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arXiv · 2507.22142

A note on multiplicative-inverse chaining in finite fields

Divyarthi Mohan·R. Ravindraraj
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Abstract

We consider chaining multiplicative-inverse operations in finite fields under alternating polynomial bases. When using two distinct polynomial bases to alternate the inverse operation we obtain a partition of $\mathbb F_{p^n}\setminus \mathbb F_p$ into disjoint cycles of even length. This allows a natural interpretation of the cycles as permutation cycles. Finally, we explore chaining under more than two polynomial bases.

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Divyarthi Mohan, R. Ravindraraj. 2025-07-29. A note on multiplicative-inverse chaining in finite fields. https://arxiv.org/abs/2507.22142

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