Experimental research of cryptographic properties of some lightweight algorithms

The approaches to the construction of block algorithms for lightweight cryptography are systematized, some lightweight algorithms based on Feistel networks and SP-networks are studied and their mixing and nonlinear properties are estimated. The concepts of the "exponent of strong nonlinearity" (the least number of rounds at which each coordinate function of the output block is nonlinear) and the "exponent of perfection" (the least number of rounds at which each bit of the output block essentially depends on all bits of the input block) are defined. For the PRESENT, MIDORY, SKINNY, CLEFIA, and LILLIPUT algorithms, the exact values of the exponents of the matrices of essential dependence constructed for the round functions (respectively 3, 3, 6, 5, 5), as well as the exponents of perfection (4, 3, 6, 5, 5) and exponents of strong nonlinearity (1, 1, 1, 2, 2) have been obtained. The proximity of the values for the exponents of the matrices to the values for the exponents of perfection shows the effectiveness of the application of the matrix-graph approach to the estimation of the mixing properties of cryptographic transformations. For each of these algorithms, it was experimentally established that, for 500 rounds, each coordinate function of the output block is nonlinear. This indicates the potential use of the algorithms in constructing a key schedule or lightweight hash functions.

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