On the complexity of regular-grammars with integer attributes
Journal of Computer and System Sciences
Efficient authentication from hard learning problems
EUROCRYPT'11 Proceedings of the 30th Annual international conference on Theory and applications of cryptographic techniques: advances in cryptology
On the expressive power of univariate equations over sets of natural numbers
Information and Computation
On Approximating Non-regular Languages by Regular Languages
Fundamenta Informaticae - Theory that Counts: To Oscar Ibarra on His 70th Birthday
Parsing Boolean grammars over a one-letter alphabet using online convolution
Theoretical Computer Science
On the bit-complexity of sparse polynomial and series multiplication
Journal of Symbolic Computation
A note on the space complexity of fast D-finite function evaluation
CASC'12 Proceedings of the 14th international conference on Computer Algebra in Scientific Computing
Batch proofs of partial knowledge
ACNS'13 Proceedings of the 11th international conference on Applied Cryptography and Network Security
Exact and efficient generation of geometric random variates and random graphs
ICALP'13 Proceedings of the 40th international conference on Automata, Languages, and Programming - Volume Part I
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For more than 35 years, the fastest known method for integer multiplication has been the Schönhage-Strassen algorithm running in time $O(n\log n\log\log n)$. Under certain restrictive conditions, there is a corresponding $\Omega(n\log n)$ lower bound. All this time, the prevailing conjecture has been that the complexity of an optimal integer multiplication algorithm is $\Theta(n\log n)$. We take a major step towards closing the gap between the upper bound and the conjectured lower bound by presenting an algorithm running in time $n\log n\,2^{O(\log^*n)}$. The running time bound holds for multitape Turing machines. The same bound is valid for the size of Boolean circuits.