), bigFromBase10("-4965661367192848882")},
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{bigFromBase10("9931322734385697763"), bigFromBase10("-4965661367192848881"), bigFromBase10("-4965661367192848881"), bigFromBase10("-4965661367192848881")},
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},
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inverse: []*big.Int{
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bigFromBase10("734653495049373973658254490726798021314063399421879442165"),
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bigFromBase10("147946756881789319000765030803803410728"),
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bigFromBase10("-147946756881789319005730692170996259609"),
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bigFromBase10("1469306990098747947464455738335385361643788813749140841702"),
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},
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det: new(big.Int).Set(Order),
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}
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type lattice struct {
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vectors [][]*big.Int
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inverse []*big.Int
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det *big.Int
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}
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// decompose takes a scalar mod Order as input and finds a short, positive decomposition of it wrt to the lattice basis.
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func (l *lattice) decompose(k *big.Int) []*big.Int {
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n := len(l.inverse)
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// Calculate closest vector in lattice to <k,0,0,...> with Babai's rounding.
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c := make([]*big.Int, n)
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for i := 0; i < n; i++ {
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c[i] = new(big.Int).Mul(k, l.inverse[i])
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round(c[i], l.det)
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}
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// Transform vectors according to c and subtract <k,0,0,...>.
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out := make([]*big.Int, n)
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temp := new(big.Int)
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for i := 0; i < n; i++ {
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out[i] = new(big.Int)
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for j := 0; j < n; j++ {
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temp.Mul(c[j], l.vectors[j][i])
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out[i].Add(out[i], temp)
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}
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out[i].Neg(out[i])
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out[i].Add(out[i], l.vectors[0][i]).Add(out[i], l.vectors[0][i])
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}
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out[0].Add(out[0], k)
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return out
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}
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func (l *lattice) Precompute(add func(i, j uint)) {
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n := uint(len(l.vectors))
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total := uint(1) << n
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for i := uint(0); i < n; i++ {
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for j := uint(0); j < total; j++ {
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if (j>>i)&1 == 1 {
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add(i, j)
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}
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}
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}
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}
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func (l *lattice) Multi(scalar *big.Int) []uint8 {
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decomp := l.decompose(scalar)
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maxLen := 0
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for _, x := range decomp {
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if x.BitLen() > maxLen {
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maxLen = x.BitLen()
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}
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}
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out := make([]uint8, maxLen)
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for j, x := range decomp {
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for i := 0; i < maxLen; i++ {
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out[i] += uint8(x.Bit(i)) << uint(j)
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}
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}
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return out
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}
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// round sets num to num/denom rounded to the nearest integer.
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func round(num, denom *big.Int) {
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r := new(big.Int)
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num.DivMod(num, denom, r)
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if r.Cmp(half) == 1 {
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num.Add(num, big.NewInt(1))
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}
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}
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