Study on the parameters of the matrix NTRU cryptosystem

With the rapid development of quantum computers， post-quantum cryptography has emerged as a prominent area of research in cryptography.ObjectivesIn order to avoid the decryption failure in matrix NTRU as NTRU， the Matrix NTRU algorithm was optimized.MethodsBased 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 was proposed. This method redefined the parameter space and accurately improved 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.ResultsIt was theoretically proved that the improved matrix NTRU algorithm avoided 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 were compared and analyzed 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 was 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 was further verified by experiments， and the encryption and decryption speeds were consistent with the theoretical analysis.ConclusionsThe result indicated that the matrix NTRU algorithm， optimized with adjusted parameters， possessed characteristics such as accurate encryption and decryption， as well as high efficiency.