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Conference papers

Parallel integer multiplication

Samuel Vivien 1, 2
2 CARAMBA - Cryptology, arithmetic : algebraic methods for better algorithms
Inria Nancy - Grand Est, LORIA - ALGO - Department of Algorithms, Computation, Image and Geometry
Abstract : Multiplication is a fundamental step in many algorithms. If the multiplication of two integers of n words has a complexity of M (n), divisions and squares can be computed in O(M (n)) as well and the greatest common divisor can be computed in O(M (n) log n). Thus being able to have a small value for M (n) is extremely important. To this day, the best known algorithm for reachable values is the Schönhage-Strassen algorithm which is implemented by a few arithmetic libraries. Asymptotically faster algorithms exist, however no computer is able to hold numbers big enough for those algorithms to outrun Schönhage-Strassen. The GNU Multiple Precision (GMP) library has a sequentialonly implementation of Schönhage-Strassen. However some algorithms contains a step which is a single big multiplication. Thus when trying to parallelize such an algorithm, one requires a parallel algorithm for multiplication. An example of such an algorithm is the batch factorization for Number Field Sieve. Thus people trying to implement a parallel version of such algorithms need to find an arithmetic library that implements a parallel integer multiplication. An example of such a library is the Flint (Fast LIbrary for Number Theory) library that contains a parallel implementation of Schönhage-Strassen. In this article we present an implementation of Schönhage-Strassen, that reaches a speedup of 20 for the multiplication of two integers of 10 7 words of 64 bits using a Xeon Gold with 32 cores.
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https://hal.archives-ouvertes.fr/hal-03541726
Contributor : Samuel Vivien Connect in order to contact the contributor
Submitted on : Friday, February 4, 2022 - 2:05:15 PM
Last modification on : Wednesday, May 4, 2022 - 4:37:50 PM
Long-term archiving on: : Thursday, May 5, 2022 - 6:18:05 PM

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Samuel Vivien. Parallel integer multiplication. PDP 2022 - 30th Euromicron International Conference on Parallel, Distributed, and Network-Based Processing, Mar 2022, Valladoid, Spain. ⟨10.1109/PDP55904.2022.00024⟩. ⟨hal-03541726⟩

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