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 SM ISO690:2012MARKOVSKI, Smile. Polynomial functions on the units of Z2n. In: Quasigroups and Related Systems, 2010, vol. 18, nr. 1(23), pp. 59-82. ISSN 1561-2848. |
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| Quasigroups and Related Systems | ||||||
| Volumul 18, Numărul 1(23) / 2010 / ISSN 1561-2848 | ||||||
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Polynomial functions on the group of units Qn of the ring Z2n are considered. A nite set of reduced polynomials RPn in Z[x] that induces the polynomial functions on Qn is determined. Each polynomial function on Qn 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 e ciently 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 Z2n. |
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