Generating binary diffusion layers with maximum/high branch numbers and low search complexity
Security and Communication Networks, cilt.9, sa.16, ss.3558-3569, 2016 (SCI-Expanded, Scopus)
- Yayın Türü: Makale / Tam Makale
- Cilt numarası: 9 Sayı: 16
- Basım Tarihi: 2016
- Doi Numarası: 10.1002/sec.1561
- Dergi Adı: Security and Communication Networks
- Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED), Scopus
- Sayfa Sayıları: ss.3558-3569
- Anahtar Kelimeler: binary matrix, block ciphers, branch number, diffusion layer, MDS matrix
- Trakya Üniversitesi Adresli: Evet
Özet
In this paper, we propose a new method to generate n × n binary matrices (for n = k·2t where k and t are positive integers) with a maximum/high of branch numbers and a minimum number of fixed points by using 2t×2t Hadamard (almost) maximum distance separable matrices and k × k cyclic binary matrix groups. By using the proposed method, we generate n × n (for n = 6, 8, 12, 16, and 32) binary matrices with a maximum of branch numbers, which are efficient in software implementations. The proposed method is also applicable with m × m circulant matrices to generate n × n(for n = k·m) binary matrices with a maximum/high of branch numbers. For this case, some examples for 16 × 16, 48 × 48, and 64 × 64 binary matrices with branch numbers of 8, 15, and 18, respectively, are presented. Copyright © 2016 John Wiley & Sons, Ltd.