adding BN254 Snarks generators (#193)

adding generator values based on
https://github.com/ethereum/EIPs/blob/master/EIPS/eip-197.md

Signed-off-by: Csaba Kiraly <csaba.kiraly@gmail.com>

constantine/math/curves/bn254_snarks_generators.nim

@@ -0,0 +1,44 @@
+# Constantine
+# Copyright (c) 2018-2019    Status Research & Development GmbH
+# Copyright (c) 2020-Present Mamy André-Ratsimbazafy
+# Licensed and distributed under either of
+#   * MIT license (license terms in the root directory or at http://opensource.org/licenses/MIT).
+#   * Apache v2 license (license terms in the root directory or at http://www.apache.org/licenses/LICENSE-2.0).
+# at your option. This file may not be copied, modified, or distributed except according to those terms.
+
+import
+  ../config/curves,
+  ../elliptic/ec_shortweierstrass_affine,
+  ../io/[io_fields, io_extfields]
+
+# Generators
+# -----------------------------------------------------------------
+# https://github.com/ethereum/EIPs/blob/master/EIPS/eip-197.md
+
+# The group G_1 is defined on the curve Y^2 = X^3 + 3 over the field F_p 
+# with p = 21888242871839275222246405745257275088696311157297823662689037894645226208583
+# with generator P1 = (1, 2).
+const BN254_Snarks_generator_G1* = ECP_ShortW_Aff[Fp[BN254_Snarks], G1](
+  x: Fp[BN254_Snarks].fromHex"0x1",
+  y: Fp[BN254_Snarks].fromHex"0x2"
+)
+
+# The group G_2 is defined on the curve Y^2 = X^3 + 3/(i+9)
+# over a different field F_p^2 = F_p[i] / (i^2 + 1) (p is the same as above) 
+# with generator
+# P2 = (
+#   11559732032986387107991004021392285783925812861821192530917403151452391805634 * i +
+#   10857046999023057135944570762232829481370756359578518086990519993285655852781,
+#   4082367875863433681332203403145435568316851327593401208105741076214120093531 * i +
+#   8495653923123431417604973247489272438418190587263600148770280649306958101930
+# )
+const BN254_Snarks_generator_G2* = ECP_ShortW_Aff[Fp2[BN254_Snarks], G2](
+  x: Fp2[BN254_Snarks].fromHex(
+    "0x1800DEEF121F1E76426A00665E5C4479674322D4F75EDADD46DEBD5CD992F6ED",
+    "0x198E9393920D483A7260BFB731FB5D25F1AA493335A9E71297E485B7AEF312C2"
+  ),
+  y: Fp2[BN254_Snarks].fromHex(
+    "0x12C85EA5DB8C6DEB4AAB71808DCB408FE3D1E7690C43D37B4CE6CC0166FA7DAA",
+    "0x90689D0585FF075EC9E99AD690C3395BC4B313370B38EF355ACDADCD122975B"
+  )
+)

constantine/math/curves/zoo_generators.nim

@@ -9,7 +9,8 @@
 import
   std/macros,
   ../config/curves,
-  ./bls12_381_generators
+  ./bls12_381_generators,
+  ./bn254_snarks_generators
 
 {.experimental: "dynamicbindsym".}