Open AccessPosted Content
A Decade of Lattice Cryptography.
TL;DR: Lattice-based cryptography is the use of conjectured hard problems on point lattices in Rn as the foundation for secure cryptographic systems as mentioned in this paper, which is the main feature of lattice cryptography.
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Abstract: 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.
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Citations
Implementation and Evaluation of Improved Gaussian Sampling for Lattice Trapdoors
TL;DR: In this paper, a new Gaussian sampling algorithm for lattice trapdoors with prime moduli is proposed, which can be used for a wide range of cryptographic primitives including digital signatures, attributed-based encryption, program obfuscation and others.
(Quasi-)Linear-Time Algorithms for the Closest Vector Problem in (Semi-)Equiangular Lattices
Kenta Takahashi
- 22 Jun 2025
TL;DR: Researchers propose novel (quasi-)linear-time algorithms for the closest vector problem in (semi-)equiangular lattices, including root lattices A_n, D_n, and Coxeter-Barnes lattice A_n^r, with improved time complexities of O(n log n) and O(n) for restricted classes.
Journal Article
Hardness of the (Approximate) Shortest Vector Problem: A Simple Proof via Reed-Solomon Codes
Huck Bennett,Chris Peikert +1 more
TL;DR: It is shown that a close deterministic analogue of the local density construction would improve on the state-of-the-art explicit Reed-Solomon list-decoding lower bounds of Guruswami and Rudra (STOC 2005 and IEEE Transactions on Information Theory 2006).
•Posted Content
Algebraic and Euclidean Lattices: Optimal Lattice Reduction and Beyond
TL;DR: A framework generalizing lattice reduction algorithms to module lattices is introduced in order to practically and efficiently solve the $\gamma$-Hermite Module-SVP problem over arbitrary cyclotomic fields and provides speedups for many previous number theoretical algorithms.
The Complexity of the Shortest Vector Problem
TL;DR: In this article , the authors present known results and open questions related to the complexity of the Shortest Vector Problem (SVP) on point lattices, and present a survey.
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Pascal Paillier
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