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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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.
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•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.
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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.
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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
•Posted Content
Improved (Hierarchical) Inner-Product Encryption from Lattices.
TL;DR: In this article, Abdalla, De Caro, and Mochetti proposed the first lattice-based IBE scheme with public parameters of size O(μn2 lg3 q) = O (μn5), where n is the security parameter.
SPRING: Fast Pseudorandom Functions from Rounded Ring Products
Abhishek Banerjee,Hai Brenner,Gaëtan Leurent,Chris Peikert,Alon Rosen +4 more
- 03 Mar 2014
TL;DR: Recently, Banerjee, Peikert and Rosen proposed new theoretical pseudorandom function candidates based on “rounded products” in certain polynomial rings, which have rigorously provable security based on worst-case lattice problems.
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Cryptanalysis of the multilinear map on the ideal lattices.
Jung Hee Cheon,Changmin Lee +1 more
TL;DR: In this paper, the authors improved the zeroizing attack on the multilinear map of Garg, Gentry and Halevi (GGH) by applying a lattice reduction to a sublattice obtained from the Hermit Normal Form of 〈g〉 and showed that if g has a large residual degree, one can find a short element of g in polynomial time of n.
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A Hybrid Gaussian Sampler for Lattices over Rings
Léo Ducas,Thomas Prest +1 more
TL;DR: A Gaussian Sampler optimized for lattices over the ring of integer of a cyclotomic number eld is presented, at a high-level it works as Klein's sampler but uses an e cient variant of Peikert's Sampler as a subroutine.
11
•Journal Article
The Shortest Vector Problem in L 2 is NP-hard for Randomized Reductions.
TL;DR: There is a prob-abilistic Turing-machine which in polynomial time reduces any problem in NP to instances of the shortest vector problem, provided that it can use an oracle which returns the solution of the longest vector problem if an instance of it is presented (by giving a basis of the corresponding lattice).