2020-12-29
A canonical form for positive definite matrices
Publication
Publication
Presented at the
14th Algorithmic Number Theory Symposium (June 2020), Virtual, Online
We exhibit an explicit, deterministic algorithm for finding a canonical form for a positive definite matrix under unimodular integral transformations. We use characteristic sets of short vectors and partition-backtracking graph software. The algorithm runs in a number of arithmetic operations that is exponential in the dimension n, but it is practical and more efficient than canonical forms based on Minkowski reduction.
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doi.org/10.2140/obs.2020.4.179 | |
The Open Book Series | |
14th Algorithmic Number Theory Symposium | |
Organisation | Cryptology |
Dutour Sikirić, M., Haensch, A., Voight, J., & van Woerden, W. (2020). A canonical form for positive definite matrices. In Proceedings of the 14th Algorithmic Number Theory Symposium, ANTS-XIV (pp. 179–195). doi:10.2140/obs.2020.4.179 |