The necessary conditions for the key generation of the quantum- resistant AJPS-1 cryptosystem

Authors

  • Dariya Yadukha аспірантка НН ФТІ НТУУ «КПІ ім. Ігоря Сікорського», асистент кафедри математичних методів захисту інформації НН ФТІ НТУУ «КПІ ім. Ігоря Сікорського», пр. Берестейський, 37, 03056, м. Київ

Keywords:

криптосистема AJPS, постквантова криптосистема, число Мерсенна, вага Геммінга

Abstract

The paper analyzes the post-quantum AJPS-1 cryptosystem, which participated in the first round of the NIST post-quantum crypto primitives competition. The weak values of the public key of the cryptosystem are found and the necessary conditions for the public key to ensure the security of the cryptosystem are given. By generalizing other known attacks on AJPS-1, recommendations for choice of secret and public keys are given. The double encryption approach has been applied to the AJPS-1 cryptosystem, and it has been proved that there are no restrictions on the public key in this case.

References

Post-Quantum CryptographyStandardization.NationalInstituteofStandardsandTechnology, Available:https://csrc.nist.gov/Projects/post-quantum-cryptography/Post-Quantum-Cryptography-Standardization.

D.Aggarwal, A. Joux, A. Prakash, M. Santha.A New Public-Key CryptosystemviaMersenneNumbers. IACR CryptologyePrintArchive. – Available: https://eprint.iacr.org/2017/481.

S. Baktir, B. Sunar.OptimalExtensionFieldInversionintheFrequencyDomain. ArithmeticofFiniteFields. Siena: Springer, 2008.

M. Beunardeau, A. Connolly, R. Geraud, D. Naccache.OntheHardnessoftheMersenneLowHammingRatioAssumption.Available: https://eprint.iacr.org/2017/522.

M. Tiepelt, A. Szepieniec.Quantum LLL withanApplicationtoMersenneNumberCryptosystems.ProgressinCryptology –LATINCRYPT 2019.

Published

2023-06-29

How to Cite

Yadukha, D. (2023). The necessary conditions for the key generation of the quantum- resistant AJPS-1 cryptosystem. PHYSICO-MATHEMATICAL MODELLING AND INFORMATIONAL TECHNOLOGIES, (37), 154–158. Retrieved from https://fmmit.lviv.ua/index.php/fmmit/article/view/324