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**2020/1493**

**Title:**

Verified fast formulas for control bits for permutation networks

**Authors:**
Daniel J. Bernstein

**Abstract:**

This paper presents detailed and computer-verified proofs of formulas that, given a permutation pi of 2^m indices with m>=1, produce control bits for a standard permutation network that uses 2^m(m-1/2) swaps to apply pi to a list. The formulas match the control bits computed by a serial algorithm of Stone (1968) and a parallel algorithm of Nassimiâ€“Sahni (1982). The proofs are a step towards computer-verified correctness proofs for efficient implementations of these algorithms.

**ePrint:**
https://eprint.iacr.org/2020/1493

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