Pierre Bienvenu (Johann Radon Institute for Computational and Applied Mathematics, Austria)
will speak on
The additive index of self-mappings of finite fields
Time: 2:00PM
Date: Wed 4th November 2026
Location: N0.20 - Science North
[map]
Abstract: What makes a mapping F_q->F_q too simple, or complex enough?
Several complexity measures such as degree, sparsity, Carlitz rank and multiplicative index for cryptographic functions F_q->F_q have been studied in the literature. In 2022, Reis and Wang introduced another complexity measure, the additive index, of a self-mapping of a finite field. It measures to which extent a map piece-wise F_p-affine is - an affine map has index 1, a random map index q. In this talk, we present this notion and compare it to other complexity measures. Further, we discuss the additive index of cryptographically relevant functions such as Diffie-Hellman and the discrete logarithm. Joint work with Arne Winterhof (Austrian Academy of Sciences).
(This talk is part of the Discrete Mathematics series.)
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