crypto/bn256: full switchover to cloudflare's code (#16301)

* crypto/bn256: full switchover to cloudflare's code

* crypto/bn256: only use cloudflare for optimized architectures

* crypto/bn256: upstream fallback for non-optimized code

* .travis, build: drop support for Go 1.8 (need type aliases)

* crypto/bn256/cloudflare: enable curve mul lattice optimization

1 files changed, 115 insertions, 0 deletions

diff --git a/crypto/bn256/cloudflare/lattice.go b/crypto/bn256/cloudflare/lattice.go
new file mode 100644
index 000000000..f9ace4d9f
--- /dev/null
+++ b/crypto/bn256/cloudflare/lattice.go
@@ -0,0 +1,115 @@
+package bn256
+
+import (
+	"math/big"
+)
+
+var half = new(big.Int).Rsh(Order, 1)
+
+var curveLattice = &lattice{
+	vectors: [][]*big.Int{
+		{bigFromBase10("147946756881789319000765030803803410728"), bigFromBase10("147946756881789319010696353538189108491")},
+		{bigFromBase10("147946756881789319020627676272574806254"), bigFromBase10("-147946756881789318990833708069417712965")},
+	},
+	inverse: []*big.Int{
+		bigFromBase10("147946756881789318990833708069417712965"),
+		bigFromBase10("147946756881789319010696353538189108491"),
+	},
+	det: bigFromBase10("43776485743678550444492811490514550177096728800832068687396408373151616991234"),
+}
+
+var targetLattice = &lattice{
+	vectors: [][]*big.Int{
+		{bigFromBase10("9931322734385697761"), bigFromBase10("9931322734385697761"), bigFromBase10("9931322734385697763"), bigFromBase10("9931322734385697764")},
+		{bigFromBase10("4965661367192848881"), bigFromBase10("4965661367192848881"), bigFromBase10("4965661367192848882"), bigFromBase10("-9931322734385697762")},
+		{bigFromBase10("-9931322734385697762"), bigFromBase10("-4965661367192848881"), bigFromBase10("4965661367192848881"), bigFromBase10("-4965661367192848882")},
+		{bigFromBase10("9931322734385697763"), bigFromBase10("-4965661367192848881"), bigFromBase10("-4965661367192848881"), bigFromBase10("-4965661367192848881")},
+	},
+	inverse: []*big.Int{
+		bigFromBase10("734653495049373973658254490726798021314063399421879442165"),
+		bigFromBase10("147946756881789319000765030803803410728"),
+		bigFromBase10("-147946756881789319005730692170996259609"),
+		bigFromBase10("1469306990098747947464455738335385361643788813749140841702"),
+	},
+	det: new(big.Int).Set(Order),
+}
+
+type lattice struct {
+	vectors [][]*big.Int
+	inverse []*big.Int
+	det     *big.Int
+}
+
+// decompose takes a scalar mod Order as input and finds a short, positive decomposition of it wrt to the lattice basis.
+func (l *lattice) decompose(k *big.Int) []*big.Int {
+	n := len(l.inverse)
+
+	// Calculate closest vector in lattice to <k,0,0,...> with Babai's rounding.
+	c := make([]*big.Int, n)
+	for i := 0; i < n; i++ {
+		c[i] = new(big.Int).Mul(k, l.inverse[i])
+		round(c[i], l.det)
+	}
+
+	// Transform vectors according to c and subtract <k,0,0,...>.
+	out := make([]*big.Int, n)
+	temp := new(big.Int)
+
+	for i := 0; i < n; i++ {
+		out[i] = new(big.Int)
+
+		for j := 0; j < n; j++ {
+			temp.Mul(c[j], l.vectors[j][i])
+			out[i].Add(out[i], temp)
+		}
+
+		out[i].Neg(out[i])
+		out[i].Add(out[i], l.vectors[0][i]).Add(out[i], l.vectors[0][i])
+	}
+	out[0].Add(out[0], k)
+
+	return out
+}
+
+func (l *lattice) Precompute(add func(i, j uint)) {
+	n := uint(len(l.vectors))
+	total := uint(1) << n
+
+	for i := uint(0); i < n; i++ {
+		for j := uint(0); j < total; j++ {
+			if (j>>i)&1 == 1 {
+				add(i, j)
+			}
+		}
+	}
+}
+
+func (l *lattice) Multi(scalar *big.Int) []uint8 {
+	decomp := l.decompose(scalar)
+
+	maxLen := 0
+	for _, x := range decomp {
+		if x.BitLen() > maxLen {
+			maxLen = x.BitLen()
+		}
+	}
+
+	out := make([]uint8, maxLen)
+	for j, x := range decomp {
+		for i := 0; i < maxLen; i++ {
+			out[i] += uint8(x.Bit(i)) << uint(j)
+		}
+	}
+
+	return out
+}
+
+// round sets num to num/denom rounded to the nearest integer.
+func round(num, denom *big.Int) {
+	r := new(big.Int)
+	num.DivMod(num, denom, r)
+
+	if r.Cmp(half) == 1 {
+		num.Add(num, big.NewInt(1))
+	}
+}