This document describes Schnorr NIZK proof, a non-interactive variant of the three-pass Schnorr identification scheme. The Schnorr NIZK proof allows one to prove the knowledge of a discrete logarithm without leaking any information about its value. It can serve as a useful building block for many cryptographic protocols to ensure the participants follow the protocol specification honestly. This document specifies the Schnorr NIZK proof in both the finite field and the elliptic curve settings.