Skip to Main content Skip to Navigation
Journal articles

Convolutional block codes with cryptographic properties over the semi-direct product Z / N Z ⋊ Z / M Z

Marion Candau 1, 2 Roland Gautier 2 Johannes Huisman 1
2 Lab-STICC_UBO_CACS_COM
UBO - Université de Brest, Lab-STICC - Laboratoire des sciences et techniques de l'information, de la communication et de la connaissance
Abstract : Classic convolutional codes are defined as the convolution of a message and a transfer function over Z. In this paper, we study time-varying convolutional codes over a finite group G of the form Z / N Z ⋊ Z / M Z. The goal of this study is to design codes with cryptographic properties. To define a message u of length k over the group G, we choose a subset E of G that changes at each encoding, and we put u = ∑i ui E(i ). These subsets E are generated chaotically by a dynamical system, walking from a starting point (x, y) on a space paved by rectangles, each rectangle representing an element of G. So each iteration of the dynamical system gives an element of the group which is saved on the current E. The encoding is done by a convolution product with a fixed transfer function. We have found a criterion to check whether an element in the group algebra can be used as a transfer function. The decoding process is realized by syndrome decoding. We have computed the minimum distance for the group G = Z/7Z ⋊ Z/3Z. We found that it is slightly smaller than those of the best linear block codes. Nevertheless, our codes induce a symmetric cryptosystem whose key is the starting point (x, y) of the dynamical system. Consequently, these codes are a compromise between error correction and security.
Complete list of metadatas

https://hal.univ-brest.fr/hal-01163421
Contributor : Roland Gautier <>
Submitted on : Friday, June 12, 2015 - 6:27:43 PM
Last modification on : Wednesday, June 24, 2020 - 4:19:24 PM

Identifiers

Citation

Marion Candau, Roland Gautier, Johannes Huisman. Convolutional block codes with cryptographic properties over the semi-direct product Z / N Z ⋊ Z / M Z. Designs, Codes and Cryptography, Springer Verlag, 2016, pp.395-407. ⟨10.1007/s10623-015-0101-7⟩. ⟨hal-01163421⟩

Share

Metrics

Record views

436