Cryptographically Secure CRC for Lightweight Message Authentication

A simple and practical hashing scheme based on Cyclic Redundancy Check (CRC) is presented. Similarly to previously proposed cryptographically secure CRCs, the presented one detects both, random and malicious, errors without increasing bandwidth. However, we use a product of irreducible polynomials instead of a single irreducible polynomial for generating the CRC. This is an advantage since smaller irreducible polynomials are easier to compute. The price we pay is that the probability that two different messages map into the same CRC increases. We provide a detailed quantitative analysis of the achieved security as a function of message and CRC sizes. The presented method seems to be particularly attractive for the authentication of short messages

A New Multi-Linear Universal Hash Family

A new universal hash family is described. Messages are sequences over a finite field \rF_q while keys are sequences over an extension field \rF_{q^n}. A linear map $\psi$ from \rF_{q^n} to itself is used to compute the output digest. Of special interest is the case $q=2$. For this case, we show that there is an efficient way to implement $\psi$ using a tower field representation of \rF_{q^n}. From a practical point of view, the focus of our constructions is small hardware and other resource constrained applications. For such platforms, our constructions compare favourably to previous work

A shift register construction of unconditionally secure authentication codes

We consider the authentication problem, using the model described by Simmons. Several codes have been constructed using combinatorial designs and finite geometries. We introduce a new way of constructing authentication codes using LFSR-sequences. A central part of the construction is an encoding matrix derived from these LFSR-sequences. Necessary criteria for this matrix in order to give authentication codes that provides protection aginst impersonation and substitution attacks will be given. These codes also provide perfect secrecy if the source states have a uniform distribution. Moreover, the codes give a natural splitting of the key into two parts, one part used aginst impersonation attacks and a second part used against substitution attacks and for secrecy simultaneously. Since the construction is based on the theory of LFSR-sequences it is very suitable for implementation and a simple implementation of the construction is given