Modification of the post-quantum key encapsulation mechanism “Zemlyanika”

The cryptographic scheme of the key encapsulation mechanism (KEM) Zemlyanika (“Strawberry”), based on the problem of modular learning with errors (Module-Learning With Errors, Module-LWE), uses a reduction module in the form of a power of two, which provides highly efficient modular arithmetic, but excludes the use of number-theoretic transformations (Number Theoretical Transform, NTT) for performing polynomial multiplication. This leads to the use of asymptotically less efficient and approximate algorithms, which cause problems with accuracy, flexibility of parameterization, and complexity of protection against side-channel attacks. The purpose of the study is to overcome the system limitations of the original scheme by replacing the reduction module with a quasi-secondary one. The scientific novelty lies in a comprehensive analysis of the correctness and stability of the modified scheme during such a transition. It is shown that the proposed reduction module makes it possible to implement asymptotically optimal NTT multiplication, while maintaining an effective reduction that is close in speed to power-law reduction. The decapsulation correctness condition is slightly tightened (a decrease in the correctness limit by about 0.49%), which is controllable and compensable. It is shown that the use of a simple reduction module of a similar size does not significantly affect the complexity of known lattice attacks in the Core-SVP model, since durability is determined by the geometric properties of the lattice, rather than the arithmetic of the reduction module. The result of the work is a balanced architectural solution that increases the computational efficiency and flexibility of KEM Zemlyanika parameterization without compromising cryptographic strength, with a predicted acceleration of encapsulation and decapsulation operations by 1.8-2.6 times for various parameter sets.