On the Construction of 20 × 20 and 2 4 × 24 Binary Matrices with Good Implementation Properties for Lightweight Block Ciphers and Hash Functions

Abstract EN

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.