Solving low-density subset sum problems
Journal of the ACM (JACM)
Minkowski's convex body theorem and integer programming
Mathematics of Operations Research
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
Improved low-density subset sum algorithms
Computational Complexity
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
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 method for obtaining digital signatures and public-key cryptosystems
Communications of the ACM
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
Complexity of Lattice Problems
Complexity of Lattice Problems
Random Lattices and a Conjectured 0 - 1 Law about Their Polynomial Time Computable Properties
FOCS '02 Proceedings of the 43rd Symposium on Foundations of Computer Science
A Lattice-Based Public-Key Cryptosystem
SAC '98 Proceedings of the Selected Areas in Cryptography
CRYPTO '99 Proceedings of the 19th Annual International Cryptology Conference on Advances in Cryptology
Cryptanalysis of the Goldreich-Goldwasser-Halevi Cryptosystem from Crypto '97
CRYPTO '99 Proceedings of the 19th Annual International Cryptology Conference on Advances in Cryptology
Quantum Public-Key Cryptosystems
CRYPTO '00 Proceedings of the 20th 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
Eliminating Decryption Errors in the Ajtai-Dwork Cryptosystem
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
Tensor-Based Trapdoors for CVP and Their Application to Public Key Cryptography
Proceedings of the 7th IMA International Conference on Cryptography and Coding
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
NTRU: A Ring-Based Public Key Cryptosystem
ANTS-III Proceedings of the Third International Symposium on Algorithmic Number Theory
Improving Lattice Based Cryptosystems Using the Hermite Normal Form
CaLC '01 Revised Papers from the International Conference on Cryptography and Lattices
Finding Small Solutions to Small Degree Polynomials
CaLC '01 Revised Papers from the International Conference on Cryptography and Lattices
Improved algorithms for integer programming and related lattice problems
STOC '83 Proceedings of the fifteenth annual ACM symposium on Theory of computing
On breaking generalized knapsack public key cryptosystems
STOC '83 Proceedings of the fifteenth annual ACM symposium on Theory of computing
On lattices, learning with errors, random linear codes, and cryptography
Proceedings of the thirty-seventh annual ACM symposium on Theory of computing
Representing hard lattices with O(n log n) bits
Proceedings of the thirty-seventh annual ACM symposium on Theory of computing
Explicit Hard Instances of the Shortest Vector Problem
PQCrypto '08 Proceedings of the 2nd International Workshop on Post-Quantum Cryptography
Fast LLL-type lattice reduction
Information and Computation
Finding a small root of a univariate modular equation
EUROCRYPT'96 Proceedings of the 15th annual international conference on Theory and application of cryptographic techniques
EUROCRYPT'97 Proceedings of the 16th annual international conference on Theory and application of cryptographic techniques
An improved low-density subset sum algorithm
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
Cryptanalysis of the Paeng-Jung-Ha cryptosystem from PKC 2003
PKC'07 Proceedings of the 10th international conference on Practice and theory in public-key cryptography
Multi-bit cryptosystems based on lattice problems
PKC'07 Proceedings of the 10th international conference on Practice and theory in public-key cryptography
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
Adapting density attacks to low-weight knapsacks
ASIACRYPT'05 Proceedings of the 11th international conference on Theory and Application of Cryptology and Information Security
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
Sampling methods for shortest vectors, closest vectors and successive minima
ICALP'07 Proceedings of the 34th international conference on Automata, Languages and Programming
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Lattice reduction is known to be a very powerful tool in modern cryptanalysis. In the literature, there are many lattice reduction algorithms that have been proposed with various time complexity (from quadratic to subexponential). These algorithms can be utilized to find a short vector of a lattice with a small norm. Over time, shorter vector will be found by incorporating these methods. In this paper, we take a different approach by presenting a methodology that can be applied to any lattice reduction algorithms, with the implication that enables us to find a shorter vector (i.e. a smaller solution) while requiring shorter computation time. Instead of applying a lattice reduction algorithm to a complete lattice, we work on a sublattice with a smaller dimension chosen in the function of the lattice reduction algorithm that is being used. This way, the lattice reduction algorithm will be fully utilized and hence, it will produce a better solution. Furthermore, as the dimension of the lattice becomes smaller, the time complexity will be better. Hence, our methodology provides us with a new direction to build a lattice that is resistant to lattice reduction attacks. Moreover, based on this methodology, we also propose a recursive method for producing an optimal approach for lattice reduction with optimal computational time, regardless of the lattice reduction algorithm used. We evaluate our technique by applying it to break the lattice challenge by producing the shortest vector known so far. Our results outperform the existing known results and hence, our results achieve the record in the lattice challenge problem.