On the comparison of methods for asymmetric execution of cryptographic primitives and protocols in the context of using small parameters and short keys

The paper systematically considers methods of changing the execution of known standard cryptographic primitives, symmetric and asymmetric, as well as cryptographic protocols using short (low-entropy) keys and small parameters that allow increasing their strength. The proposed changes are related to the introduction of asymmetry in the complexity of the work of legitimate users, which should lead to an increase in the complexity of decryption algorithms for an adversary or cryptanalyst. Security is considered in relation to the use of standard and universal attack methods by the adversary, such as the method of full testing of keys due to the small size of these keys, as well as methods for solving problems of discrete logarithm or factorization of large integers, the size of which is limited by the small size of the cryptosystem parameters. Security is considered in relation to the use of standard and universal attack methods by the adversary, such as the method of full testing of keys due to the small size of these keys, as well as methods for solving problems of discrete logarithm or factorization of large integers, the size of which is limited by the small size of the cryptosystem parameters. This work is of an overview nature, which allows you to look at what is common in the proposed methods for different situations of using cryptography with short keys and small parameters. © 2021, The Author(s), under exclusive licence to Springer-Verlag France SAS, part of Springer Nature.