Abstract
The aim of the work is to evaluate the cryptographic properties of the pCollapser family of pseudo-random functions (PRF) based on the study of the properties of its mini_pCollapser_12x12 miniversionusing fixed substitutions with extremely low cryptographic properties. As a comparison element,we used a mini-version of a typical function based on an SP-net, containing a similar number of fixedsubstitutions, and having a similar input/output dimension equal to 12 bits. To achieve this goal, thefollowing tasks were solved: – determination of the structure of the studied functions and the number ofrounds; – definition of a model for the formation of fixed substitutions with extremely low cryptographicproperties; – generation of sets of 6-bit fixed substitutions with extremely low cryptographic properties; – inclusion of the substitutions obtained into the functions under study and determination of the maincryptographic properties of functions – the maximum dominance value for individual key values and themaximum dominance value averaged over the entire set of keys, the maximum and averaged over theentire set of keys value in the difference distribution table, algebraic degree and algebraic immunity;– analysis of the obtained results. The paper presents two models for the formation of fixed substitutionswith extremely low cryptographic properties – based on the mixing of cell values in a pre-filled tableand based on the simplest ARX function (consisting of modulo addition, cyclic shift and XOR). The useof fixed substitutions with extremely low non-linearity makes it possible to estimate how complex (nonlinear)the function under study is and what minimum level of non-linearity is necessary to effectivelydestroy the statistical dependencies between input/output data. In addition, it becomes clear that ARXfunctions can be used as non-linear elements, which often have controversial and clearly low cryptographicproperties, but allow creating high-speed software and hardware implementations. It has beendetermined that the PRF pCollapser mini-version, in contrast to the typical function based on the SPnetwork, makes it possible to obtain a high-quality non-linear function from the set of ARX-functionswith extremely low cryptographic properties, given that no other non-linear elements are presented inpCollapser. The obtained results reflect the existence of a fundamental difference between thepCollapser PRF and a typical SP-network based PRF and confirm the correctness of the concept ofPD-sbox pseudo-dynamic substitutions and the pCollapser function consisting of them as a whole.
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