LFSR-based Hashing and Authentication

We present simple and efficient hash functions applicable to secure authentication of information. The constructions are mainly intended for message authentication in systems implementing stream cipher encryption and are suitable for other applications as well. The proposed hash functions are implemented through linear feedback shift registers and therefore attractive for hardware applications. As an example, a single 64 bit LFSR will be used to authenticate 1 Gbit of information with a failure probability of less than 2−30. One of the constructions is the cryptographic version of the well known cyclic redundancy codes (CRC); the other is based on Toeplitz hashing where the matrix entries are generated by a LFSR. The later construction achieves essentially the same hashing and authentication strength of a completely random matrix but at a substantially lower cost in randomness, key size and implementation complexity. Of independent interest is our characterization of the properties required from a family of hash functions in order to be secure for authentication when combined with a (secure) stream cipher.