Python matrix tools over $\mathbb{Z}_q$
This page provides the Python library matrixzq with functions to carry out matrix operations over $\mathbb{Z}_q$ ($\mathbb{Z}/q\mathbb{Z}$) in pure Python without using Numpy or Scipy.
Where q is a positive integer greater than 1. All matrix elements are expected to be nonnegative integers in the range [0, q-1]. All computations are carried out modulo q.
The modulus q does not have to be prime for most matrix arithmetical operations (add, multiply), but it must be prime to carry out operations that involve division (invert, solve).
|
matrixzq.py | Main library source code |
|
matrixzq_t.py | Some tests |
|
matrixzq-1.0.0.zip | Download all as zip |
Background
We wanted pure Python code to operate on matrices modulo an integer q to demonstrate some principles of lattice-based encryption schemes using Learning-With-Errors (LWE). We found the excellent code "BASIC Linear Algebra Tools in Pure Python without Numpy or Scipy" by Thom Ives at
https://github.com/ThomIves/BasicLinearAlgebraToolsPurePy
https://integratedmlai.com/basic-linear-algebra-tools-in-pure-python-without-numpy-or-scipy
This code is inspired and partly derived from Thom's excellent work. Thank you, Thom.
We have provided basic Python functions rather than a more-complicated class so you can easily extract and work with the underlying list of lists.
Contact us
To comment on this page or to tell us about a mistake, please send us a message.
This page first published 7 August 2023. Last updated 7 August 2023.
