Jean-Guillaume Dumas

Title: Jean-Guillaume Dumas

Main Research Question: How can we efficiently compute the dot product of two vectors over word-size finite fields?

Methodology: The author compared the practical behaviors of a wide range of implementation techniques using different representations. These techniques include floating point representations, discrete logarithms, tabulations, Montgomery reduction, and delayed modulus.

Results: The author found that the Montgomery representation was the most efficient method for computing the dot product. This method uses a reduction designed by Montgomery, which allows for efficient multiplication and division by using shifts and bit-masks instead of machine remaindering.

Implications: The results suggest that the Montgomery representation is a practical and efficient method for computing the dot product over word-size finite fields. This could have significant implications for linear algebra routines, matrix multiplication, and other algorithms that rely on the dot product.

In conclusion, the Montgomery representation is a promising technique for computing the dot product over word-size finite fields. It offers efficiency and could have wide-ranging implications for various algorithms and applications.

Link to Article: https://arxiv.org/abs/0404008v1 Authors: arXiv ID: 0404008v1