High-speed convolution and correlation
AFIPS '66 (Spring) Proceedings of the April 26-28, 1966, Spring joint computer conference
Conditions for the Existence of Fast Number Theoretic Transforms
IEEE Transactions on Computers
The Discrete Fourier Transform Over Finite Rings with Application to Fast Convolution
IEEE Transactions on Computers
Fast Multipliers for Number Theoretic Transforms
IEEE Transactions on Computers
A Parallel Architecture for Digital Filtering Using Fermat Number Transforms
IEEE Transactions on Computers
Comments on ``On the Definition and Generation of Walsh Functions''
IEEE Transactions on Computers
Correction to ``Discrete Convolutions via Mersenne Transforms''
IEEE Transactions on Computers
Computer-Aided Design
Pipeline architectures for radix-2 new Mersenne number transform
IEEE Transactions on Circuits and Systems Part I: Regular Papers - Special section on 2008 custom integrated circuits conference (CICC 2008)
Computation of convolutions and discrete Fourier transforms by polynomial transforms
IBM Journal of Research and Development
Linear filtering technique for computing Mersenne and fermat number transforms
IBM Journal of Research and Development
Digital filtering using complex Mersenne transforms
IBM Journal of Research and Development
Complex convolutions via Fermat number transforms
IBM Journal of Research and Development
ISCIS'06 Proceedings of the 21st international conference on Computer and Information Sciences
Pattern analysis under number theoretic transforms
EUROCAST'11 Proceedings of the 13th international conference on Computer Aided Systems Theory - Volume Part II
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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A transform analogous to the discrete Fourier transform is defined in the ring of integers with a multiplication and addition modulo a Mersenne number. The arithmetic necessary to perform the transform requires only additions and circular shifts of the bits in a word. The inverse transform is similar. It is shown that the product of the transforms of two sequences is congruent to the transform of their circular convolution. Therefore, a method of computing circular convolutions without quantization error and with only very few multiplications is revealed.