Journal of Algorithms
On the complexity of the multiplication of matrices of small formats
Journal of Complexity
The Middle Product Algorithm I
Applicable Algebra in Engineering, Communication and Computing
Five, Six, and Seven-Term Karatsuba-Like Formulae
IEEE Transactions on Computers
Comments on "Five, Six, and Seven-Term Karatsuba-Like Formulae"
IEEE Transactions on Computers
ARITH '07 Proceedings of the 18th IEEE Symposium on Computer Arithmetic
Symmetric Tensors and Symmetric Tensor Rank
SIAM Journal on Matrix Analysis and Applications
Improved Polynomial Multiplication Formulas over $IF₂$ Using Chinese Remainder Theorem
IEEE Transactions on Computers
On multiplication in finite fields
Journal of Complexity
Efficient multiplication in F3lm, m ≥ 1 and 5 ≤ l ≤ 18
AFRICACRYPT'08 Proceedings of the Cryptology in Africa 1st international conference on Progress in cryptology
Algebraic Complexity Theory
Multiplication of polynomials modulo xn
Theoretical Computer Science
On the arithmetic operations over finite fields of characteristic three with low complexity
Journal of Computational and Applied Mathematics
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We describe a unified framework to search for optimal formulae evaluating bilinear or quadratic maps. This framework applies to polynomial multiplication and squaring, finite field arithmetic, matrix multiplication, etc. We then propose a new algorithm to solve problems in this unified framework. With an implementation of this algorithm, we prove the optimality of various published upper bounds, and find improved upper bounds.