LI Z C，WU Q H，SONG J S，et al.Study on the parameters of the matrix NTRU cryptosystem［J］.Journal of Henan Polytechnic University（Natural Science），doi:10.16186/j.cnki.1673-9787.2023100040.

doi:10.16186/j.cnki.1673-9787.2023100040.

Received：2023-10-19

Revised：2023-12-27

Online：2024-10-15

Study on the parameters of the matrix NTRU cryptosystem

LI Zichen¹，WU Qinghao¹，SONG Jiashuo²，PENG Haipeng²

（1.School of Information Engineering,Beijing Institute of Graphic Communication,Beijing 102600,China；2.School of Cybersecurity,Beijing University of Posts and Telecommunications,Beijing 100876,China）

Abstract: With the rapid development of quantum computers， post-quantum cryptography has emerged as a prominent area of research in cryptography. Objectives In order to avoid the decryption failure in matrix NTRU as NTRU， the Matrix NTRU algorithm is optimised. Methods Based on the method of constraining the parameter space in congruent cryptographic algorithms， a method for optimal selection of the parameter space of matrix NTRU cryptographic regimes is proposed. This method redefined the parameter space and accurately improves the choice of parameters， allowing control of the operation of matrix elements within a specific range. By compressing the original parameter space， decryption failures caused by modulo operations going out of bounds were avoided. Results It is theoretically proven that the improved matrix NTRU algorithm avoids encryption and decryption failures. In order to test the performance of the improved matrix NTRU， a theoretical analysis was first carried out. The improved matrix NTRU and NTRU cipher algorithms are compared and analysed in terms of key and plaintext security， key length， ciphertext extension， encryption and decryption speed. By choosing a suitable value of d， the message and key security of the improved matrix NTRU algorithm is several times greater than the message and key security of the NTRU algorithm. The public and private key lengths and ciphertext extensions are the same as in the NTRU scheme. The improved matrix NTRU algorithm is n times faster than the NTRU algorithm for encryption and decryption. Finally， the efficiency of the improved matrix NTRU is further verified by experiments， and the encryption and decryption speeds are consistent with the theoretical analysis. Conclusion The result indicated that the matrix NTRU algorithm， optimized with adjusted parameters， possesses characteristics such as accurate encryption and decryption， as well as high efficiency.

Key words: matrix NTRU；decryption failure；matrix ring；post-quantum cipher