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### Abstract

We give a verified implementation of the Schönhage-Strassen Multiplication on Integers based on the original paper by Schönhage and Strassen and verify its asymptotic complexity of $\mathcal{O}\left(n \log n \log \log n\right)$ bit operations.
Integers are represented as LSBF (least significant bit first) boolean lists. The running time is verified using the Time Monad defined in Root-Balanced Trees by Nipkow. For verifying correctness, we adapt the formalization of Number Theoretic Transforms (NTTs) by Ammer and Kreuzer to the context of rings that need not be fields.

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### Related publications

- https://mediatum.ub.tum.de/1717658