I am reading about ZKP and I found this interesting question about changing this protocol from interactive Schnorr identification protocol to non-interactive and I need help in solving it :
Peggy (prover) and Victor (verifier) have shared primes p,q such that q|p-1 and a generator $g$ such that $1<g<p$ and $g^q=1 \bmod p.$
Peggy has a private key $s$ and a public key $v=g^s$ ($v$ is known to Victor). Peggy wishes to convince Victor that she knows the secret exponent s without revealing what s is. She performs the following interactive protocol with Victor.
Peggy chooses a random $r$ from $[0,q-1]$, calculates $x =g^r \bmod p$, and sends $x$ to Victor.
Victor chooses a random challenge $e$ from $[1,\ldots,2t-1]$ where $t$ is a security parameter and sends $e$ to Peggy.
Peggy calculates $y = r-se \bmod q$ and sends it to Victor.
- Victor checks that $x= g^yv^e \bmod p$. If so, then Victor “accepts”; otherwise, Victor “rejects”