On the Differential Spectrum and the APcN Property of a Class of Power Functions Over Finite Fields
In this paper, we investigate the power function F(x)=x^{d} over the finite field \mathbb {F}_{2^{4n}} , where n is a positive integer and d=2^{3n}+2^{2n}+2^{n}-1 . We prove that this power function is AP c\text{N} with respect to all c\in \mathbb {F}_{2^{4n}}\setminus \{1\} satisfying c^{...
Gespeichert in:
| Veröffentlicht in: | IEEE transactions on information theory 2023-01, Vol.69 (1), p.582-597 |
|---|---|
| Hauptverfasser: | , , , , , |
| Format: | Artikel |
| Sprache: | eng |
| Schlagworte: | |
| Online-Zugang: | Volltext bestellen |
| Tags: |
Tag hinzufügen
Keine Tags, Fügen Sie den ersten Tag hinzu!
|
| container_end_page | 597 |
|---|---|
| container_issue | 1 |
| container_start_page | 582 |
| container_title | IEEE transactions on information theory |
| container_volume | 69 |
| creator | Tu, Ziran Li, Nian Wu, Yanan Zeng, Xiangyong Tang, Xiaohu Jiang, Yupeng |
| description | In this paper, we investigate the power function F(x)=x^{d} over the finite field \mathbb {F}_{2^{4n}} , where n is a positive integer and d=2^{3n}+2^{2n}+2^{n}-1 . We prove that this power function is AP c\text{N} with respect to all c\in \mathbb {F}_{2^{4n}}\setminus \{1\} satisfying c^{2^{2n}+1}=1 , and we determine its c -differential spectrum. To the best of our knowledge, this is the second class of AP c\text{N} power functions over finite fields of even characteristic. By the same proof ideas, we completely determine the differential spectrum of this function, and give an affirmative answer to a recent conjecture proposed by Budaghyan, Calderini, Carlet, Davidova and Kaleyski. |
| doi_str_mv | 10.1109/TIT.2022.3198133 |
| format | Article |
| fullrecord | <record><control><sourceid>proquest_RIE</sourceid><recordid>TN_cdi_ieee_primary_9854915</recordid><sourceformat>XML</sourceformat><sourcesystem>PC</sourcesystem><ieee_id>9854915</ieee_id><sourcerecordid>2757181266</sourcerecordid><originalsourceid>FETCH-LOGICAL-c291t-63b43e5ac5fb197d134d6f4ece1d1accdc18ca7738d86ecd45fefe819e73cbcc3</originalsourceid><addsrcrecordid>eNo9kFFLwzAUhYMoOKfvgi8Bnzt7m6RNHsd0OhA3cD6XLLnBjq6tSabs39u64dO5h3vOvfARcgvpBCBVD-vFepKlWTZhoCQwdkZGIESRqFzwczJKU5CJ4lxekqsQtr3lArIRMcuGxk-kj5Vz6LGJla7pe4cm-v2O6sb-bacr80ZXvu3QxwNtHdV0VusQhnHV_qCn831jYtU2gS6_B1s1VcResLbhmlw4XQe8OemYfMyf1rOX5HX5vJhNXxOTKYhJzjacodBGuA2owgLjNnccDYIFbYw1II0uCiatzNFYLhw6lKCwYGZjDBuT--Pdzrdfewyx3LZ73_Qvy6wQBUjI8rxPpceU8W0IHl3Z-Wqn_aGEtBxQlj3KckBZnlD2lbtjpULE_7iSgisQ7Bc72nA1</addsrcrecordid><sourcetype>Aggregation Database</sourcetype><iscdi>true</iscdi><recordtype>article</recordtype><pqid>2757181266</pqid></control><display><type>article</type><title>On the Differential Spectrum and the APcN Property of a Class of Power Functions Over Finite Fields</title><source>IEEE Electronic Library (IEL)</source><creator>Tu, Ziran ; Li, Nian ; Wu, Yanan ; Zeng, Xiangyong ; Tang, Xiaohu ; Jiang, Yupeng</creator><creatorcontrib>Tu, Ziran ; Li, Nian ; Wu, Yanan ; Zeng, Xiangyong ; Tang, Xiaohu ; Jiang, Yupeng</creatorcontrib><description><![CDATA[In this paper, we investigate the power function <inline-formula> <tex-math notation="LaTeX">F(x)=x^{d} </tex-math></inline-formula> over the finite field <inline-formula> <tex-math notation="LaTeX">\mathbb {F}_{2^{4n}} </tex-math></inline-formula>, where <inline-formula> <tex-math notation="LaTeX">n </tex-math></inline-formula> is a positive integer and <inline-formula> <tex-math notation="LaTeX">d=2^{3n}+2^{2n}+2^{n}-1 </tex-math></inline-formula>. We prove that this power function is AP<inline-formula> <tex-math notation="LaTeX">c\text{N} </tex-math></inline-formula> with respect to all <inline-formula> <tex-math notation="LaTeX">c\in \mathbb {F}_{2^{4n}}\setminus \{1\} </tex-math></inline-formula> satisfying <inline-formula> <tex-math notation="LaTeX">c^{2^{2n}+1}=1 </tex-math></inline-formula>, and we determine its <inline-formula> <tex-math notation="LaTeX">c </tex-math></inline-formula>-differential spectrum. To the best of our knowledge, this is the second class of AP<inline-formula> <tex-math notation="LaTeX">c\text{N} </tex-math></inline-formula> power functions over finite fields of even characteristic. By the same proof ideas, we completely determine the differential spectrum of this function, and give an affirmative answer to a recent conjecture proposed by Budaghyan, Calderini, Carlet, Davidova and Kaleyski.]]></description><identifier>ISSN: 0018-9448</identifier><identifier>EISSN: 1557-9654</identifier><identifier>DOI: 10.1109/TIT.2022.3198133</identifier><identifier>CODEN: IETTAW</identifier><language>eng</language><publisher>New York: IEEE</publisher><subject>Boolean functions ; c-differential uniformity ; Ciphers ; Differential spectrum ; differential uniformity ; Fields (mathematics) ; Mathematics ; power function ; Power measurement ; Research and development ; Resistance ; Resists</subject><ispartof>IEEE transactions on information theory, 2023-01, Vol.69 (1), p.582-597</ispartof><rights>Copyright The Institute of Electrical and Electronics Engineers, Inc. (IEEE) 2023</rights><lds50>peer_reviewed</lds50><woscitedreferencessubscribed>false</woscitedreferencessubscribed><citedby>FETCH-LOGICAL-c291t-63b43e5ac5fb197d134d6f4ece1d1accdc18ca7738d86ecd45fefe819e73cbcc3</citedby><cites>FETCH-LOGICAL-c291t-63b43e5ac5fb197d134d6f4ece1d1accdc18ca7738d86ecd45fefe819e73cbcc3</cites><orcidid>0000-0002-8351-8766 ; 0000-0002-7938-7812 ; 0000-0003-4913-7844 ; 0000-0002-5823-557X ; 0000-0003-1347-2560</orcidid></display><links><openurl>$$Topenurl_article</openurl><openurlfulltext>$$Topenurlfull_article</openurlfulltext><thumbnail>$$Tsyndetics_thumb_exl</thumbnail><linktohtml>$$Uhttps://ieeexplore.ieee.org/document/9854915$$EHTML$$P50$$Gieee$$H</linktohtml><link.rule.ids>314,778,782,794,27907,27908,54741</link.rule.ids><linktorsrc>$$Uhttps://ieeexplore.ieee.org/document/9854915$$EView_record_in_IEEE$$FView_record_in_$$GIEEE</linktorsrc></links><search><creatorcontrib>Tu, Ziran</creatorcontrib><creatorcontrib>Li, Nian</creatorcontrib><creatorcontrib>Wu, Yanan</creatorcontrib><creatorcontrib>Zeng, Xiangyong</creatorcontrib><creatorcontrib>Tang, Xiaohu</creatorcontrib><creatorcontrib>Jiang, Yupeng</creatorcontrib><title>On the Differential Spectrum and the APcN Property of a Class of Power Functions Over Finite Fields</title><title>IEEE transactions on information theory</title><addtitle>TIT</addtitle><description><![CDATA[In this paper, we investigate the power function <inline-formula> <tex-math notation="LaTeX">F(x)=x^{d} </tex-math></inline-formula> over the finite field <inline-formula> <tex-math notation="LaTeX">\mathbb {F}_{2^{4n}} </tex-math></inline-formula>, where <inline-formula> <tex-math notation="LaTeX">n </tex-math></inline-formula> is a positive integer and <inline-formula> <tex-math notation="LaTeX">d=2^{3n}+2^{2n}+2^{n}-1 </tex-math></inline-formula>. We prove that this power function is AP<inline-formula> <tex-math notation="LaTeX">c\text{N} </tex-math></inline-formula> with respect to all <inline-formula> <tex-math notation="LaTeX">c\in \mathbb {F}_{2^{4n}}\setminus \{1\} </tex-math></inline-formula> satisfying <inline-formula> <tex-math notation="LaTeX">c^{2^{2n}+1}=1 </tex-math></inline-formula>, and we determine its <inline-formula> <tex-math notation="LaTeX">c </tex-math></inline-formula>-differential spectrum. To the best of our knowledge, this is the second class of AP<inline-formula> <tex-math notation="LaTeX">c\text{N} </tex-math></inline-formula> power functions over finite fields of even characteristic. By the same proof ideas, we completely determine the differential spectrum of this function, and give an affirmative answer to a recent conjecture proposed by Budaghyan, Calderini, Carlet, Davidova and Kaleyski.]]></description><subject>Boolean functions</subject><subject>c-differential uniformity</subject><subject>Ciphers</subject><subject>Differential spectrum</subject><subject>differential uniformity</subject><subject>Fields (mathematics)</subject><subject>Mathematics</subject><subject>power function</subject><subject>Power measurement</subject><subject>Research and development</subject><subject>Resistance</subject><subject>Resists</subject><issn>0018-9448</issn><issn>1557-9654</issn><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>2023</creationdate><recordtype>article</recordtype><sourceid>RIE</sourceid><recordid>eNo9kFFLwzAUhYMoOKfvgi8Bnzt7m6RNHsd0OhA3cD6XLLnBjq6tSabs39u64dO5h3vOvfARcgvpBCBVD-vFepKlWTZhoCQwdkZGIESRqFzwczJKU5CJ4lxekqsQtr3lArIRMcuGxk-kj5Vz6LGJla7pe4cm-v2O6sb-bacr80ZXvu3QxwNtHdV0VusQhnHV_qCn831jYtU2gS6_B1s1VcResLbhmlw4XQe8OemYfMyf1rOX5HX5vJhNXxOTKYhJzjacodBGuA2owgLjNnccDYIFbYw1II0uCiatzNFYLhw6lKCwYGZjDBuT--Pdzrdfewyx3LZ73_Qvy6wQBUjI8rxPpceU8W0IHl3Z-Wqn_aGEtBxQlj3KckBZnlD2lbtjpULE_7iSgisQ7Bc72nA1</recordid><startdate>202301</startdate><enddate>202301</enddate><creator>Tu, Ziran</creator><creator>Li, Nian</creator><creator>Wu, Yanan</creator><creator>Zeng, Xiangyong</creator><creator>Tang, Xiaohu</creator><creator>Jiang, Yupeng</creator><general>IEEE</general><general>The Institute of Electrical and Electronics Engineers, Inc. (IEEE)</general><scope>97E</scope><scope>RIA</scope><scope>RIE</scope><scope>AAYXX</scope><scope>CITATION</scope><scope>7SC</scope><scope>7SP</scope><scope>8FD</scope><scope>JQ2</scope><scope>L7M</scope><scope>L~C</scope><scope>L~D</scope><orcidid>https://orcid.org/0000-0002-8351-8766</orcidid><orcidid>https://orcid.org/0000-0002-7938-7812</orcidid><orcidid>https://orcid.org/0000-0003-4913-7844</orcidid><orcidid>https://orcid.org/0000-0002-5823-557X</orcidid><orcidid>https://orcid.org/0000-0003-1347-2560</orcidid></search><sort><creationdate>202301</creationdate><title>On the Differential Spectrum and the APcN Property of a Class of Power Functions Over Finite Fields</title><author>Tu, Ziran ; Li, Nian ; Wu, Yanan ; Zeng, Xiangyong ; Tang, Xiaohu ; Jiang, Yupeng</author></sort><facets><frbrtype>5</frbrtype><frbrgroupid>cdi_FETCH-LOGICAL-c291t-63b43e5ac5fb197d134d6f4ece1d1accdc18ca7738d86ecd45fefe819e73cbcc3</frbrgroupid><rsrctype>articles</rsrctype><prefilter>articles</prefilter><language>eng</language><creationdate>2023</creationdate><topic>Boolean functions</topic><topic>c-differential uniformity</topic><topic>Ciphers</topic><topic>Differential spectrum</topic><topic>differential uniformity</topic><topic>Fields (mathematics)</topic><topic>Mathematics</topic><topic>power function</topic><topic>Power measurement</topic><topic>Research and development</topic><topic>Resistance</topic><topic>Resists</topic><toplevel>peer_reviewed</toplevel><toplevel>online_resources</toplevel><creatorcontrib>Tu, Ziran</creatorcontrib><creatorcontrib>Li, Nian</creatorcontrib><creatorcontrib>Wu, Yanan</creatorcontrib><creatorcontrib>Zeng, Xiangyong</creatorcontrib><creatorcontrib>Tang, Xiaohu</creatorcontrib><creatorcontrib>Jiang, Yupeng</creatorcontrib><collection>IEEE All-Society Periodicals Package (ASPP) 2005-present</collection><collection>IEEE All-Society Periodicals Package (ASPP) 1998-Present</collection><collection>IEEE Electronic Library (IEL)</collection><collection>CrossRef</collection><collection>Computer and Information Systems Abstracts</collection><collection>Electronics & Communications Abstracts</collection><collection>Technology Research Database</collection><collection>ProQuest Computer Science Collection</collection><collection>Advanced Technologies Database with Aerospace</collection><collection>Computer and Information Systems Abstracts Academic</collection><collection>Computer and Information Systems Abstracts Professional</collection><jtitle>IEEE transactions on information theory</jtitle></facets><delivery><delcategory>Remote Search Resource</delcategory><fulltext>fulltext_linktorsrc</fulltext></delivery><addata><au>Tu, Ziran</au><au>Li, Nian</au><au>Wu, Yanan</au><au>Zeng, Xiangyong</au><au>Tang, Xiaohu</au><au>Jiang, Yupeng</au><format>journal</format><genre>article</genre><ristype>JOUR</ristype><atitle>On the Differential Spectrum and the APcN Property of a Class of Power Functions Over Finite Fields</atitle><jtitle>IEEE transactions on information theory</jtitle><stitle>TIT</stitle><date>2023-01</date><risdate>2023</risdate><volume>69</volume><issue>1</issue><spage>582</spage><epage>597</epage><pages>582-597</pages><issn>0018-9448</issn><eissn>1557-9654</eissn><coden>IETTAW</coden><abstract><![CDATA[In this paper, we investigate the power function <inline-formula> <tex-math notation="LaTeX">F(x)=x^{d} </tex-math></inline-formula> over the finite field <inline-formula> <tex-math notation="LaTeX">\mathbb {F}_{2^{4n}} </tex-math></inline-formula>, where <inline-formula> <tex-math notation="LaTeX">n </tex-math></inline-formula> is a positive integer and <inline-formula> <tex-math notation="LaTeX">d=2^{3n}+2^{2n}+2^{n}-1 </tex-math></inline-formula>. We prove that this power function is AP<inline-formula> <tex-math notation="LaTeX">c\text{N} </tex-math></inline-formula> with respect to all <inline-formula> <tex-math notation="LaTeX">c\in \mathbb {F}_{2^{4n}}\setminus \{1\} </tex-math></inline-formula> satisfying <inline-formula> <tex-math notation="LaTeX">c^{2^{2n}+1}=1 </tex-math></inline-formula>, and we determine its <inline-formula> <tex-math notation="LaTeX">c </tex-math></inline-formula>-differential spectrum. To the best of our knowledge, this is the second class of AP<inline-formula> <tex-math notation="LaTeX">c\text{N} </tex-math></inline-formula> power functions over finite fields of even characteristic. By the same proof ideas, we completely determine the differential spectrum of this function, and give an affirmative answer to a recent conjecture proposed by Budaghyan, Calderini, Carlet, Davidova and Kaleyski.]]></abstract><cop>New York</cop><pub>IEEE</pub><doi>10.1109/TIT.2022.3198133</doi><tpages>16</tpages><orcidid>https://orcid.org/0000-0002-8351-8766</orcidid><orcidid>https://orcid.org/0000-0002-7938-7812</orcidid><orcidid>https://orcid.org/0000-0003-4913-7844</orcidid><orcidid>https://orcid.org/0000-0002-5823-557X</orcidid><orcidid>https://orcid.org/0000-0003-1347-2560</orcidid></addata></record> |
| fulltext | fulltext_linktorsrc |
| identifier | ISSN: 0018-9448 |
| ispartof | IEEE transactions on information theory, 2023-01, Vol.69 (1), p.582-597 |
| issn | 0018-9448 1557-9654 |
| language | eng |
| recordid | cdi_ieee_primary_9854915 |
| source | IEEE Electronic Library (IEL) |
| subjects | Boolean functions c-differential uniformity Ciphers Differential spectrum differential uniformity Fields (mathematics) Mathematics power function Power measurement Research and development Resistance Resists |
| title | On the Differential Spectrum and the APcN Property of a Class of Power Functions Over Finite Fields |
| url | https://sfx.bib-bvb.de/sfx_tum?ctx_ver=Z39.88-2004&ctx_enc=info:ofi/enc:UTF-8&ctx_tim=2025-01-17T07%3A30%3A28IST&url_ver=Z39.88-2004&url_ctx_fmt=infofi/fmt:kev:mtx:ctx&rfr_id=info:sid/primo.exlibrisgroup.com:primo3-Article-proquest_RIE&rft_val_fmt=info:ofi/fmt:kev:mtx:journal&rft.genre=article&rft.atitle=On%20the%20Differential%20Spectrum%20and%20the%20APcN%20Property%20of%20a%20Class%20of%20Power%20Functions%20Over%20Finite%20Fields&rft.jtitle=IEEE%20transactions%20on%20information%20theory&rft.au=Tu,%20Ziran&rft.date=2023-01&rft.volume=69&rft.issue=1&rft.spage=582&rft.epage=597&rft.pages=582-597&rft.issn=0018-9448&rft.eissn=1557-9654&rft.coden=IETTAW&rft_id=info:doi/10.1109/TIT.2022.3198133&rft_dat=%3Cproquest_RIE%3E2757181266%3C/proquest_RIE%3E%3Curl%3E%3C/url%3E&disable_directlink=true&sfx.directlink=off&sfx.report_link=0&rft_id=info:oai/&rft_pqid=2757181266&rft_id=info:pmid/&rft_ieee_id=9854915&rfr_iscdi=true |