FlipFields-New Building Blocks for Cryptograpic Primitives?

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$1+1 \equiv 0$---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 generalizati