Algorithms to construct Minkowski reduced and Hermite reduced lattice bases
Theoretical Computer Science
Sphere-packings, lattices, and groups
Sphere-packings, lattices, and groups
A hierarchy of polynomial time lattice basis reduction algorithms
Theoretical Computer Science
A more efficient algorithm for lattice basis reduction
Journal of Algorithms
The algebraic eigenvalue problem
The algebraic eigenvalue problem
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
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
Approximating shortest lattice vectors is not harder than approximating closet lattice vectors
Information Processing Letters
A sieve algorithm for the shortest lattice vector problem
STOC '01 Proceedings of the thirty-third annual ACM symposium on Theory of computing
A linear space algorithm for computing the hermite normal form
Proceedings of the 2001 international symposium on Symbolic and algebraic computation
Public-Key Cryptosystems from Lattice Reduction Problems
CRYPTO '97 Proceedings of the 17th Annual International Cryptology Conference on Advances in Cryptology
Cryptanalysis of the Revised NTRU Signature Scheme
EUROCRYPT '02 Proceedings of the International Conference on the Theory and Applications of Cryptographic Techniques: Advances in Cryptology
NTRU: A Ring-Based Public Key Cryptosystem
ANTS-III Proceedings of the Third International Symposium on Algorithmic Number Theory
Some Recent Progress on the Complexity of Lattice Problems
COCO '99 Proceedings of the Fourteenth Annual IEEE Conference on Computational Complexity
Approximating-CVP to within Almost-Polynomial Factors is NP-Hard
FOCS '98 Proceedings of the 39th Annual Symposium on Foundations of Computer Science
Improved algorithms for integer programming and related lattice problems
STOC '83 Proceedings of the fifteenth annual ACM symposium on Theory of computing
Sampling Short Lattice Vectors and the Closest Lattice Vector Problem
CCC '02 Proceedings of the 17th IEEE Annual Conference on Computational Complexity
Hardness of Approximating the Shortest Vector Problem in High Lp Norms
FOCS '03 Proceedings of the 44th Annual IEEE Symposium on Foundations of Computer Science
Lattice problems and norm embeddings
Proceedings of the thirty-eighth annual ACM symposium on Theory of computing
Tensor-based hardness of the shortest vector problem to within almost polynomial factors
Proceedings of the thirty-ninth annual ACM symposium on Theory of computing
Limits on the Hardness of Lattice Problems in \ell _p Norms
CCC '07 Proceedings of the Twenty-Second Annual IEEE Conference on Computational Complexity
Fast LLL-type lattice reduction
Information and Computation
Hypercubic lattice reduction and analysis of GGH and NTRU signatures
EUROCRYPT'03 Proceedings of the 22nd international conference on Theory and applications of cryptographic techniques
NTRUSign: digital signatures using the NTRU lattice
CT-RSA'03 Proceedings of the 2003 RSA conference on The cryptographers' track
Improved analysis of Kannan's shortest lattice vector algorithm
CRYPTO'07 Proceedings of the 27th annual international cryptology conference on Advances in cryptology
Modular number systems: beyond the mersenne family
SAC'04 Proceedings of the 11th international conference on Selected Areas in Cryptography
ANTS'06 Proceedings of the 7th international conference on Algorithmic Number Theory
EUROCRYPT'05 Proceedings of the 24th annual international conference on Theory and Applications of Cryptographic Techniques
CRYPTO'06 Proceedings of the 26th annual international conference on Advances in Cryptology
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
Closest point search in lattices
IEEE Transactions on Information Theory
The Hardness of the Closest Vector Problem With Preprocessing Over Norm
IEEE Transactions on Information Theory
Sampling methods for shortest vectors, closest vectors and successive minima
ICALP'07 Proceedings of the 34th international conference on Automata, Languages and Programming
Gröbner bases for public key cryptography
Proceedings of the twenty-first international symposium on Symbolic and algebraic computation
Efficient lattice-based signature scheme
International Journal of Applied Cryptography
Improving BDD cryptosystems in general lattices
ISPEC'11 Proceedings of the 7th international conference on Information security practice and experience
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In Crypto 1997, Goldreich, Goldwasser and Halevi (GGH) proposed a lattice analogue of McEliece public key cryptosystem, which security is related to the hardness of approximating the closest vector problem (CVP) in a lattice. Furthermore, they also described how to use the same principle of their encryption scheme to provide a signature scheme. Practically, this cryptosystem uses the euclidean norm, l2- norm, which has been used in many algorithms based on lattice theory. Nonetheless, many drawbacks have been studied and these could lead to cryptanalysis of the scheme. In this paper, we present a novel method of reducing a vector under the l∞-norm and propose a digital signature scheme based on it. Our scheme takes advantage of the l∞-norm to increase the resistance of the GGH scheme and to decrease the signature length. Furthermore, after some other improvements, we obtain a very efficient signature scheme, that trades the security level, speed and space.