A cryptographic method and system is described, the method and system including providing a key pair that includes a private key and a corresponding public key, which defines a multivariate polynomial mapping, computing, using a processor and the private key, a digital signature for a message such that a first application of the mapping to the digital signature gives a first result, and a second application of the mapping to the message gives a second result that is equal to the first result, and conveying the message with the digital signature to a recipient for authentication using the public key. Related hardware, methods, and systems are also described.