Communications of the ACM - Special issue on parallelism
Large integer multiplication on hypercubes
Journal of Parallel and Distributed Computing
Modern computer algebra
Fast Transforms: Algorithms, Analyses, Applications
Fast Transforms: Algorithms, Analyses, Applications
Rapid multiplication modulo the sum and difference of highly composite numbers
Mathematics of Computation
Proceedings of the ACM SIGGRAPH/EUROGRAPHICS conference on Graphics hardware
Algorithms for Quad-Double Precision Floating Point Arithmetic
ARITH '01 Proceedings of the 15th IEEE Symposium on Computer Arithmetic
Algorithms in Real Algebraic Geometry (Algorithms and Computation in Mathematics)
Algorithms in Real Algebraic Geometry (Algorithms and Computation in Mathematics)
A new Mixed Radix Conversion algorithm MRC-II
Journal of Systems Architecture: the EUROMICRO Journal
A Fully Parallel Mixed-Radix Conversion Algorithm for Residue Number Applications
IEEE Transactions on Computers
Larrabee: a many-core x86 architecture for visual computing
ACM SIGGRAPH 2008 papers
High performance discrete Fourier transforms on graphics processors
Proceedings of the 2008 ACM/IEEE conference on Supercomputing
Exploiting the Power of GPUs for Asymmetric Cryptography
CHES '08 Proceeding sof the 10th international workshop on Cryptographic Hardware and Embedded Systems
Toward acceleration of RSA using 3D graphics hardware
Cryptography and Coding'07 Proceedings of the 11th IMA international conference on Cryptography and coding
Modular resultant algorithm for graphics processors
ICA3PP'10 Proceedings of the 10th international conference on Algorithms and Architectures for Parallel Processing - Volume Part I
Towards efficient arithmetic for lattice-based cryptography on reconfigurable hardware
LATINCRYPT'12 Proceedings of the 2nd international conference on Cryptology and Information Security in Latin America
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We present the algorithm to multiply univariate polynomials with integer coefficients efficiently using the Number Theoretic transform (NTT) on Graphics Processing Units (GPU). The same approach can be used to multiply large integers encoded as polynomials. Our algorithm exploits fused multiply-add capabilities of the graphics hardware. NTT multiplications are executed in parallel for a set of distinct primes followed by reconstruction using the Chinese Remainder theorem (CRT) on the GPU. Our benchmarking experiences show the NTT multiplication performance up to 77 GMul/s. We compared our approach with CPU-based implementations of polynomial and large integer multiplication provided by NTL and GMP libraries.