Polynomial functions on the units of Z_{2^n}

Smile Markovski; Danilo Gligoroski; Zoran Sunic

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arXiv · 1008.1012

Polynomial functions on the units of Z_{2^n}

Smile Markovski·Danilo Gligoroski·Zoran Sunic

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Abstract

Polynomial functions on the group of units Q_n of the ring Z_{2^n} are considered. A finite set of reduced polynomials RP_n in Z[x] that induces the polynomial functions on Q_n is determined. Each polynomial function on Q_n is induced by a unique reduced polynomial - the reduction being made using a suitable ideal in Z[x]. The set of reduced polynomials forms a multiplicative 2-group. The obtained results are used to efficiently construct families of exponential cardinality of, so called, huge k-ary quasigroups, which are useful in the design of various types of cryptographic primitives. Along the way we provide a new (and simpler) proof of a result of Rivest characterizing the permutational polynomials on Z_{2^n}.

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BibTeX RIS

Smile Markovski, Danilo Gligoroski, Zoran Sunic. 2010-08-05. Polynomial functions on the units of Z_{2^n}. https://arxiv.org/abs/1008.1012

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