Merge pull request #40 from logos-co/PoE

add proof of equivalence PoC

proof_of_equivalence/Circom/proof_of_equivalence.circom

@@ -0,0 +1,103 @@
+//test
+pragma circom 2.1.9;
+
+include "../../circom_circuits/hash/poseidon/poseidon_16_to_1_Jubjub.circom";
+include "../../circom_circuits/hash/poseidon/poseidon_4_to_1_Jubjub.circom";
+
+template coefficient_hash(){
+    signal input coefficients[2048];
+
+    signal output hash;
+
+    component hasher[136];
+    hasher[0] = permutation_16_to_1();
+    hasher[0].in[0] <== 0;
+    for(var i = 1; i<16; i++){
+        hasher[0].in[i] <== coefficients[i-1];
+    }
+
+
+    for(var i = 1; i<136; i++){
+        hasher[i] = permutation_16_to_1();
+        hasher[i].in[0] <== hasher[i-1].out[0];
+        for(var j = 1; j<16; j++){
+            hasher[i].in[j] <== hasher[i-1].out[j] + coefficients[15*i+j-1];
+        }
+    }
+    
+    component final_hasher = hash_16_to_1();
+    for (var i =0; i<8; i++){
+        final_hasher.in[i] <== hasher[135].out[i] + coefficients[2040+i];
+    }
+    for (var i =8; i<16; i++){
+        final_hasher.in[i] <== hasher[135].out[i];
+    }
+
+    hash <== final_hasher.out;
+}
+
+template drawn_random_point(){
+    signal input da_commitment[2];
+    signal input hash_of_data;
+
+    signal output x_0;
+
+    component final_hasher = hash_4_to_1();
+
+    final_hasher.in[0] <== 0;
+    final_hasher.in[1] <== da_commitment[0];
+    final_hasher.in[2] <== da_commitment[1];
+    final_hasher.in[3] <== hash_of_data;
+
+    x_0 <== final_hasher.out;
+}
+
+template evaluate_polynomial(){
+    signal input coefficients[2048];
+    signal input evaluation_point;
+
+    signal output result;
+
+    signal intermediate_values[2046];
+    intermediate_values[2045] <== coefficients[2047] * evaluation_point + coefficients[2046];
+    for(var i = 2044; i >= 0; i--){
+        intermediate_values[i] <== coefficients[i + 1] + intermediate_values[i+1] * evaluation_point;
+    }
+
+    result <== coefficients[0] + intermediate_values[0] * evaluation_point;
+}
+
+template proof_of_equivalence(){
+    signal input coefficients[2048];
+    signal input da_commitment[2];
+
+    signal output x_0;
+    signal output y_0;
+    signal output coefficients_hash;
+
+    //Hash of the coefficients
+    component coefficient_hasher = coefficient_hash();
+    for(var i = 0; i<2048; i++){
+        coefficient_hasher.coefficients[i] <== coefficients[i];
+    }
+    coefficients_hash <== coefficient_hasher.hash;
+
+    //Hash the coefficient hash with the da_commitment
+    component point_drawer = drawn_random_point();
+    point_drawer.da_commitment[0] <== da_commitment[0];
+    point_drawer.da_commitment[1] <== da_commitment[1];
+    point_drawer.hash_of_data <== coefficients_hash;
+    x_0 <== point_drawer.x_0;
+
+    //Evaluate the polynomial at x_0
+    component evaluator = evaluate_polynomial();
+    evaluator.evaluation_point <== x_0;
+    for(var i =0; i<2048; i++){
+        evaluator.coefficients[i] <== coefficients[i];
+    }
+
+    y_0 <== evaluator.result;
+}
+
+
+component main {public [da_commitment]} = proof_of_equivalence();