Generalisation of Hadamard matrix to generate involutory MDS matrices for lightweight cryptography

Meltem Kurt Pehlivanoğlu; Muharrem Tolga Sakallı; Sedat Akleylek; Nevcihan Duru; Vincent Rijmen

Generalisation of Hadamard matrix to generate involutory MDS matrices for lightweight cryptography

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Author(s): Meltem Kurt Pehlivanoğlu¹ ; Muharrem Tolga Sakallı² ; Sedat Akleylek³ ; Nevcihan Duru¹ ; Vincent Rijmen⁴
- Affiliations: 1: Department of Computer Engineering , Kocaeli University , Kocaeli , Turkey ;
  2: Department of Computer Engineering , Trakya University , Edirne , Turkey ;
  3: Department of Computer Engineering , Ondokuz Mayis University , Samsun , Turkey ;
  4: Department of ESAT/COSIC , KU Leuven and imec , Belgium
Source: Volume 12, Issue 4, July 2018, p. 348 – 355
DOI: 10.1049/iet-ifs.2017.0156 , Print ISSN 1751-8709, Online ISSN 1751-8717

Received 10/04/2017, Accepted 02/01/2018, Revised 21/11/2017, Published 04/01/2018

In this study, the authors generalise Hadamard matrix over $F 2 m$ and propose a new form of Hadamard matrix, which they call generalised Hadamard (GHadamard) matrix. Then, they focus on generating lightweight (involutory) maximum distance separable (MDS) matrices. They also extend this idea to any $k × k$ matrix form, where k is not necessarily a power of 2. The new matrix form, GHadamard matrix, is used to generate new $4 × 4$ involutory MDS matrices over $F 2 4$ and $F 2 8$ , and $8 × 8$ involutory/non-involutory MDS matrices over $F 2 4$ by considering the minimum exclusive OR (XOR) count, which is a metric defined to estimate the hardware implementation cost. In this context, they improve the best-known results of XOR counts for $8 × 8$ involutory/non-involutory MDS matrices over $F 2 4$ .

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Generalisation of Hadamard matrix to generate involutory MDS matrices for lightweight cryptography

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