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Journal of Computer Research and Development

Recent Advances in Lattice-Based Cryptography

Pingyuan Zhang, Han Jiang, Jie Cai, Chenguang Wang, Zhihua Zheng, Qiuliang Xu

Published Oct 1, 2017• 0 citations
Publisher
DOI
10.7544/issn1000-1239.2017.20170628

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Digital signatures are an important primitive for building secure systems and are used in most real-world security protocols. However, almost all popular signature schemes are either based on the factoring assumption (RSA) or the hardness of the discrete logarithm problem (DSA/ECDSA). In the case of classical cryptanalytic advances or progress on the development of quantum computers, the hardness of these closely related problems might be seriously weakened. A potential alternative approach is the construction of signature schemes based on the hardness of certain lattice problems that are assumed to be intractable by quantum computers. Due to significant research advancements in recent years, lattice-based schemes have now become practical and appear to be a very viable alternative to number-theoretic cryptography. In this article, we focus on recent developments and the current state of the art in lattice-based digital signatures and provide a comprehensive survey discussing signature schemes with respect to practicality. Additionally, we discuss future research areas that are essential for the continued development of lattice-based cryptography.
Recent advances in quantum computing have high-lighted the vulnerabilities in contemporary RSA encryption. Shor's approach for factoring numbers is becoming more tractable as quantum computing advances. This jeopardizes the security of any cryptographic system that is based on the complexity of factorisation. Many other crypto-systems based on theories like Elliptic Curve Cryptography are also vulnerable. To keep a cryptographic system safe against a quantum adversary, we must develop approaches based on a hard mathematical problem that is not vulnerable to quantum computer attacks, and we must develop Post Quantum Cryptography (PQC). One potential option is the use of lattices in a system called ring Learning with Errors (rLWE). Several techniques for postquantum encryption have been submitted to NIST. This paper studies the different speeds of different lattice-based protocols.