Solving low-density subset sum problems
Journal of the ACM (JACM)
Parallel lattice basis reduction
ISSAC '92 Papers from the international symposium on Symbolic and algebraic computation
A public-key cryptosystem with worst-case/average-case equivalence
STOC '97 Proceedings of the twenty-ninth annual ACM symposium on Theory of computing
Complexity Analysis of a Parallel Lattice Basis Reduction Algorithm
SIAM Journal on Computing
A sieve algorithm for the shortest lattice vector problem
STOC '01 Proceedings of the thirty-third annual ACM symposium on Theory of computing
Complexity of Lattice Problems
Complexity of Lattice Problems
Lattice Reduction by Random Sampling and Birthday Methods
STACS '03 Proceedings of the 20th Annual Symposium on Theoretical Aspects of Computer Science
A procedure for determining algebraic integers of given norm
EUROCAL '83 Proceedings of the European Computer Algebra Conference on Computer Algebra
Parallel gcd and Lattice Basis Reduction
CONPAR '92/ VAPP V Proceedings of the Second Joint International Conference on Vector and Parallel Processing: Parallel Processing
Public-Key Cryptosystems from Lattice Reduction Problems
CRYPTO '97 Proceedings of the 17th Annual International Cryptology Conference on Advances in Cryptology
Cryptanalysis of the RSA Schemes with Short Secret Exponent from Asiacrypt '99
ASIACRYPT '00 Proceedings of the 6th International Conference on the Theory and Application of Cryptology and Information Security: Advances in Cryptology
Lattice Basis Reduction: Improved Practical Algorithms and Solving Subset Sum Problems
FCT '91 Proceedings of the 8th International Symposium on Fundamentals of Computation Theory
The Effectiveness of Lattice Attacks Against Low-Exponent RSA
PKC '99 Proceedings of the Second International Workshop on Practice and Theory in Public Key Cryptography
NTRU: A Ring-Based Public Key Cryptosystem
ANTS-III Proceedings of the Third International Symposium on Algorithmic Number Theory
An Efficient Parallel Block-Reduction Algorithm
ANTS-III Proceedings of the Third International Symposium on Algorithmic Number Theory
Improved algorithms for integer programming and related lattice problems
STOC '83 Proceedings of the fifteenth annual ACM symposium on Theory of computing
Hardness of approximating the shortest vector problem in lattices
Journal of the ACM (JACM)
Lattice problems and norm embeddings
Proceedings of the thirty-eighth annual ACM symposium on Theory of computing
Trapdoors for hard lattices and new cryptographic constructions
STOC '08 Proceedings of the fortieth annual ACM symposium on Theory of computing
Finding short lattice vectors within mordell's inequality
STOC '08 Proceedings of the fortieth annual ACM symposium on Theory of computing
GPU-Accelerated Montgomery Exponentiation
ICCS '07 Proceedings of the 7th international conference on Computational Science, Part I: ICCS 2007
AES Encryption Implementation and Analysis on Commodity Graphics Processing Units
CHES '07 Proceedings of the 9th international workshop on Cryptographic Hardware and Embedded Systems
SWIFFT: A Modest Proposal for FFT Hashing
Fast Software Encryption
Exploiting the Power of GPUs for Asymmetric Cryptography
CHES '08 Proceeding sof the 10th international workshop on Cryptographic Hardware and Embedded Systems
Rigorous and Efficient Short Lattice Vectors Enumeration
ASIACRYPT '08 Proceedings of the 14th International Conference on the Theory and Application of Cryptology and Information Security: Advances in Cryptology
EUROCRYPT '09 Proceedings of the 28th Annual International Conference on Advances in Cryptology: the Theory and Applications of Cryptographic Techniques
Public-key cryptosystems from the worst-case shortest vector problem: extended abstract
Proceedings of the forty-first annual ACM symposium on Theory of computing
Parallel Lattice Basis Reduction Using a Multi-threaded Schnorr-Euchner LLL Algorithm
Euro-Par '09 Proceedings of the 15th International Euro-Par Conference on Parallel Processing
Fiat-Shamir with Aborts: Applications to Lattice and Factoring-Based Signatures
ASIACRYPT '09 Proceedings of the 15th International Conference on the Theory and Application of Cryptology and Information Security: Advances in Cryptology
Efficient Public Key Encryption Based on Ideal Lattices
ASIACRYPT '09 Proceedings of the 15th International Conference on the Theory and Application of Cryptology and Information Security: Advances in Cryptology
Factoring integers and computing discrete logarithms via diophantine approximation
EUROCRYPT'91 Proceedings of the 10th annual international conference on Theory and application of cryptographic techniques
Attacking the Chor-Rivest cryptosystem by improved lattice reduction
EUROCRYPT'95 Proceedings of the 14th annual international conference on Theory and application of cryptographic techniques
Improved analysis of Kannan's shortest lattice vector algorithm
CRYPTO'07 Proceedings of the 27th annual international cryptology conference on Advances in cryptology
Toward acceleration of RSA using 3D graphics hardware
Cryptography and Coding'07 Proceedings of the 11th IMA international conference on Cryptography and coding
EUROCRYPT'08 Proceedings of the theory and applications of cryptographic techniques 27th annual international conference on Advances in cryptology
Asymptotically efficient lattice-based digital signatures
TCC'08 Proceedings of the 5th conference on Theory of cryptography
Faster exponential time algorithms for the shortest vector problem
SODA '10 Proceedings of the twenty-first annual ACM-SIAM symposium on Discrete Algorithms
A parallel lattice basis reduction for mesh-connected processor arrays and parallel complexity
SPDP '93 Proceedings of the 1993 5th IEEE Symposium on Parallel and Distributed Processing
Practical lattice basis sampling reduction
ANTS'06 Proceedings of the 7th international conference on Algorithmic Number Theory
ANTS'06 Proceedings of the 7th international conference on Algorithmic Number Theory
Cryptographics: secret key cryptography using graphics cards
CT-RSA'05 Proceedings of the 2005 international conference on Topics in Cryptology
EUROCRYPT'05 Proceedings of the 24th annual international conference on Theory and Applications of Cryptographic Techniques
Accelerating lattice reduction with FPGAs
LATINCRYPT'10 Proceedings of the First international conference on Progress in cryptology: cryptology and information security in Latin America
Parallel enumeration of shortest lattice vectors
Euro-Par'10 Proceedings of the 16th international Euro-Par conference on Parallel processing: Part II
Analysis of gauss-sieve for solving the shortest vector problem in lattices
WALCOM'11 Proceedings of the 5th international conference on WALCOM: algorithms and computation
Algorithms for the shortest and closest lattice vector problems
IWCC'11 Proceedings of the Third international conference on Coding and cryptology
A parallel implementation of GaussSieve for the shortest vector problem in lattices
PaCT'11 Proceedings of the 11th international conference on Parallel computing technologies
Random sampling for short lattice vectors on graphics cards
CHES'11 Proceedings of the 13th international conference on Cryptographic hardware and embedded systems
Extreme enumeration on GPU and in clouds: how many dollars you need to break SVP challenges
CHES'11 Proceedings of the 13th international conference on Cryptographic hardware and embedded systems
Full lattice basis reduction on graphics cards
WEWoRC'11 Proceedings of the 4th Western European conference on Research in Cryptology
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In this paper we present an algorithm for parallel exhaustive search for short vectors in lattices. This algorithm can be applied to a wide range of parallel computing systems. To illustrate the algorithm, it was implemented on graphics cards using CUDA, a programming framework for NVIDIA graphics cards. We gain large speedups compared to previous serial CPU implementations. Our implementation is almost 5 times faster in high lattice dimensions. Exhaustive search is one of the main building blocks for lattice basis reduction in cryptanalysis. Our work results in an advance in practical lattice reduction.