Picnic is one of the alternative finalists for the NIST standard for PQC (Post Quantum Cryptography) [1]. In the method, we generate a random plaintext block (\(p\)), and a random secret key (\(sk\)). Next we compute \(C = LowMC(sk, p)\), and then determine the public key of \(pk= ( C, p)\). To sign we define knowledge the knowlege of \(sk\) so that \(C= LowMC(sk, p)\), and where the message m and public key pk are integrated wit the proof for the signature. With this the signature is basically a proof of knowledge of \(sk\) using the message as nonce value. LowMC defines a family of block ciphers that can be used in multi-party computations (MPC) and fully homomorphic encryption methods [2].
Related: [Kyber KEM][Kyber KEX][Dilithium Dig Sig Speed][Factoring signature (ECC)][Factoring signature (Logs)][Falcon Digital Signature][Rainbow Digital Signature][Dilithium Digital Signature][SPHINCS+]