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

Parth D. Shah, Priteshkumar Prajapati, Dhaval Patel

Communications in computer and information scienceJan 1, 20253 citations

Learning with Errors: A Lattice-Based Keystone of Post-Quantum Cryptography

Maria E. Sabani, Ilias Κ. Savvas, Georgia Garani

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.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.

SignalsApr 13, 202427 citations

STP‐LWE: A Variant of Learning with Error for a Flexible Encryption

Bo Gao, Yanfeng Shi, Chunli Yang +3 more

We construct a flexible lattice based scheme based on semitensor product learning with errors (STP‐LWE), which is a variant of learning with errors problem. We have proved that STP‐LWE is hard when LWE is hard. Our scheme is proved to be secure against indistinguishable chosen message attacks, and it can achieve a balance between the security and efficiency in the hierarchical encryption systems. In addition, our scheme is almost as efficient as the dual encryption in GPV08.

Mathematical Problems in EngineeringJan 1, 201411 citations

Error Correction and Ciphertext Quantization in Lattice Cryptography

Daniele Micciancio, Mark Schultz-Wu

Lecture notes in computer scienceJan 1, 20237 citations

Efficient Laconic Cryptography from Learning with Errors

Nico Döttling, Dimitris Kolonelos, Russell W. F. Lai +3 more

Lecture notes in computer scienceJan 1, 202347 citations

Lattice-Based Cryptography

Seong Oun Hwang, Intae Kim, Wai‐Kong Lee

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.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.

CRC Press eBooksFeb 19, 20210 citations

Universal product learning with errors: A new variant of LWE for lattice-based cryptography

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