Schnorr Signature Algorithm

A Schnorr signature is a digital signature algorithm whose security rests on the difficulty of the discrete logarithm problem, valued for producing signatures that are both compact and comparatively simple to verify next to earlier discrete-logarithm-based schemes. Generating a key pair starts with a randomly chosen private key from which a corresponding public key is derived by mathematical exponentiation; signing a message involves picking a fresh random nonce, computing a hash that binds the nonce and the message together, and combining that hash with the private key to produce the signature, while verification uses only the public key, the message and the signature to reconstruct and check the same relationship, confirming the signature is authentic without ever exposing the private key. Claus Schnorr published his underlying identification protocol in 1990 and the signature scheme derived from it in 1991; the scheme was covered by a United States patent that expired in February 2010, after which its use became unencumbered.