The art of computer programming, volume 2 (3rd ed.): seminumerical algorithms
The art of computer programming, volume 2 (3rd ed.): seminumerical algorithms
More on Squaring and Multiplying Large Integers
IEEE Transactions on Computers
ARITH '07 Proceedings of the 18th IEEE Symposium on Computer Arithmetic
A gmp-based implementation of schönhage-strassen's large integer multiplication algorithm
Proceedings of the 2007 international symposium on Symbolic and algebraic computation
WAIFI '07 Proceedings of the 1st international workshop on Arithmetic of Finite Fields
WAIFI '07 Proceedings of the 1st international workshop on Arithmetic of Finite Fields
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
Code Generation for Polynomial Multiplication
CASC '09 Proceedings of the 11th International Workshop on Computer Algebra in Scientific Computing
Iterative Toom-Cook methods for very unbalanced long integer multiplication
Proceedings of the 2010 International Symposium on Symbolic and Algebraic Computation
Multiplication of polynomials modulo xn
Theoretical Computer Science
The Karatsuba integer middle product
Journal of Symbolic Computation
A new algorithm for long integer cube computation with some insight into higher powers
CASC'12 Proceedings of the 14th international conference on Computer Algebra in Scientific Computing
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Karatsuba and Toom-Cook are well-known methods used to multiply efficiently long integers. There have been different proposal about the interpolating values used to determine the matrix to be inverted and the sequence of operations to invert it. A deffinitive word about which is the optimal matrix (values) and the (number of) basic operations to invert it seems still not to have been said. In this paper we present some particular examples of useful matrices and a method to generate automatically, by means of optimised exhaustive searches on a graph, the best sequence of basic operations to invert them.