Polynomial functions on the units of Z2n

Markovski Smile

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2023-02-27 17:14

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MARKOVSKI, 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

Polynomial functions on the units of Z2n

Pag. 59-82

Markovski Smile

Disponibil în IBN: 16 decembrie 2013

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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 eciently 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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