The Forgery Attack on the Post-Quantum AJPS-2 Cryptosystem and Modification of the AJPS-2 Cryptosystem by Changing the Class of Numbers Used as a Module

Abstract

In recent years, post-quantum (quantum-resistant) cryptography has been actively researched, in particular, due to the National Institute of Standards and Technology's (NIST) Post-Quantum Cryptography Competition (PQC), which has been running since 2017. One of the participants in the first round of the competition is the Mersenne-756839 key encapsulation mechanism based on the AJPS-2 encryption scheme. The arithmetic modulo Mersenne number is used to construct the cryptoprimitives of the AJPS family. In this paper, we propose a forgery attack on the AJPS-2 cryptosystem using an active eavesdropper, and two modifications of the post-quantum AJPS-2 cryptosystem, namely, the modification of AJPS-2 using the arithmetic modulo generalized Mersenne number and Crandall number. Moreover, new algebraic problems are defined, on the complexity of which the security of the created modifications is based. The advantages of these modifications are the extension of the number class used as a module in the cryptosystem and the security against the forgery attack with the active eavesdropper, which was successful in the original AJPS-2.