[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()