Security analysis of promising key encapsulation mechanisms in the core-SVP model

The study of key encapsulation mechanisms on structured lattices is one of the important directions in modern post-quantum cryptography, as many mechanisms are either already standardized (DSTU 8961:2019 "Skelya") or are promising candidates for standardization (CRYSTALS-Kyber). Estimating the complexity of lattice reduction for cryptographic schemes is an old problem. Asymptotic estimates differ greatly from experimental values, therefore, a number of heuristic methods were developed to solve practical problems. The coreSVP model is a standard means of assessing the security of cryptographic schemes on lattices. The purpose of the work is to analyze the encapsulation mechanisms of DSTU 8961:2019 "Skelya" and CRYSTALS-Kyber keys in the coreSVP model. The analysis was performed using two popular heuristics – GSA (Geometric Series Assumption) and the Chen-Nguyen simulator. The analysis showed that the Chen-Nguyen simulator gives slightly lower estimates than the GSA heuristic. As a result of the analysis, it was found that 8961:2019 The “Skelya” and CRYSTALS-Kyber in the coreSVP model for classical computers have slightly lower than declared security values, but for quantum computers the key encapsulation mechanisms provide the declared security levels. Note that during the analysis, the accuracy of the GSA heuristics and the Chen-Nguyen simulator were analyzed separately. Examples of parameters for which heuristics do not give sufficiently accurate results are given. The performed analysis does not take into account the algebraic structure of lattices used in 8961:2019 "Skelya" and CRYSTALS-Kyber. The inclusion of an algebraic structure in the analysis is a further direction of work. The use of simulators is a promising direction, however, more accurate simulators that take into account the structuring of LWE and NTRU arrays are needed.