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| Ultima descărcare din IBN: 2023-02-27 17:14 |
 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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Dublin Core Export
<?xml version='1.0' encoding='utf-8'?> <oai_dc:dc xmlns:dc='http://purl.org/dc/elements/1.1/' xmlns:oai_dc='http://www.openarchives.org/OAI/2.0/oai_dc/' xmlns:xsi='http://www.w3.org/2001/XMLSchema-instance' xsi:schemaLocation='http://www.openarchives.org/OAI/2.0/oai_dc/ http://www.openarchives.org/OAI/2.0/oai_dc.xsd'> <dc:creator>Markovski, S.</dc:creator> <dc:date>2010-01-01</dc:date> <dc:description xml:lang='en'>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.</dc:description> <dc:source>Quasigroups and Related Systems 23 (1) 59-82</dc:source> <dc:title>Polynomial functions on the units of Z2n</dc:title> <dc:type>info:eu-repo/semantics/article</dc:type> </oai_dc:dc>
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