Combined authentication schemes with increasing level of resistance and methods for improving the security of electronic signature schemes

Abstract

The highly topical and groundbreaking issue of many studies is quantum technology. More and more articles appear not only in the world's leading scientific publications, but also in the media, on the creation of a quantum computer capable of solving the factorization problem (FP), the discrete logarithm in a simple finite field problem (DLSFFP) and discrete logarithm in the group of points of an elliptic curve problem (DLECP) in polynomial time. Some scientists give a 20-year timeline to implement a full-scale quantum computer [1]. This means that cryptographic mechanisms based on the above tasks will lose their cryptographic stability. Such mechanisms include the current standard of the Russian Federation GOST 34.10-2012 Information technology. Cryptographic information security. Processes of formation and verification of electronic digital and the current standard of the United States of America ECDSA, and many other protocols.In view of the above, methods of improving the safety of combined authentication schemes are an important topic of research. The article considers possible ways of combining different number theory problems and lattice theory problems in one electronic signature (ES) scheme. A distinctive feature of the proposed schemes is the use of post-quantum short integer solution (SIS) problem related to the lattice theory. It provides a higher level of cryptographic strength.The paper presents general methods of combining several difficult tasks in one scheme. These methods are based on induction output and can be used for increasing the resistance of electronic signature schemes. Induction consists in reducing the mechanisms used in particular schemes to more general methods.Due to this, it is possible to increase the resistance of existing authentication schemes, including potential attacks performed on the quantum computer. The paper also shows that the proposed methods can be applied to any electronic signature schemes based on lattice theory.