Schnorrbased

Schnorrbased refers to cryptographic schemes that build on or are inspired by the Schnorr signature scheme, named after Claus-Peter Schnorr, who introduced it in the early 1990s. The approach is grounded in the hardness of the discrete logarithm problem in a cyclic group and emphasizes concise, efficiently verifiable signatures.

In a typical Schnorr-based signature system, there is a cyclic group G of prime order q with generator g, a private key x chosen from Z_q, and a public key X = g^x. To sign a message m, a party selects a nonce k in Z_q, computes R = g^k, and derives e = H(m, R) using a cryptographic hash function H. The signature component is s = k + e x mod q, and the signature is the pair (e, s) (or, equivalently, the pair (R, s)). To verify, one computes R' = g^s X^{-e} and checks that e equals H(m, R').

Schnorr-based schemes are often constructed via the Fiat-Shamir heuristic, which makes signatures non-interactive in the random oracle model. Their security reduces to the discrete log problem, yielding EUF-CMA security under standard assumptions. The signatures are typically short and require only a few exponentiations to verify, enabling efficient verification and compact storage.

Applications include signature aggregation, multisignature schemes, and privacy-preserving protocols. In modern blockchain systems, Schnorr-based signatures are employed to enable Taproot-style capabilities and off-chain scaling, with Bitcoin's BIP-340 defining a Schnorr signature variant for its protocol. Variants differ in how R is represented, how e is computed, and how nonces are generated.