[example] add Groth16 prover example

examples/groth16_proof_example.nim

@@ -0,0 +1,51 @@
+import constantine/proof_systems/manual_groth16,
+ constantine/named/algebras
+#import ../math/[arithmetic, extension_fields],
+# ../math/io/[io_bigints, io_fields, io_ec, io_extfields],
+# ../platforms/abstractions,
+# ../named/[algebras, properties_fields, properties_curves],
+# ../math/elliptic/[ec_shortweierstrass_affine, ec_shortweierstrass_jacobian, ec_scalar_mul, ec_multi_scalar_mul, ec_scalar_mul_vartime],
+# ../named/zoo_generators,
+# ../csprngs/sysrand
+#import ./groth16_utils
+
+const T = BN254_Snarks
+
+let wtns = parseWtnsFile("./groth16_files/three_fac_js/witness.wtns").toWtns[:T]()
+let zkey = parseZkeyFile("./groth16_files/three_fac_final.zkey").toZkey[:T]()
+let r1cs = parseR1csFile("./groth16_files/three_fac.r1cs").toR1CS()
+
+var ctx = Groth16Prover[T].init(zkey, wtns, r1cs)
+
+const rSJ = @[
+ byte 143, 55, 118, 73, 42, 115, 60, 77,
+ 95, 209, 41, 144, 250, 137, 138, 71,
+ 176, 242, 186, 232, 179, 30, 88, 255,
+ 198, 161, 182, 150, 220, 149, 33, 19
+]
+const sSJ = @[
+ byte 213, 105, 105, 27, 129, 249, 139, 158,
+ 221, 68, 37, 163, 59, 71, 19, 108,
+ 60, 153, 183, 156, 25, 148, 37, 9,
+ 85, 205, 250, 246, 132, 142, 244, 36
+]
+
+# construct the random element `r` from snarkjs "secret" r
+let r = toFr[BN254_Snarks](rSJ)
+# and `s`
+let s = toFr[BN254_Snarks](sSJ)
+
+ctx.r = r
+ctx.s = s
+
+let (A_p, B2_p, C_p) = ctx.prove()
+
+echo "\n==============================\n"
+echo "A_p#16 = ", A_p.toHex()
+echo "A_p#10 = ", A_p.toDecimal()
+echo "------------------------------"
+echo "B_p#16 = ", B2_p.toHex()
+echo "B_p#10 = ", B2_p.toDecimal()
+echo "------------------------------"
+echo "C_p#16 = ", C_p.toHex()
+echo "C_p#10 = ", C_p.toDecimal()