A polynomial time algorithm for computing the HNF of a module over the integers of a number field

Authors:
Jean-François Biasse;Claus Fieker
Affiliations:
Calgary, Alberta;Universität Kaiserslautern, Kaiserslautern - Germany
Venue:
Proceedings of the 37th International Symposium on Symbolic and Algebraic Computation
Year:
2012

Citing 7
Cited 0

Generalized Compact Knapsacks, Cyclic Lattices, and Efficient One-Way Functions from Worst-Case Complexity Assumptions

FOCS '02 Proceedings of the 43rd Symposium on Foundations of Computer Science
Generalized Compact Knapsacks, Cyclic Lattices, and Efficient One-Way Functions

Computational Complexity
An LLL Algorithm with Quadratic Complexity

SIAM Journal on Computing
Efficient Public Key Encryption Based on Ideal Lattices

ASIACRYPT '09 Proceedings of the 15th International Conference on the Theory and Application of Cryptology and Information Security: Advances in Cryptology
Generalized compact knapsacks are collision resistant

ICALP'06 Proceedings of the 33rd international conference on Automata, Languages and Programming - Volume Part II
Efficient collision-resistant hashing from worst-case assumptions on cyclic lattices

TCC'06 Proceedings of the Third conference on Theory of Cryptography
Constructions of codes from number fields

IEEE Transactions on Information Theory

Quantified Score

Hi-index	0.00

Visualization

Abstract

We present a variation of the modular algorithm for computing the Hermite Normal Form of an OK-module presented by Cohen [4], where OK is the ring of integers of a number field K. An approach presented in [4] based on reductions modulo ideals was conjectured to run in polynomial time by Cohen, but so far, no such proof was available in the literature. In this paper, we present a modification of the approach of [4] to prevent the coefficient swell and we rigorously assess its complexity with respect to the size of the input and the invariants of the field K.