Proof of Exponent (POE)

The POE protocol is a building block of other protocols. Given the relation

$$ y = g^x $$

where \(g\) is a known generator point, \(y\) is a known public point and \(x\) is the secret witness. A Zero-Knowledge proof of exponent is used to show knowledge of \(x\) such that the previous relation holds.

Protocol (Interactive)

Cost Analysis (EC Operations)

Prover Complexity

• 1 EC multiplications

Verifier Complexity

• 2 EC multiplications
• 1 EC addition

Usage in Tongo

POE is directly used in Tongo to prove account ownership in all operations. It is also used indirectly as a building block of other SHE protocols.