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FFT-based division to improve DEEP composition polynomial computation #281

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Al-Kindi-0 opened this issue May 9, 2024 · 0 comments
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Al-Kindi-0 commented May 9, 2024

The computation of the DEEP composition polynomial became more involved with the changes brought in #274 . The complexity introduced by the multi-point quotient term due to the Lagrange kernel means that one has to divide by a polynomial of degree $\log(n) + 1$ where $n$ is the trace length. For moderately sized traces the current implementation using iterated synthetic division should be good enough but for large traces it might payoff to do the bulk of the computation of that aforementioned term using FFT, especially when multi-core is enabled.

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