A Fast Provably Secure Cryptographic Hash Function

We propose a family of fast and provably secure cryptographic hash functions. The security of these functions relies directly on the well-known syndrome decoding problem for linear codes. Attacks on this problem are well identified and their complexity is known. This enables us to study precisely the practical security of the hash functions and propose valid parameters for implementation. Furthermore, the design proposed here is fully scalable, with respect to security, hash size and output rate.