Fast Fourier Orthogonalization

@article{Ducas2015FastFO,
  title={Fast Fourier Orthogonalization},
  author={L{\'e}o Ducas and Thomas Prest},
  journal={IACR Cryptology ePrint Archive},
  year={2015},
  volume={2015},
  pages={1014}
}
The classical fast Fourier transform (FFT) allows to compute in quasi-linear time the product of two polynomials, in the circular convolution ring R[x]/(xd -1) --- a task that naively requires quadratic time. Equivalently, it allows to accelerate matrix-vector products when the matrix is circulant. In this work, we discover that the ideas of the FFT can be applied to speed up the orthogonalization process of matrices with circulant blocks of size d x d. We show that, when d is composite, it is… CONTINUE READING

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