Research on affine equivalence enumeration of the three families vectorial function
In recent years,Qu-Tan-Tan-Li function,Zha-Hu-Sun function and Tang-Carlet-Tang function have been proposed with differential uniformity 4 and many good cryptographic properties.the counting problem of affine equivalent to the three families cryptographic functions was investigated.By using some pro...
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| Format: | Article |
| Language: | zho |
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Editorial Department of Journal on Communications
2017-11-01
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| Series: | Tongxin xuebao |
| Subjects: | |
| Online Access: | http://www.joconline.com.cn/zh/article/doi/10.11959/j.issn.1000-436x.2017206/ |
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| author | Feng YUAN Ji-jun JIANG Yang YANG Sheng-wei XU |
| author_facet | Feng YUAN Ji-jun JIANG Yang YANG Sheng-wei XU |
| author_sort | Feng YUAN |
| collection | DOAJ |
| description | In recent years,Qu-Tan-Tan-Li function,Zha-Hu-Sun function and Tang-Carlet-Tang function have been proposed with differential uniformity 4 and many good cryptographic properties.the counting problem of affine equivalent to the three families cryptographic functions was investigated.By using some properties of finite fields,the upper and lower bound of the number of affine equivalent to the Zha-Hu-Sun function,and the upper bound of the number of affine equivalent to the Qu-Tan-Tan-Li function and Tang-Carlet-Tang function were computed,respectively.Moreover,a conjecture was given about the exact number of affine equivalent to the Zha-Hu-Sun function.Results show that there are at least<inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML"> <msup> <mn>2</mn> <mrow> <mn>53</mn></mrow> </msup> <msup> <mrow><mo>[</mo> <mrow> <mstyle displaystyle="true"> <munderover> <mo>∏</mo> <mrow> <mi>i</mi><mo>=</mo><mn>1</mn></mrow> <mn>8</mn> </munderover> <mrow> <mo stretchy="false">(</mo><msup> <mn>2</mn> <mi>i</mi> </msup> <mo>−</mo><mn>1</mn><mo stretchy="false">)</mo></mrow> </mstyle></mrow> <mo>]</mo></mrow> <mn>2</mn> </msup> </math></inline-formula>cryptographic functions of affine equivalent to the Zha-Hu-Sun function over finite field GF(2<sup>8</sup>),which can be chosen as S-boxes of block ciphers. |
| format | Article |
| id | doaj-art-405cf58cb47540c7abba9434f0fb0542 |
| institution | Kabale University |
| issn | 1000-436X |
| language | zho |
| publishDate | 2017-11-01 |
| publisher | Editorial Department of Journal on Communications |
| record_format | Article |
| series | Tongxin xuebao |
| spelling | doaj-art-405cf58cb47540c7abba9434f0fb05422025-01-14T07:13:20ZzhoEditorial Department of Journal on CommunicationsTongxin xuebao1000-436X2017-11-0138849259713319Research on affine equivalence enumeration of the three families vectorial functionFeng YUANJi-jun JIANGYang YANGSheng-wei XUIn recent years,Qu-Tan-Tan-Li function,Zha-Hu-Sun function and Tang-Carlet-Tang function have been proposed with differential uniformity 4 and many good cryptographic properties.the counting problem of affine equivalent to the three families cryptographic functions was investigated.By using some properties of finite fields,the upper and lower bound of the number of affine equivalent to the Zha-Hu-Sun function,and the upper bound of the number of affine equivalent to the Qu-Tan-Tan-Li function and Tang-Carlet-Tang function were computed,respectively.Moreover,a conjecture was given about the exact number of affine equivalent to the Zha-Hu-Sun function.Results show that there are at least<inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML"> <msup> <mn>2</mn> <mrow> <mn>53</mn></mrow> </msup> <msup> <mrow><mo>[</mo> <mrow> <mstyle displaystyle="true"> <munderover> <mo>∏</mo> <mrow> <mi>i</mi><mo>=</mo><mn>1</mn></mrow> <mn>8</mn> </munderover> <mrow> <mo stretchy="false">(</mo><msup> <mn>2</mn> <mi>i</mi> </msup> <mo>−</mo><mn>1</mn><mo stretchy="false">)</mo></mrow> </mstyle></mrow> <mo>]</mo></mrow> <mn>2</mn> </msup> </math></inline-formula>cryptographic functions of affine equivalent to the Zha-Hu-Sun function over finite field GF(2<sup>8</sup>),which can be chosen as S-boxes of block ciphers.http://www.joconline.com.cn/zh/article/doi/10.11959/j.issn.1000-436x.2017206/cryptographycryptographic functionsS-boxaffine equivalenceenumeration |
| spellingShingle | Feng YUAN Ji-jun JIANG Yang YANG Sheng-wei XU Research on affine equivalence enumeration of the three families vectorial function Tongxin xuebao cryptography cryptographic functions S-box affine equivalence enumeration |
| title | Research on affine equivalence enumeration of the three families vectorial function |
| title_full | Research on affine equivalence enumeration of the three families vectorial function |
| title_fullStr | Research on affine equivalence enumeration of the three families vectorial function |
| title_full_unstemmed | Research on affine equivalence enumeration of the three families vectorial function |
| title_short | Research on affine equivalence enumeration of the three families vectorial function |
| title_sort | research on affine equivalence enumeration of the three families vectorial function |
| topic | cryptography cryptographic functions S-box affine equivalence enumeration |
| url | http://www.joconline.com.cn/zh/article/doi/10.11959/j.issn.1000-436x.2017206/ |
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