On the Construction of 20×20 and 24×24 Binary Matrices with Good Implementation Properties for Lightweight Block Ciphers and Hash Functions
We present an algebraic construction based on state transform matrix (companion matrix) for n×n (where n≠2k, 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 implement...
| Main Authors: | , , , , |
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| Format: | Article |
| Language: | English |
| Published: |
Hindawi Limited
2014-01-01
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| Series: | Mathematical Problems in Engineering |
| Online Access: | http://dx.doi.org/10.1155/2014/540253 |
| Summary: | We present an algebraic construction based on state transform matrix (companion matrix) for n×n (where n≠2k, 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≠2k, k being a positive integer) binary matrices with high branch number and low number of fixed points. |
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| ISSN: | 1024-123X 1563-5147 |