A hierarchy of polynomial time lattice basis reduction algorithms
Theoretical Computer Science
A course in computational algebraic number theory
A course in computational algebraic number theory
Generating hard instances of lattice problems (extended abstract)
STOC '96 Proceedings of the twenty-eighth annual ACM symposium on Theory of computing
A public-key cryptosystem with worst-case/average-case equivalence
STOC '97 Proceedings of the twenty-ninth annual ACM symposium on Theory of computing
On the limits of non-approximability of lattice problems
STOC '98 Proceedings of the thirtieth 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
On the complexity of computing short linearly independent vectors and short bases in a lattice
STOC '99 Proceedings of the thirty-first annual ACM symposium on Theory of computing
Public-Key Cryptosystems from Lattice Reduction Problems
CRYPTO '97 Proceedings of the 17th Annual International Cryptology Conference on Advances in Cryptology
Cryptanalysis of the Ajtai-Dwork Cryptosystem
CRYPTO '98 Proceedings of the 18th Annual International Cryptology Conference on Advances in Cryptology
An Improved Worst-Case to Average-Case Connection for Lattice Problems
FOCS '97 Proceedings of the 38th Annual Symposium on Foundations of Computer Science
Approximating-CVP to within Almost-Polynomial Factors is NP-Hard
FOCS '98 Proceedings of the 39th Annual Symposium on Foundations of Computer Science
The Shortest Vector in a Lattice is Hard to Approximate to within Some Constant
FOCS '98 Proceedings of the 39th Annual Symposium on Foundations of Computer Science
A new paradigm for collision-free hashing: incrementality at reduced cost
EUROCRYPT'97 Proceedings of the 16th 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
Lattice Reduction by Random Sampling and Birthday Methods
STACS '03 Proceedings of the 20th Annual Symposium on Theoretical Aspects of Computer Science
Lattice Basis Reduction with Dynamic Approximation
WAE '00 Proceedings of the 4th International Workshop on Algorithm Engineering
A Lattice Based Public Key Cryptosystem Using Polynomial Representations
PKC '03 Proceedings of the 6th International Workshop on Theory and Practice in Public Key Cryptography: Public Key Cryptography
Improving Lattice Based Cryptosystems Using the Hermite Normal Form
CaLC '01 Revised Papers from the International Conference on Cryptography and Lattices
Dimension Reduction Methods for Convolution Modular Lattices
CaLC '01 Revised Papers from the International Conference on Cryptography and Lattices
The Two Faces of Lattices in Cryptology
CaLC '01 Revised Papers from the International Conference on Cryptography and Lattices
Cryptanalysis of a Public Key Cryptosystem Proposed at ACISP 2000
ACISP '01 Proceedings of the 6th Australasian Conference on Information Security and Privacy
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
Broadcast Attacks against Lattice-Based Cryptosystems
ACNS '09 Proceedings of the 7th International Conference on Applied Cryptography and Network Security
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
Known---Plaintext---Only Attack on RSA---CRT with Montgomery Multiplication
CHES '09 Proceedings of the 11th International Workshop on Cryptographic Hardware and Embedded Systems
SCN'10 Proceedings of the 7th international conference on Security and cryptography for networks
Lattice Polly Cracker cryptosystems
Journal of Symbolic Computation
Improved Nguyen-Vidick heuristic sieve algorithm for shortest vector problem
Proceedings of the 6th ACM Symposium on Information, Computer and Communications Security
Improving BDD cryptosystems in general lattices
ISPEC'11 Proceedings of the 7th international conference on Information security practice and experience
Analyzing blockwise lattice algorithms using dynamical systems
CRYPTO'11 Proceedings of the 31st annual conference on Advances in cryptology
Adapting density attacks to low-weight knapsacks
ASIACRYPT'05 Proceedings of the 11th international conference on Theory and Application of Cryptology and Information Security
On achieving chosen ciphertext security with decryption errors
AAECC'06 Proceedings of the 16th international conference on Applied Algebra, Algebraic Algorithms and Error-Correcting Codes
Making change and finding repfigits: balancing a knapsack
ICMS'06 Proceedings of the Second international conference on Mathematical Software
EUROCRYPT'05 Proceedings of the 24th annual international conference on Theory and Applications of Cryptographic Techniques
Lattice enumeration using extreme pruning
EUROCRYPT'10 Proceedings of the 29th Annual international conference on Theory and Applications of Cryptographic Techniques
Learning a parallelepiped: cryptanalysis of GGH and NTRU signatures
EUROCRYPT'06 Proceedings of the 24th annual international conference on The Theory and Applications of Cryptographic Techniques
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
A general NTRU-Like framework for constructing lattice-based public-key cryptosystems
WISA'11 Proceedings of the 12th international conference on Information Security Applications
A new lattice-based public-key cryptosystem mixed with a knapsack
CANS'11 Proceedings of the 10th international conference on Cryptology and Network Security
Lattice signatures without trapdoors
EUROCRYPT'12 Proceedings of the 31st Annual international conference on Theory and Applications of Cryptographic Techniques
An efficient LLL gram using buffered transformations
CASC'07 Proceedings of the 10th international conference on Computer Algebra in Scientific Computing
Solving BDD by enumeration: an update
CT-RSA'13 Proceedings of the 13th international conference on Topics in Cryptology
A note on BDD problems with λ2 -gap
Information Processing Letters
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Recent results of Ajtai on the hardness of lattice problems have inspired several cryptographic protocols. At Crypto '97, Goldreich, Goldwasser and Halevi proposed a public-key cryptosystem based on the closest vector problem in a lattice, which is known to be NP-hard. We show that there is a major flaw in the design of the scheme which has two implications: any ciphertext leaks information on the plaintext, and the problem of decrypting ciphertexts can be reduced to a special closest vector problem which is much easier than the general problem. As an application, we solved four out of the five numerical challenges proposed on the Internet by the authors of the cryptosystem. At least two of those four challenges were conjectured to be intractable. We discuss ways to prevent the flaw, but conclude that, even modified, the scheme cannot provide sufficient security without being impractical.