Faster polynomial multiplication via multipoint Kronecker substitution

Authors:
David Harvey
Affiliations:
Courant Institute of Mathematical Sciences, New York University, 251 Mercer Street, New York, NY 10012-1185, United States
Venue:
Journal of Symbolic Computation
Year:
2009

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Abstract

We present several new algorithms for dense polynomial multiplication in Z[x] based on the Kronecker substitution method. Instead of reducing to a single integer multiplication, we reduce to several smaller multiplications. We describe an implementation of multiplication in (Z/nZ)[x] for a word-sized modulus n based on these methods, and compare its performance to that of NTL and Magma.