The Modification of the Quantum-Resistant AJPS-1 Cryptographic Primitive

Abstract


 
 
 In recent years, quantum-resistant cryptography has been steadily developing, which is due, in particular, to the post-quantum cryptosystems competition of the National Institute of Standards and Technology (NIST), which has been ongoing since 2017. One of the participants in the first round of the competition is the AJPS cryptosystem. In this work, we propose the modification of the AJPS cryptosystem for bit-by-bit encryption by changing the numbers class used in the cryptosystem as a module. This modification increases the variability of the cryptosystem parameters.
 
 

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

“…replacing the Mersenne numbers with other classes of numbers. In our previous paper [6], a modification of the AJPS-1 cryptosystem was constructed using generalized Mersenne numbers instead of Mersenne numbers, and a comparative analysis of the original AJPS-1 cryptosystem and the constructed modification using generalized Mersenne numbers was performed. In this work, two modifications of the AJPS-2 cryptosystem are developed: using generalized Mersenne numbers and Crandall numbers.…”