Decomposition of permutations in a finite field
We describe a method to decompose any power permutation, as a sequence of power permutations of lower algebraic degree. As a result we obtain decompositions of the inversion in GF(2 n ) for small n from 3 up to 16, as well as for the APN functions, when n = 5. More precisely, we find decompositions...
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| Veröffentlicht in: | Cryptography and communications 2019-05, Vol.11 (3), p.379-384 |
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| container_title | Cryptography and communications |
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| creator | Nikova, Svetla Nikov, Ventzislav Rijmen, Vincent |
| description | We describe a method to decompose any power permutation, as a sequence of power permutations of lower algebraic degree. As a result we obtain decompositions of the inversion in GF(2
n
) for small
n
from 3 up to 16, as well as for the APN functions, when
n
= 5. More precisely, we find decompositions into
quadratic
power permutations for any
n
not multiple of 4 and decompositions into
cubic
power permutations for
n
multiple of 4. Finally, we use the Theorem of Carlitz to prove that for 3 ≤
n
≤ 16 any
n
-bit permutation can be decomposed in quadratic and cubic permutations. |
| doi_str_mv | 10.1007/s12095-018-0317-2 |
| format | Article |
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n
) for small
n
from 3 up to 16, as well as for the APN functions, when
n
= 5. More precisely, we find decompositions into
quadratic
power permutations for any
n
not multiple of 4 and decompositions into
cubic
power permutations for
n
multiple of 4. Finally, we use the Theorem of Carlitz to prove that for 3 ≤
n
≤ 16 any
n
-bit permutation can be decomposed in quadratic and cubic permutations.</description><identifier>ISSN: 1936-2447</identifier><identifier>EISSN: 1936-2455</identifier><identifier>DOI: 10.1007/s12095-018-0317-2</identifier><language>eng</language><publisher>New York: Springer US</publisher><subject>Circuits ; Coding and Information Theory ; Communications Engineering ; Computer Science ; Data Structures and Information Theory ; Decomposition ; Fields (mathematics) ; Information and Communication ; Mathematics of Computing ; Networks ; Permutations ; Special Issue: Mathematical Methods for Cryptography</subject><ispartof>Cryptography and communications, 2019-05, Vol.11 (3), p.379-384</ispartof><rights>Springer Science+Business Media, LLC, part of Springer Nature 2018</rights><rights>Copyright Springer Nature B.V. 2019</rights><lds50>peer_reviewed</lds50><oa>free_for_read</oa><woscitedreferencessubscribed>false</woscitedreferencessubscribed><citedby>FETCH-LOGICAL-c359t-8872147a70fae131e7d943340688affeea8dc2a83d0968c4d0d0185b43712aba3</citedby><cites>FETCH-LOGICAL-c359t-8872147a70fae131e7d943340688affeea8dc2a83d0968c4d0d0185b43712aba3</cites></display><links><openurl>$$Topenurl_article</openurl><openurlfulltext>$$Topenurlfull_article</openurlfulltext><thumbnail>$$Tsyndetics_thumb_exl</thumbnail><linktopdf>$$Uhttps://link.springer.com/content/pdf/10.1007/s12095-018-0317-2$$EPDF$$P50$$Gspringer$$H</linktopdf><linktohtml>$$Uhttps://link.springer.com/10.1007/s12095-018-0317-2$$EHTML$$P50$$Gspringer$$H</linktohtml><link.rule.ids>314,776,780,27903,27904,41467,42536,51298</link.rule.ids></links><search><creatorcontrib>Nikova, Svetla</creatorcontrib><creatorcontrib>Nikov, Ventzislav</creatorcontrib><creatorcontrib>Rijmen, Vincent</creatorcontrib><title>Decomposition of permutations in a finite field</title><title>Cryptography and communications</title><addtitle>Cryptogr. Commun</addtitle><description>We describe a method to decompose any power permutation, as a sequence of power permutations of lower algebraic degree. As a result we obtain decompositions of the inversion in GF(2
n
) for small
n
from 3 up to 16, as well as for the APN functions, when
n
= 5. More precisely, we find decompositions into
quadratic
power permutations for any
n
not multiple of 4 and decompositions into
cubic
power permutations for
n
multiple of 4. Finally, we use the Theorem of Carlitz to prove that for 3 ≤
n
≤ 16 any
n
-bit permutation can be decomposed in quadratic and cubic permutations.</description><subject>Circuits</subject><subject>Coding and Information Theory</subject><subject>Communications Engineering</subject><subject>Computer Science</subject><subject>Data Structures and Information Theory</subject><subject>Decomposition</subject><subject>Fields (mathematics)</subject><subject>Information and Communication</subject><subject>Mathematics of Computing</subject><subject>Networks</subject><subject>Permutations</subject><subject>Special Issue: Mathematical Methods for Cryptography</subject><issn>1936-2447</issn><issn>1936-2455</issn><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>2019</creationdate><recordtype>article</recordtype><recordid>eNp1kEtPwzAQhC0EEqXwA7hF4my660dsH1F5SpW4wNlyExulauJgpwf-Pa6C4MRpdqVvZldDyDXCLQKoVUYGRlJATYGjouyELNDwmjIh5envLNQ5uch5B1BLJviCrO59E_sx5m7q4lDFUI0-9YfJHddcdUPlqtAN3eSL-H17Sc6C22d_9aNL8v748LZ-ppvXp5f13YY2XJqJaq0YCuUUBOeRo1etEZwLqLV2IXjvdNswp3kLptaNaKEtr8ut4AqZ2zq-JDdz7pji58Hnye7iIQ3lpGUMTS21kaJQOFNNijknH-yYut6lL4tgj73YuRdbwu2xF8uKh82eXNjhw6e_5P9N301MY-E</recordid><startdate>20190515</startdate><enddate>20190515</enddate><creator>Nikova, Svetla</creator><creator>Nikov, Ventzislav</creator><creator>Rijmen, Vincent</creator><general>Springer US</general><general>Springer Nature B.V</general><scope>AAYXX</scope><scope>CITATION</scope></search><sort><creationdate>20190515</creationdate><title>Decomposition of permutations in a finite field</title><author>Nikova, Svetla ; Nikov, Ventzislav ; Rijmen, Vincent</author></sort><facets><frbrtype>5</frbrtype><frbrgroupid>cdi_FETCH-LOGICAL-c359t-8872147a70fae131e7d943340688affeea8dc2a83d0968c4d0d0185b43712aba3</frbrgroupid><rsrctype>articles</rsrctype><prefilter>articles</prefilter><language>eng</language><creationdate>2019</creationdate><topic>Circuits</topic><topic>Coding and Information Theory</topic><topic>Communications Engineering</topic><topic>Computer Science</topic><topic>Data Structures and Information Theory</topic><topic>Decomposition</topic><topic>Fields (mathematics)</topic><topic>Information and Communication</topic><topic>Mathematics of Computing</topic><topic>Networks</topic><topic>Permutations</topic><topic>Special Issue: Mathematical Methods for Cryptography</topic><toplevel>peer_reviewed</toplevel><toplevel>online_resources</toplevel><creatorcontrib>Nikova, Svetla</creatorcontrib><creatorcontrib>Nikov, Ventzislav</creatorcontrib><creatorcontrib>Rijmen, Vincent</creatorcontrib><collection>CrossRef</collection><jtitle>Cryptography and communications</jtitle></facets><delivery><delcategory>Remote Search Resource</delcategory><fulltext>fulltext</fulltext></delivery><addata><au>Nikova, Svetla</au><au>Nikov, Ventzislav</au><au>Rijmen, Vincent</au><format>journal</format><genre>article</genre><ristype>JOUR</ristype><atitle>Decomposition of permutations in a finite field</atitle><jtitle>Cryptography and communications</jtitle><stitle>Cryptogr. Commun</stitle><date>2019-05-15</date><risdate>2019</risdate><volume>11</volume><issue>3</issue><spage>379</spage><epage>384</epage><pages>379-384</pages><issn>1936-2447</issn><eissn>1936-2455</eissn><abstract>We describe a method to decompose any power permutation, as a sequence of power permutations of lower algebraic degree. As a result we obtain decompositions of the inversion in GF(2
n
) for small
n
from 3 up to 16, as well as for the APN functions, when
n
= 5. More precisely, we find decompositions into
quadratic
power permutations for any
n
not multiple of 4 and decompositions into
cubic
power permutations for
n
multiple of 4. Finally, we use the Theorem of Carlitz to prove that for 3 ≤
n
≤ 16 any
n
-bit permutation can be decomposed in quadratic and cubic permutations.</abstract><cop>New York</cop><pub>Springer US</pub><doi>10.1007/s12095-018-0317-2</doi><tpages>6</tpages><oa>free_for_read</oa></addata></record> |
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| ispartof | Cryptography and communications, 2019-05, Vol.11 (3), p.379-384 |
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| language | eng |
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| subjects | Circuits Coding and Information Theory Communications Engineering Computer Science Data Structures and Information Theory Decomposition Fields (mathematics) Information and Communication Mathematics of Computing Networks Permutations Special Issue: Mathematical Methods for Cryptography |
| title | Decomposition of permutations in a finite field |
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