In this study, the authors elaborate on a recently proposed variant of the public‐key McEliece and Niederreiter cryptosystems using generalised Reed–Solomon (GRS) codes as private codes. The use of these codes brings known advantages in terms of public key size, but particular care is needed in the choice of parameters not to endanger the system security. In fact, the considered system exploits a strong disguising technique of the private code within the public code. However, it has recently been pointed out that some new attacks exist which may threaten some instances of such a system, therefore the choice of parameters needs to consider some further constraints compared to the original version. After outlining these constraints, the authors propose a new modification of the system achieving greater flexibility in the parameter choice. Moreover, the new system exhibits a lower complexity than the original GRS code‐based system. Its very competitive features such as key size and encryption rate are highlighted with respect to classic systems.

The standard algebraic decoding algorithm of cyclic codes [n, k, d] up to the BCH bound δ = 2t + 1 is very efficient and practical for relatively small n while it becomes unpractical for large n as its computational complexity is O(nt). Aim of this paper is to show how to make this algebraic decoding computationally more efficient: in the case of binary codes, for example, the complexity of the syndrome computation drops from O(nt) to O(t√n), while the average complexity of the error location drops from O(nt) to max{O(t√n), O(t log2(t)log log(t)log(n))}.

The paper studies the problem of securely storing biometric passwords, such as fingerprints and irises. With the help of coding theory Juels and Wattenberg derived in 1999 a scheme where similar input strings will be accepted as the same biometric. In the same time nothing could be learned from the stored data. They called their scheme a fuzzy commitment scheme. In this paper we will revisit the solution of Juels and Wattenberg and we will provide answers to two important questions: what type of error-correcting codes should be used and what happens if biometric templates are not uniformly distributed, i.e. the biometric data come with redundancy. Answering the first question will lead us to the search for low-rate large-minimum distance error-correcting codes which come with efficient decoding algorithms up to the designed distance. In order to answer the second question we relate the rate required with a quantity connected to the “entropy” of the string, trying to estimate a sort of “capacity”, if we want to see a flavor of the converse of Shannon's noisy coding theorem. Finally we deal with side-problems arising in a practical implementation and we propose a possible solution to the main one that seems to have so far prevented in many situations real life applications of the fuzzy scheme.