On the Construction of 20 × 20 and 24 × 24 Binary Matrices with Good Implementation Properties for Lightweight Block Ciphers and Hash Functions

SAKALLI, MUHARREM; Akleylek, Sedat; ASLAN, BORA; Buluş, Ercan; BÜYÜKSARAÇOĞLU SAKALLI, FATMA

doi:10.1155/2014/540253

On the Construction of 20 × 20 and 24 × 24 Binary Matrices with Good Implementation Properties for Lightweight Block Ciphers and Hash Functions

SAKALLI M. T., Akleylek S., ASLAN B., Buluş E., BÜYÜKSARAÇOĞLU SAKALLI F.

Mathematical Problems in Engineering, cilt.2014, 2014 (SCI-Expanded, Scopus)

Yayın Türü: Makale / Tam Makale
Cilt numarası: 2014
Basım Tarihi: 2014
Doi Numarası: 10.1155/2014/540253
Dergi Adı: Mathematical Problems in Engineering
Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED), Scopus
Kırklareli Üniversitesi Adresli: Evet

Özet

We present an algebraic construction based on state transform matrix (companion matrix) for n × n (where n ≠ 2^k, k being a positive integer) binary matrices with high branch number and low number of fixed points. We also provide examples for 20 × 20 and 24 × 24 binary matrices having advantages on implementation issues in lightweight block ciphers and hash functions. The powers of the companion matrix for an irreducible polynomial over GF (2) with degree 5 and 4 are used in finite field Hadamard or circulant manner to construct 20 × 20 and 24 × 24 binary matrices, respectively. Moreover, the binary matrices are constructed to have good software and hardware implementation properties. To the best of our knowledge, this is the first study for n × n (where n ≠ 2^k, k being a positive integer) binary matrices with high branch number and low number of fixed points.