implemented bls12_381 built-in primitives

lib/ak-381/groth16.ak

@@ -1,29 +1,41 @@
-use aiken/builtin.{bls12_381_final_verify, bls12_381_miller_loop}
+use aiken.{G1Element, G2Element}  // ,MillerLoopResult
+use aiken/builtin.{bls12_381_final_verify, bls12_381_miller_loop, bls12_381_g1_scalar_mul, bls12_381_g1_add, bls12_381_mul_miller_loop_result}
+use aiken/list.{head, map2, reduce, tail}
 
-type VerificationKey {
+pub type VerificationKey {
   nPublic: Int,
-  vkAlpha: List<Int>,
-  vkBeta: List<List<Int>>,
-  vkGamma: List<List<Int>>,
-  vkDelta: List<List<Int>>,
-  vkAlphaBeta: List<List<List<Int>>>,
-  vkIC: List<List<Int>>,
+  vkAlpha: G1Element,
+  vkBeta: G2Element,
+  vkGamma: G2Element,
+  vkDelta: G2Element,
+  vkAlphaBeta: List<G2Element>,
+  vkIC: List<G1Element>
 }
 
-type Proof {
-  piA: List<Int>,
-  piB: List<List<Int>>,
-  piC: List<Int>,
+pub type Proof {
+  piA: G1Element,
+  piB: G2Element,
+  piC: G1Element
 }
 
-pub fn pairing(alfa: G1, beta: G2) -> Bool {
-  todo
+pub fn pairing(g1: G1Element, g2: G2Element) {
+    bls12_381_miller_loop(g1, g2)
 }
 
-pub fn groth_verify(
-  vk: VerificationKey,
-  proof: Proof,
-  public: List<Int>,
-) -> Bool {
-  todo
+pub fn groth_verify(vk: VerificationKey, proof: Proof, public: List<Int>) -> Bool {
+   // let n = vk.nPublic
+
+   let eAB = pairing(proof.piA, proof.piB)
+   let eAlphaBeta = pairing(vk.vkAlpha, vk.vkBeta)
+
+   expect Some(vkICHead) = head(vk.vkIC)
+   expect Some(vkICTail) = tail(vk.vkIC)
+   let derived_vkIC = map2(public, vkICTail, bls12_381_g1_scalar_mul)
+   let vkI = reduce(derived_vkIC, vkICHead, bls12_381_g1_add)
+   let eIGamma = pairing(vkI, vk.vkGamma)
+   let eCDelta = pairing(proof.piC, vk.vkDelta)
+
+   let mlr1 = bls12_381_mul_miller_loop_result(eAlphaBeta, eIGamma)
+   let mlr2 = bls12_381_mul_miller_loop_result(mlr1, eCDelta)
+   bls12_381_final_verify(eAB, mlr2)
 }