Lattice-Based Cryptography

Nasheem Khan, Chandrashekhar Diwakar, Vinod Kumar

Lattice-based cryptography (LBC) has been the subject of numerous studies conducted by researchers during the past few years. LBC is a part of post-quantum cryptography, and it has undergone rapid development in recent years and is very attractive due to the low asymptotic complexity and potential resistance to quantum computing attacks. LBC is considered a quantum-safe alternative for the replacement of currently used schemes based on RSA and discrete logarithms on prime fields, elliptic curves, etc. This paper is intended to be a survey about LBC, its applications, and its future scope.

Daniele Micciancio, Oded Regev

Chris Peikert

Lattice-based cryptography is the use of conjectured hard problems on point lattices in ℝn as the foundation for secure cryptographic systems. Attractive features of lattice cryptography include apparent resistance to quantum attacks (in contrast with most number-theoretic cryptography), high asymptotic efficiency and parallelism, security under worst-case intractability assumptions, and solutions to long-standing open problems in cryptography. This work surveys most of the major developments in lattice cryptography over the past ten years. The main focus is on the foundational short integer solution (SIS) and learning with errors (LWE) problems (and their more efficient ring-based variants), their provable hardness assuming the worst-case intractability of standard lattice problems, and their many cryptographic applications.

Chuck Easttom

Xiaoyun Wang, Guangwu Xu, Yang Yu

Amanda Davenport, Sachin S. Shetty

In this paper, we provide a mathematical background and analysis of Lattice Based Cryptography for the less mathematically mature reader. Discussing the benefits and constraints of Lattice Based Crypto, we compare and contrast with Elliptic Curve Cryptography to provide an understanding of what the limitations of Lattice Based Cryptography are, and what needs to be achieved for the quantum resistant protocols to be deploy-able to any and all devices.