Hermite normal form computation using modulo determinant arithmetic
Mathematics of Operations Research
Residual hermite normal form computations
ACM Transactions on Mathematical Software (TOMS)
Fast parallel computation of hermite and smith forms of polynomial matrices
SIAM Journal on Algebraic and Discrete Methods
Asymptotically fast triangularization of matrices over rings
SIAM Journal on Computing
Beyond unimodular transformations
The Journal of Supercomputing
Computing Popov and Hermite forms of polynomial matrices
ISSAC '96 Proceedings of the 1996 international symposium on Symbolic and algebraic computation
Asymptotically fast computation of Hermite normal forms of integer matrices
ISSAC '96 Proceedings of the 1996 international symposium on Symbolic and algebraic computation
Generating hard instances of lattice problems (extended abstract)
STOC '96 Proceedings of the twenty-eighth annual ACM symposium on Theory of computing
On the worst-case complexity of integer Gaussian elimination
ISSAC '97 Proceedings of the 1997 international symposium on Symbolic and algebraic computation
Modern computer algebra
Diophantine linear system solving
ISSAC '99 Proceedings of the 1999 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
Improving Lattice Based Cryptosystems Using the Hermite Normal Form
CaLC '01 Revised Papers from the International Conference on Cryptography and Lattices
Fast LLL-type lattice reduction
Information and Computation
Computation of storage requirements for multi-dimensional signal processing applications
IEEE Transactions on Very Large Scale Integration (VLSI) Systems
Efficient lattice-based signature scheme
International Journal of Applied Cryptography
Broadcast Attacks against Lattice-Based Cryptosystems
ACNS '09 Proceedings of the 7th International Conference on Applied Cryptography and Network Security
Fast LLL-type lattice reduction
Information and Computation
A digital signature scheme based on CV P∞
PKC'08 Proceedings of the Practice and theory in public key cryptography, 11th international conference on Public key cryptography
SCN'10 Proceedings of the 7th international conference on Security and cryptography for networks
Computing hermite forms of polynomial matrices
Proceedings of the 36th international symposium on Symbolic and algebraic computation
Basis of solutions for a system of linear inequalities in integers: computation and applications
MFCS'05 Proceedings of the 30th international conference on Mathematical Foundations of Computer Science
Bonsai trees, or how to delegate a lattice basis
EUROCRYPT'10 Proceedings of the 29th Annual international conference on Theory and Applications of Cryptographic Techniques
On decomposable semigroups and applications
Journal of Symbolic Computation
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Computing the Hermite Normal Form of an n × n integer matrix using the best current algorithms typically requires &Ogr;(n3 log M) space, where M is a bound on the entries of the input matrix. Although polynomial in the input size (which is &Ogr;(n2 log M)), this space blow-up can easily become a serious issue in practice when working on big integer matrices. In this paper we present a new algorithm for computing the Hermite Normal Form which uses only &Ogr;(n2 log M) space (i.e., essentially the same as the input size). When implemented using standard algorithms for integer and matrix multiplication, our algorithm has the same time complexity of the asymptotically fastest (but space inefficient) algorithms. We also present a heuristic algorithm for HNF that achieves a substantial speedup when run on randomly generated input matrices.