Sphere-packings, lattices, and groups
Sphere-packings, lattices, and groups
A hierarchy of polynomial time lattice basis reduction algorithms
Theoretical Computer Science
Parallel lattice basis reduction
ISSAC '92 Papers from the international symposium on Symbolic and algebraic computation
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 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
Proceedings of the thirty-fifth annual ACM symposium on Theory of computing
Improved algorithms for integer programming and related lattice problems
STOC '83 Proceedings of the fifteenth annual ACM symposium on Theory of computing
EUROCRYPT'08 Proceedings of the theory and applications of cryptographic techniques 27th annual international conference on Advances in cryptology
Rankin's constant and blockwise lattice reduction
CRYPTO'06 Proceedings of the 26th annual international conference on Advances in Cryptology
Symplectic lattice reduction and NTRU
EUROCRYPT'06 Proceedings of the 24th annual international conference on The Theory and Applications of Cryptographic Techniques
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
Low-dimensional lattice basis reduction revisited
ACM Transactions on Algorithms (TALG)
EUROCRYPT'08 Proceedings of the theory and applications of cryptographic techniques 27th annual international conference on Advances in cryptology
Proceedings of the forty-second ACM symposium on Theory of computing
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
Improved Nguyen-Vidick heuristic sieve algorithm for shortest vector problem
Proceedings of the 6th ACM Symposium on Information, Computer and Communications Security
Lattice reduction algorithms: theory and practice
EUROCRYPT'11 Proceedings of the 30th Annual international conference on Theory and applications of cryptographic techniques: advances in cryptology
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
On the modular inversion hidden number problem
Journal of Symbolic Computation
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
BKZ 2.0: better lattice security estimates
ASIACRYPT'11 Proceedings of the 17th international conference on The Theory and Application of Cryptology and Information Security
Functional encryption for threshold functions (or fuzzy IBE) from lattices
PKC'12 Proceedings of the 15th international conference on Practice and Theory in Public Key Cryptography
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The celebrated Lenstra-Lenstra-Lovász lattice basis reduction algorithm (LLL) can naturally be viewed as an algorithmic version of Hermite's inequality on Hermite's constant. We present a polynomial-time blockwise reduction algorithm based on duality which can similarly be viewed as an algorithmic version of Mordell's inequality on Hermite's constant. This achieves a better and more natural approximation factor for the shortest vector problem than Schnorr's algorithm and its transference variant by Gama, Howgrave-Graham, Koy and Nguyen. Furthermore, we show that this approximation factor is essentially tight in the worst case.