feat(circom): fully constraint is_valid_merkle_branch_out

beacon-light-client/circom/circuits/is_valid_merkle_branch_out.circom

@@ -3,6 +3,7 @@ pragma circom 2.1.5;
 include "hash_two.circom";
 include "../../../node_modules/circomlib/circuits/comparators.circom";
 include "utils/arrays.circom";
+include "utils/numerical.circom";
 
 template IsValidMerkleBranchOut(N) {
   signal input branch[N][256];
@@ -14,12 +15,27 @@ template IsValidMerkleBranchOut(N) {
 
   component hashers[N];
   component isZero[N];
+  component pow[N];
+  component divisionByTwo[N];
+  component divisionByPow[N];
 
   for(var i = 0; i < N; i++) {
     hashers[i] = HashTwo();
     isZero[i] = IsZero();
 
-    isZero[i].in <-- (index \ (2**i)) % 2;
+    pow[i] = Pow(256);
+    pow[i].base <== 2;
+    pow[i].power <== i;
+
+    divisionByPow[i] = DivisionBy();
+    divisionByPow[i].dividend <== index;
+    divisionByPow[i].divisor <== pow[i].out;
+
+    divisionByTwo[i] = DivisionBy();
+    divisionByTwo[i].dividend <== divisionByPow[i].quotient;
+    divisionByTwo[i].divisor <== 2;
+
+    isZero[i].in <== divisionByTwo[i].remainder;
 
     var current[256];