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CORR
2008
Springer

Simultaneous Modular Reduction and Kronecker Substitution for Small Finite Fields

8 years 10 months ago
Simultaneous Modular Reduction and Kronecker Substitution for Small Finite Fields
We present algorithms to perform modular polynomial multiplication or modular dot product efficiently in a single machine word. We pack polynomials into integers and perform several modular operations with machine integer or floating point arithmetic. The modular polynomials are converted into integers using Kronecker substitution (evaluation at a sufficiently large integer). With some control on the sizes and degrees, arithmetic operations on the polynomials can be performed directly with machine integers or floating point numbers and the number of conversions can be reduced. We also present efficient ways to recover the modular values of the coefficients. This leads to practical gains of quite large constant factors for polynomial multiplication, prime field linear algebra and small extension field arithmetic.
Jean-Guillaume Dumas, Laurent Fousse, Bruno Salvy
Added 09 Dec 2010
Updated 09 Dec 2010
Type Journal
Year 2008
Where CORR
Authors Jean-Guillaume Dumas, Laurent Fousse, Bruno Salvy
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