Fast 2-Variable Integer Programming
Proceedings of the 8th International IPCO Conference on Integer Programming and Combinatorial Optimization
Fast Reduction of Ternary Quadratic Forms
CaLC '01 Revised Papers from the International Conference on Cryptography and Lattices
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
Analyzing blockwise lattice algorithms using dynamical systems
CRYPTO'11 Proceedings of the 31st annual conference on Advances in cryptology
EUROCRYPT'05 Proceedings of the 24th annual international conference on Theory and Applications of Cryptographic Techniques
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The author shows that a shortest basis for the 2-dimensional lattice Lambda (u, v) generated by an input pair u, v in Z/sup 2/ can be computed in O(M(n) log n) where n is the bit-size of the input numbers and M(n) is the complexity of multiplying two n-bit integers. This generalizes Schonhage's technique (1971) for fast integer GCD to a higher dimension.