An algorithm for exact division
Journal of Symbolic Computation
Integer and polynomial multiplication: towards optimal toom-cook matrices
Proceedings of the 2007 international symposium on Symbolic and algebraic computation
Integer and polynomial multiplication: towards optimal toom-cook matrices
Proceedings of the 2007 international symposium on Symbolic and algebraic computation
A New Analysis of the McEliece Cryptosystem Based on QC-LDPC Codes
SCN '08 Proceedings of the 6th international conference on Security and Cryptography for Networks
Iterative Toom-Cook methods for very unbalanced long integer multiplication
Proceedings of the 2010 International Symposium on Symbolic and Algebraic Computation
Efficient multiplication in finite field extensions of degree 5
AFRICACRYPT'11 Proceedings of the 4th international conference on Progress in cryptology in Africa
CHES'11 Proceedings of the 13th international conference on Cryptographic hardware and embedded systems
Efficient multiplication over extension fields
WAIFI'12 Proceedings of the 4th international conference on Arithmetic of Finite Fields
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Toom-Cook strategy is a well-known method for building algorithms to efficiently multiply dense univariate polynomials. Efficiency of the algorithm depends on the choice of interpolation points and on the exact sequence of operations for evaluation and interpolation. If carefully tuned, it gives the fastest algorithm for a wide range of inputs.This work smoothly extends the Toom strategy to polynomial rings, with a focus on . Moreover a method is proposed to find the faster Toom multiplication algorithm for any given splitting order. New results found with it, for polynomials in characteristic 2, are presented.A new extension for multivariate polynomials is also introduced; through a new definition of density leading Toom strategy to be efficient.