arXiv subjects

Zhichuang Liang

Publications and source records attributed to Zhichuang Liang.

3 recordsLinked to original sources

arXiv2022

Number Theoretic Transform and Its Applications in Lattice-based Cryptosystems: A Survey

Number theoretic transform (NTT) is the most efficient method for multiplying two polynomials of high degree with integer coefficients, due to its series of advantages in terms of algorithm and implementation, and is consequently widely-used and particularly fundamental in the practical implementations of lattice-based cryptographic schemes. Especially, recent works have shown that NTT can be utilized in those schemes without NTT-friendly rings, and can outperform other multiplication algorithms. In this paper, we first review the basic concepts of polynomial multiplication, convolution and NTT. Subsequently, we systematically introduce basic radix-2 fast NTT algorithms in an algebraic way via Chinese Remainder Theorem. And then, we elaborate recent advances about the methods to weaken restrictions on parameter conditions of NTT. Furthermore, we systematically introduce how to choose appropriate strategy of NTT algorithms for the various given rings. Later, we introduce the applications of NTT in the lattice-based cryptographic schemes of NIST post-quantum cryptography standardization competition. Finally, we try to present some possible future research directions.

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arXiv2022

Compact and Efficient KEMs over NTRU Lattices

The NTRU lattice is a promising candidate to construct practical cryptosystems, in particular key encapsulation mechanism (KEM), resistant to quantum computing attacks. Nevertheless, there are still some inherent obstacles to NTRU-based KEM schemes in having integrated performance, taking security, bandwidth, error probability, and computational efficiency \emph{as a whole}, that is as good as and even better than their \{R,M\}LWE-based counterparts. In this work, we solve this problem by presenting a new family of NTRU-based KEM schemes, referred to as CTRU and CNTR. By bridging low-dimensional lattice codes and high-dimensional NTRU-lattice-based cryptography with careful design and analysis, to the best of our knowledge CTRU and CNTR are the first NTRU-based KEM schemes with scalable ciphertext compression via only one \emph{single} ciphertext polynomial, and are the first that could outperform \{R,M\}LWE-based KEM schemes in integrated performance. For instance, compared to Kyber that is currently the only standardized KEM by NIST, on the recommended parameter set CNTR-768 has about $12\%$ smaller ciphertext size while encapsulating 384-bit keys compared to the fixed 256-bit key size of Kyber, security strengthened by $(8,7)$ bits for classical and quantum security respectively, and significantly lower error probability ($2^{-230}$ of CNTR-768 vs. $2^{-164}$ of Kyber-768). In comparison with the state-of-the-art AVX2 implementation of Kyber-768, CNTR-768 is faster by 1.9X in KeyGen, 2.6X in Encaps, and 1.2X in Decaps, respectively. When compared to the NIST Round 3 finalist NTRU-HRSS, our CNTR-768 has about $15\%$ smaller ciphertext size, and the security is strengthened by $(55,49)$ bits for classical and quantum security respectively. As for the AVX2 implementation, CNTR-768 is faster than NTRU-HRSS by 19X in KeyGen, 2.3X in Encaps, and 1.6X in Decaps, respectively.

cs.CR↗

arXiv2021

OSKR/OKAI: Systematic Optimization of Key Encapsulation Mechanisms from Module Lattice

In this work, we make \emph{systematic} optimizations of key encapsulation mechanisms (KEM) based on module learning-with-errors (MLWE), covering algorithmic design, fundamental operation of number-theoretic transform (NTT), approaches to expanding encapsulated key size, and optimized implementation coding. We focus on Kyber (now in the Round-3 finalist of NIST PQC standardization) and Aigis (a variant of Kyber proposed at PKC 2020). By careful analysis, we first observe that the algorithmic design of Kyber and Aigis can be optimized by the mechanism of asymmetric key consensus with noise (AKCN) proposed in \cite{JZ16,JZ19}. Specifically, the decryption process can be simplified with AKCN, leading to a both faster and less error-prone decryption process. Moreover, the AKCN-based optimized version has perfect compatibility with the deployment of Kyber/Aigis in reality, as they can run on the same parameters, the same public key, and the same encryption process. We make a systematic study of the variants of NTT proposed in recent years for extending its applicability scope, make concrete analysis of their exact computational complexity, and in particular show their equivalence. We then present a new variant named hybrid-NTT (H-NTT), combining the advantages of existing NTT methods, and derive its optimality in computational complexity. The H-NTT technique not only has larger applicability scope but also allows for modular and unified implementation codes of NTT operations even with varying module dimensions. We analyze and compare the different approaches to expand the size of key to be encapsulated (specifically, 512-bit key for dimension of 1024), and conclude with the most economic approach. To mitigate the compatibility issue in implementations we adopt the proposed H-NTT method.

cs.CR↗