$1+1 \equiv 0$---while looking strange at first glance, this is certainly true in GF(2). In this paper we propose the two field-like structures \FlipInts\ and \FlipPolys\ as potential alternative building block for crypographic schemes---in particular in the post-quantum setting. Both structures have $2^d$ elements for some positive integer $d$ and are derived from the natural numbers $N$ in the first case and the univariate polynomial ring GF(2)$[t]$ in the second case. We call the generalization of these two structures FlipFields. In addition, we see examples how they can be used for post-quantum cryptography, in particular Unbalanced Oil and Vinegar, Learning with Errors and Saber. There is also a discussion of cryptographic primitives that are most likely not suitable for FlipFields or at least not easy to tweak. As the structures are very new, this paper also includes a list of OpenProblems.
BibTeX
@misc{cryptoeprint:2026/1088,
author = {Christopher Wolf},
title = {{FlipFields}-New Building Blocks for Cryptograpic Primitives?},
howpublished = {Cryptology {ePrint} Archive, Paper 2026/1088},
year = {2026},
url = {https://eprint.iacr.org/2026/1088}
}
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