On the parameters of 2-GOST round key generator

Information security with low resources determines the importance of construction lightweight implementations for known cryptographic algorithms. In 2014, a low-resource implementation of GOST 28147-89 called 2-GOST was presented. Despite attained advantages, the scheme had yet a potential to enhance cryptographic strength by, for example, modifying the key schedule. In 2018, a new algorithm for the generation of round keys for 2-GOST was proposed. The round key generator was based on the shift register of length 8 over the set of binary vectors of length 32. At the same time, the register feedback parameters were not sufficiently substantiated. The aim of this paper is to determine the best (or close to the best) three feedback taps for feedback function and justification of the proposed solution. The first quality criterion is defined by the characteristics of the input data mixing by the register transformation, the second one — by the efficiency of the implementation. As a characteristic of mixing, we use the index of local perfection of register transformation, namely the number of iterations, after which each bit of the generated round key depends essentially on all bits of the initial state. The optimal three feedback taps are identified and the characteristics of the key schedule quality for the proposed and original schemes are compared. It is established that in the initial scheme the value of the local perfection index is the highest among all the feedback functions in the class under the study (the worst index in terms of mixing). We offer the alternative scheme with the smallest index of local perfection and the similar implementation. For both schemes (original and alternative), we carry out the statistical testing of the generator output sequences.