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.
read more
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.
read more
Chat with Paper
AI Agents for this Paper
Find similar papers on Google Scholar, PubMed and Arxiv
Write a critical review of this paper
Analyze citations of this paper to find unaddressed research gaps
Citations
A Survey on Homomorphic Encryption Schemes: Theory and Implementation
TL;DR: The basics of HE and the details of the well-known Partially Homomorphic Encryption and Somewhat Homomorphic encryption schemes, which are important pillars for achieving FHE, are presented and the implementations and recent improvements in Gentry-type FHE schemes are surveyed.
865
•Posted Content
A Survey on Homomorphic Encryption Schemes: Theory and Implementation
TL;DR: The basics of HE and the details of the well-known Partially Homomorphic Encryption and Somewhat HomomorphicEncryption, which are important pillars of achieving FHE, are presented and the main FHE families, which have become the base for the other follow-up FHE schemes are presented.
765
•Book
Advances in Cryptology - CRYPTO 2006
Cynthia Dwork
- 01 Jan 2006
TL;DR: A new construction for private intersection sum with cardinality is presented that provides malicious security with abort and guarantees that both parties receive the output upon successful completion of the protocol.
400
Securing the Internet of Things in a Quantum World
TL;DR: The impacts of quantum computers on the security of the cryptographic schemes used today are demonstrated, and an overview of the recommendations for cryptographic schemes that can be secure under the attacks of both classical and quantum computers are given.
234
F1: A Fast and Programmable Accelerator for Fully Homomorphic Encryption
Nikola Samardzic,Axel Feldmann,Aleksandar Krastev,Srinivas Devadas,Ronald G. Dreslinski,Chris Peikert,Daniel Sanchez +6 more
- 18 Oct 2021
TL;DR: F1 as discussed by the authors is the first FHE accelerator that is programmable, i.e., capable of executing full FHE programs, based on an in-depth architectural analysis of the characteristics of FHE computations that reveals acceleration opportunities.
References
Lattices that admit logarithmic worst-case to average-case connection factors
Chris Peikert,Alon Rosen +1 more
- 11 Jun 2007
TL;DR: An average-case problem that is as hard as finding γ(n)-approximate shortest nonzero vectors in certain n-dimensional lattices in the worst case is exhibited, and reductions between various worst-case problems on ideal lattices are given, showing for example that the shortest vector problem is no harder than the closest vector problem.
Public-key cryptographic primitives provably as secure as subset sum
Vadim Lyubashevsky,Adriana Palacio,Gil Segev +2 more
- 09 Feb 2010
TL;DR: A semantically-secure public-key encryption scheme whose security is polynomial-time equivalent to the hardness of solving random instances of the subset sum problem and an oblivious transfer protocol that is secure against semi-honest adversaries.
New Multilinear Maps over the Integers
Jean-Sébastien Coron,Tancrède Lepoint,Mehdi Tibouchi +2 more
- 16 Aug 2015
TL;DR: Cheon et al. as mentioned in this paper proposed the first viable approach to general program obfuscation by computing the eigenvalues of a diagonalizable matrix over a multilinear map.
Toward basing fully homomorphic encryption on worst-case hardness
Craig Gentry
- 15 Aug 2010
TL;DR: A worst-case / average-case connection is proved that bases Gentry's scheme (in part) on the quantum hardness of the shortest independent vector problem (SIVP) over ideal lattices in the worst- case.