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Lattice-based key exchange protocols have attracted tremendous attention for its post-quantum security. In this work, we construct a Module-LWE-based key exchange protocol using Peikert’s error reconciliation mechanism. Compared with Kyber.KE, our key exchange protocol reduces the total communication cost by 96-byte, i.e., 3.2% ∼ 6.1%, under the different parameter sets, and without reducing the post-quantum security levels. Moreover, our key exchange protocol slightly reduces the probability of session key agreement failure and the time consumed by modular multiplication of numbers and ring elements by approximately 30%. Thus, the key exchange protocol in this paper is more suitable for the lightweight communication systems.

Cyclotomic sequences have good cryptographic properties and are closely related to difference sets. This paper proposes a new class of binary generalized cyclotomic sequences of order two and length pqr. Its linear complexity, minimal polynomial, and autocorrelation are investigated. The results show that these sequences have a large linear complexity when 2 ∈ D 1 , which means they can resist the Berlekamp-Massey attack. Furthermore, the autocorrelation values are close to 0 with a probability of approximately 1 − 1/r. Therefore, when r is a big prime, the new sequence has a good autocorrelation.

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