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

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 signature" and the current standard of the United States of America ECDSA, and many other protocols.