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Communications in computer and information science

Lattice-Based Post Quantum Cryptography Using Variations of Learning with Error (LWE)

Parth D. Shah, Priteshkumar Prajapati, Dhaval Patel

Published Jan 1, 2025• 3 citations
Publisher
DOI
10.1007/978-3-031-88039-1_5

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The swift advancement of quantum computing devices holds the potential to create robust machines that can tackle an extensive array of issues beyond the scope of conventional computers. Consequently, quantum computing machines create new risks at a velocity and scale never seen before, especially with regard to encryption. Lattice-based cryptography is regarded as post-quantum cryptography’s future and a competitor to a quantum computer attack. Thus, there are several advantages to lattice-based cryptographic protocols, including security, effectiveness, reduced energy usage and speed. In this work, we study the learning with errors (LWE) problem and the cryptosystems that are based on the LWE problem and, in addition, we present a new efficient variant of LWE cryptographic scheme.
This chapter introduces post-quantum cryptography. It describes lattice-based cryptographic constructions of post-quantum cryptography. Lattice-based cryptographic constructions are one of candidates of post-quantum cryptography, which are believed to be secure against quantum computers. Learning with errors (LWE) is one of the most promising primitives in many usages due to its lightweight operation and rigorous security reduction against the worst-case of the lattice problems that are considered to be hard to solve even after the advance of quantum computers. After the research about the connection between the LWE problem and some lattice problems, some variants of LWE, of which the secret distributions are modified from the uniform distribution, were proposed. Due to the efficiency and compactness of ring-LWE, many lattice-based cryptosystems are constructed as ring-LWE based, rather than LWE-based. The chapter explains a ring variant of Lizard scheme, called RLizard, IND-CCA secure encryption scheme.