Discrete weighted transforms and large-integer arithmetic

@article{Crandall1994DiscreteWT,
  title={Discrete weighted transforms and large-integer arithmetic},
  author={R. Crandall and B. Fagin},
  journal={Mathematics of Computation},
  year={1994},
  volume={62},
  pages={305-324}
}
It is well known that Discrete Fourier Transform (DFT) techniques may be used to multiply large integers. We introduce the concept of Discrete Weighted Transforms (DWTs) which, in certain situations, substantially improve the speed of multiplication by obviating costly zero-padding of digits. In particular, when arithmetic is to be performed modulo Fermât Numbers 22"1 + 1 , or Mersenne Numbers 29 1 , weighted transforms effectively reduce FFT run lengths. We indicate how these ideas can be… Expand
Rapid multiplication modulo the sum and difference of highly composite numbers
Integer multiplication in time O(n log n)
Some Parallel Algorithms for Integer Factorisation
Spectral arithmetic in Montgomery modular multiplication
Fast convolutions meet Montgomery
Area-Time Efficient Architecture of FFT-Based Montgomery Multiplication
...
1
2
3
4
5
...

References

SHOWING 1-10 OF 18 REFERENCES
Large Integer Multiplication on Hypercubes
  • B. Fagin
  • Computer Science
  • J. Parallel Distributed Comput.
  • 1992
The use of finite fields to compute convolutions
Real-valued fast Fourier transform algorithms
Speeding the Pollard and elliptic curve methods of factorization
A Stochastic Roundoff Error Analysis for the Fast Fourier Transform
FIR filtering by the modified Fermat number transform
...
1
2
...