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
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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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
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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
Trapdoors for lattices: simpler, tighter, faster, smaller
Daniele Micciancio,Chris Peikert +1 more
- 15 Apr 2012
TL;DR: In this article, the authors give new methods for generating and using "strong trapdoors" in cryptographic lattices, which are simultaneously simple, efficient, easy to implement (even in parallel), and asymptotically optimal with very small hidden constants.
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Fully Homomorphic Encryption over the Integers.
TL;DR: In this paper, a somewhat homomorphic encryption scheme using elementary modular arithmetic is described. But the main appeal of their approach is the conceptual simplicity. And the security of their scheme is reduced to finding an approximate integer gcd, i.e., given a list of integers that are near-multiples of a hidden integer, output that hidden integer.
On Lova´sz' lattice reduction and the nearest lattice point problem
László Babai,László Babai +1 more
TL;DR: Answering a question of Vera Sós, it is shown how Lovász’ lattice reduction can be used to find a point of a given lattice, nearest within a factor ofcd (c = const.) to a given point in Rd.
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Implementing Gentry's fully-homomorphic encryption scheme
Craig Gentry,Shai Halevi +1 more
- 15 May 2011
TL;DR: In this article, the authors describe a working implementation of a variant of Gentry's fully homomorphic encryption scheme (STOC 2009), similar to the variant used in an earlier implementation effort by Smart and Vercauteren (PKC 2010).
Efficient lattice (H)IBE in the standard model
Shweta Agrawal,Dan Boneh,Xavier Boyen +2 more
- 30 May 2010
TL;DR: This work constructs an efficient identity based encryption system based on the standard learning with errors (LWE) problem and extends this basic technique to an adaptively-secure IBE and a Hierarchical IBE.