perf: in-circuit ECDSA on secp256k1

std/algebra/weierstrass/doc.go

@@ -25,9 +25,6 @@ This package uses field emulation (unlike packages
 [github.com/consensys/gnark/std/algebra/sw_bls12377] and
 [github.com/consensys/gnark/std/algebra/sw_bls24315], which use 2-chains). This
 allows to use any curve over any native (SNARK) field. The drawback of this
-approach is the extreme cost of the operations. In R1CS, point addition on
-256-bit fields is approximately 3500 constraints and doubling is approximately
-4300 constraints. A full scalar multiplication is approximately 2M constraints.
-It is several times more in PLONKish aritmetisation.
+approach is the extreme cost of the operations.
 */
 package weierstrass

std/algebra/weierstrass/params.go

@@ -13,10 +13,11 @@ import (
 //
 // The base point is defined by (Gx, Gy).
 type CurveParams struct {
-	A  *big.Int // a in curve equation
-	B  *big.Int // b in curve equation
-	Gx *big.Int // base point x
-	Gy *big.Int // base point y
+	A  *big.Int      // a in curve equation
+	B  *big.Int      // b in curve equation
+	Gx *big.Int      // base point x
+	Gy *big.Int      // base point y
+	Gm [][2]*big.Int // m*base point coords
 }
 
 // GetSecp256k1Params returns curve parameters for the curve secp256k1. When
@@ -30,6 +31,7 @@ func GetSecp256k1Params() CurveParams {
 		B:  big.NewInt(7),
 		Gx: gx,
 		Gy: gy,
+		Gm: computeSecp256k1Table(),
 	}
 }
 
@@ -39,11 +41,13 @@ func GetSecp256k1Params() CurveParams {
 func GetBN254Params() CurveParams {
 	gx := big.NewInt(1)
 	gy := big.NewInt(2)
+
 	return CurveParams{
 		A:  big.NewInt(0),
 		B:  big.NewInt(3),
 		Gx: gx,
 		Gy: gy,
+		Gm: computeBN254Table(),
 	}
 }
 

std/algebra/weierstrass/params_compute.go

@@ -0,0 +1,60 @@
+package weierstrass
+
+import (
+	"math/big"
+
+	"github.com/consensys/gnark-crypto/ecc/bn254"
+	"github.com/consensys/gnark-crypto/ecc/secp256k1"
+)
+
+func computeSecp256k1Table() [][2]*big.Int {
+	Gjac, _ := secp256k1.Generators()
+	table := make([][2]*big.Int, 256)
+	tmp := new(secp256k1.G1Jac).Set(&Gjac)
+	aff := new(secp256k1.G1Affine)
+	jac := new(secp256k1.G1Jac)
+	for i := 1; i < 256; i++ {
+		tmp = tmp.Double(tmp)
+		switch i {
+		case 1, 2:
+			jac.Set(tmp).AddAssign(&Gjac)
+			aff.FromJacobian(jac)
+			table[i-1] = [2]*big.Int{aff.X.BigInt(new(big.Int)), aff.Y.BigInt(new(big.Int))}
+		case 3:
+			jac.Set(tmp).SubAssign(&Gjac)
+			aff.FromJacobian(jac)
+			table[i-1] = [2]*big.Int{aff.X.BigInt(new(big.Int)), aff.Y.BigInt(new(big.Int))}
+			fallthrough
+		default:
+			aff.FromJacobian(tmp)
+			table[i] = [2]*big.Int{aff.X.BigInt(new(big.Int)), aff.Y.BigInt(new(big.Int))}
+		}
+	}
+	return table[:]
+}
+
+func computeBN254Table() [][2]*big.Int {
+	Gjac, _, _, _ := bn254.Generators()
+	table := make([][2]*big.Int, 256)
+	tmp := new(bn254.G1Jac).Set(&Gjac)
+	aff := new(bn254.G1Affine)
+	jac := new(bn254.G1Jac)
+	for i := 1; i < 256; i++ {
+		tmp = tmp.Double(tmp)
+		switch i {
+		case 1, 2:
+			jac.Set(tmp).AddAssign(&Gjac)
+			aff.FromJacobian(jac)
+			table[i-1] = [2]*big.Int{aff.X.BigInt(new(big.Int)), aff.Y.BigInt(new(big.Int))}
+		case 3:
+			jac.Set(tmp).SubAssign(&Gjac)
+			aff.FromJacobian(jac)
+			table[i-1] = [2]*big.Int{aff.X.BigInt(new(big.Int)), aff.Y.BigInt(new(big.Int))}
+			fallthrough
+		default:
+			aff.FromJacobian(tmp)
+			table[i] = [2]*big.Int{aff.X.BigInt(new(big.Int)), aff.Y.BigInt(new(big.Int))}
+		}
+	}
+	return table
+}