puzzle1-writeup

puzzle-gamma-ray (writeup).md

puzzle-gamma-ray

This issue aims to construct a "secret_hack" and "nullifier_hack" to pass the circuit checking.

What are constraints of the circuit?

1. The circuit related operation is defined on MNT6.

2. The nullifier is generated by the secret through poseidon. $$nullifier = Poseidon(secret)$$

3. The generation of leaf_g.

   • Calculate $pk$, which is a point on curve MNT6 $$pk = secret * G_{MNT6}$$
   • Calculate leaf_g, which is the $x$ of $pk$ $$leaf_g = pk.x$$

4. leaf_g is on the Merkle tree with specified root.

How to construct hacking secret?

So the key is to construct the secret_hack. Clearly, there are two points on curve with the same x, which is the symmetric point of $pk$, noted as $pk'$. $$pk' = -pk$$

So $$secret_hack = -secret \ nullifier_hack = Poseidon(secret_hack) $$

All the calculation is on MNT6.