A more efficient algorithm for lattice basis reduction
Journal of Algorithms
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
Modern computer algebra
Lattice Attacks on Digital Signature Schemes
Designs, Codes and Cryptography
The Shortest Vector in a Lattice is Hard to Approximate to within Some Constant
SIAM Journal on Computing
Proceedings of the 11th Colloquium on Automata, Languages and Programming
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EUROCAL '83 Proceedings of the European Computer Algebra Conference on Computer Algebra
The optimal LLL algorithm is still polynomial in fixed dimension
Theoretical Computer Science - Latin American theoretical informatics
Polynomial factorization and nonrandomness of bits of algebraic and some transcendental numbers
STOC '84 Proceedings of the sixteenth annual ACM symposium on Theory of computing
Factoring univariate polynomials over the rationals
Factoring univariate polynomials over the rationals
H-LLL: using householder inside LLL
Proceedings of the 2009 international symposium on Symbolic and algebraic computation
An LLL Algorithm with Quadratic Complexity
SIAM Journal on Computing
EUROCRYPT'05 Proceedings of the 24th annual international conference on Theory and Applications of Cryptographic Techniques
An LLL-reduction algorithm with quasi-linear time complexity: extended abstract
Proceedings of the forty-third annual ACM symposium on Theory of computing
Recent progress in linear algebra and lattice basis reduction
Proceedings of the 36th international symposium on Symbolic and algebraic computation
Vector rational number reconstruction
Proceedings of the 36th international symposium on Symbolic and algebraic computation
Practical polynomial factoring in polynomial time
Proceedings of the 36th international symposium on Symbolic and algebraic computation
Proceedings of the 36th international symposium on Symbolic and algebraic computation
Progression-free sets and sublinear pairing-based non-interactive zero-knowledge arguments
TCC'12 Proceedings of the 9th international conference on Theory of Cryptography
Small algorithms for small systems
ACM Communications in Computer Algebra
Journal of Symbolic Computation
The complexity of factoring univariatepolynomials over the rationals: tutorial abstract
Proceedings of the 38th international symposium on International symposium on symbolic and algebraic computation
A more efficient computationally sound non-interactive zero-knowledge shuffle argument
Journal of Computer Security - Advances in Security for Communication Networks
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We present a lattice algorithm specifically designed for some classical applications of lattice reduction. The applications are for lattice bases with a generalized knapsack-type structure, where the target vectors are boundably short. For such applications, the complexity of the algorithm improves traditional lattice reduction by replacing some dependence on the bit-length of the input vectors by some dependence on the bound for the output vectors. If the bit-length of the target vectors is unrelated to the bit-length of the input, then our algorithm is only linear in the bit-length of the input entries, which is an improvement over the quadratic complexity floating-point LLL algorithms. To illustrate the usefulness of this algorithm we show that a direct application to factoring univariate polynomials over the integers leads to the first complexity bound improvement since 1984. A second application is algebraic number reconstruction, where a new complexity bound is obtained as well.