We present an algebraic construction based on state transform matrix (companion matrix) forn×n(wheren≠2k,kbeing a positive integer) binary matrices with high branch number and low number of fixed points. We also provide examples for20×20and24×24binary matrices having advantages on implementation issues in lightweight block ciphers and hash functions. The powers of the companion matrix for an irreducible polynomial overGF(2)with degree 5 and 4 are used in finite field Hadamard or circulant manner to construct20×20and24×24binary 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 forn×n(wheren≠2k,kbeing a positive integer) binary matrices with high branch number and low number of fixed points.

No abstract

No abstract

No abstract

No abstract