## On the construction of $$20 \times 20$$ and $$2 4 \times 24$$ binary matrices with good implementation properties for lightweight block ciphers and hash functions.(English)Zbl 1407.94182

Summary: We present an algebraic construction based on state transform matrix (companion matrix) for $$n \times n$$ (where $$n \neq 2^k$$, $$k$$ being a positive integer) binary matrices with high branch number and low number of fixed points. We also provide examples for $$20 \times 20$$ and $$24 \times 24$$ 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 $$\text{GF}(2)$$ with degree 5 and 4 are used in finite field Hadamard or circulant manner to construct $$20 \times 20$$ and $$24 \times 24$$ 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 $$n \times n$$ (where $$n \neq 2^k$$, $$k$$ being a positive integer) binary matrices with high branch number and low number of fixed points.

### MSC:

 94B05 Linear codes (general theory)

### Software:

SPECK; Itubee; ARIA; SIMECK; Camellia; Magma; SIMON; EPCBC
Full Text:

### References:

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