We found a match
Your institution may have rights to this item. Sign in to continue.
- Title
On the automorphisms and isomorphisms of MDS matrices and their efficient implementations.
- Authors
SAKALLI, Muharrem Tolga; AKLEYLEK, Sedat; AKKANAT, Kemal; RIJMEN, Vincent
- Abstract
In this paper, we explicitly define the automorphisms of MDS matrices over the same binary extension field. By extending this idea, we present the isomorphisms between MDS matrices over F2m and MDS matrices over F2mt, where t = 1 and m > 1, which preserves the software implementation properties in view of XOR operations and table lookups of any given MDS matrix over F2m. Then we propose a novel method to obtain distinct functions related to these automorphisms and isomorphisms to be used in generating isomorphic MDS matrices (new MDS matrices in view of implementation properties) using the existing ones. The comparison with the MDS matrices used in AES, ANUBIS, and subfield-Hadamard construction shows that we generate an involutory 4×4 MDS matrix over F28 (from an involutory 4 × 4 MDS matrix over F24) whose required number of XOR operations is the same as that of ANUBIS and the subfield-Hadamard construction, and better than that of AES. The proposed method, due to its ground field structure, is intended to be a complementary method for the current construction methods in the literature.
- Subjects
MATRICES (Mathematics); HADAMARD matrices; AUTOMORPHISMS; BLOCK ciphers; ISOMORPHISM (Mathematics)
- Publication
Turkish Journal of Electrical Engineering & Computer Sciences, 2020, Vol 28, Issue 1, p275
- ISSN
1300-0632
- Publication type
Article
- DOI
10.3906/elk-1906-151