The Frobenius FFT
نویسندگان
چکیده
Let Fq be the finite field with q elements and let ! be a primitive n-th root of unity in an extension eld Fqd of Fq. Given a polynomial P 2 Fq[x] of degree less than n, we will show that its discrete Fourier transform (P (1); P (!); :::; P (!n¡1)) 2Fqd n can be computed essentially d times faster than the discrete Fourier transform of a polynomial Q 2 Fqd[x] of degree less than n, in many cases. This result is achieved by exploiting the symmetries provided by the Frobenius automorphism of Fqd over Fq.
منابع مشابه
Frobenius Additive Fast Fourier Transform
In ISSAC 2017, van der Hoeven and Larrieu showed that evaluating a polynomial P ∈ Fq [x] of degree < n at all n-th roots of unity in Fqd can essentially be computed d-time faster than evaluating Q ∈ Fqd [x] at all these roots, assuming Fqd contains a primitive n-th root of unity [vdHL17a]. Termed the Frobenius FFT, this discovery has a profound impact on polynomial multiplication, especially fo...
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