A hierarchy of polynomial time lattice basis reduction algorithms
Theoretical Computer Science
Lattice basis reduction: improved practical algorithms and solving subset sum problems
Mathematical Programming: Series A and B
A course in computational algebraic number theory
A course in computational algebraic number theory
A public-key cryptosystem with worst-case/average-case equivalence
STOC '97 Proceedings of the twenty-ninth annual ACM symposium on Theory of computing
The shortest vector problem in L2 is NP-hard for randomized reductions (extended abstract)
STOC '98 Proceedings of the thirtieth annual ACM symposium on Theory of computing
A sieve algorithm for the shortest lattice vector problem
STOC '01 Proceedings of the thirty-third annual ACM symposium on Theory of computing
Accuracy and Stability of Numerical Algorithms
Accuracy and Stability of Numerical Algorithms
A procedure for determining algebraic integers of given norm
EUROCAL '83 Proceedings of the European Computer Algebra Conference on Computer Algebra
Cryptanalysis of the Goldreich-Goldwasser-Halevi Cryptosystem from Crypto '97
CRYPTO '99 Proceedings of the 19th Annual International Cryptology Conference on Advances in Cryptology
Public-Key Cryptosystems from Lattice Reduction Problems
CRYPTO '97 Proceedings of the 17th Annual International Cryptology Conference on Advances in Cryptology
NTRU: A Ring-Based Public Key Cryptosystem
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
Certification of the QR factor R and of lattice basis reducedness
Proceedings of the 2007 international symposium on Symbolic and algebraic computation
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
SWIFFT: A Modest Proposal for FFT Hashing
Fast Software Encryption
Improved analysis of Kannan's shortest lattice vector algorithm
CRYPTO'07 Proceedings of the 27th annual international cryptology conference on Advances in cryptology
EUROCRYPT'08 Proceedings of the theory and applications of cryptographic techniques 27th annual international conference on Advances in cryptology
Lattice-based identification schemes secure under active attacks
PKC'08 Proceedings of the Practice and theory in public key cryptography, 11th international conference on Public key cryptography
Asymptotically efficient lattice-based digital signatures
TCC'08 Proceedings of the 5th conference on Theory of cryptography
EUROCRYPT'05 Proceedings of the 24th annual international conference on Theory and Applications of Cryptographic Techniques
Rankin's constant and blockwise lattice reduction
CRYPTO'06 Proceedings of the 26th annual international conference on Advances in Cryptology
Integer parameter estimation in linear models with applications toGPS
IEEE Transactions on Signal Processing
Closest point search in lattices
IEEE Transactions on Information Theory
Faster exponential time algorithms for the shortest vector problem
SODA '10 Proceedings of the twenty-first annual ACM-SIAM symposium on Discrete Algorithms
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
Algorithms for the shortest and closest lattice vector problems
IWCC'11 Proceedings of the Third international conference on Coding and cryptology
Analyzing blockwise lattice algorithms using dynamical systems
CRYPTO'11 Proceedings of the 31st annual conference on Advances in cryptology
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
Implicit factoring with shared most significant and middle bits
PKC'10 Proceedings of the 13th international conference on Practice and Theory in Public Key Cryptography
Lattice enumeration using extreme pruning
EUROCRYPT'10 Proceedings of the 29th Annual international conference on Theory and Applications of Cryptographic Techniques
Parallel shortest lattice vector enumeration on graphics cards
AFRICACRYPT'10 Proceedings of the Third international conference on Cryptology in Africa
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The Kannan-Fincke-Pohst enumeration algorithm for the shortest and closest lattice vector problems is the keystone of all strong lattice reduction algorithms and their implementations. In the context of the fast developing lattice-based cryptography, the practical security estimates derive from floating-point implementations of these algorithms. However, these implementations behave very unexpectedly and make these security estimates debatable. Among others, numerical stability issues seem to occur and raise doubts on what is actually computed. We give here the first results on the numerical behavior of the floating-point enumeration algorithm. They provide a theoretical and practical framework for the use of floating-point numbers within strong reduction algorithms, which could lead to more sensible hardness estimates.