Permutations from APN power functions over <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML"> <msub> <mi>F</mi> <mrow> <msup> <mn>2</mn> <mrow> <mn>2</mn><mi>n</mi></mrow> </msup> </mrow> </msub> </math></inline-formula>
APN functions have the lowest differential uniform over finite fields with characteristic 2 and the APN power functions are the most classical ones.APN power functions are all 3-1 functions over <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML"> <msub> &l...
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| Format: | Article |
| Language: | English |
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POSTS&TELECOM PRESS Co., LTD
2017-10-01
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| Series: | 网络与信息安全学报 |
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| Online Access: | http://www.cjnis.com.cn/thesisDetails#10.11959/j.issn.2096-109x.2017.00203 |
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| _version_ | 1841530198271459328 |
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| author | Shi-zhu TIAN |
| author_facet | Shi-zhu TIAN |
| author_sort | Shi-zhu TIAN |
| collection | DOAJ |
| description | APN functions have the lowest differential uniform over finite fields with characteristic 2 and the APN power functions are the most classical ones.APN power functions are all 3-1 functions over <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML"> <msub> <mi>F</mi> <mrow> <msup> <mn>2</mn> <mrow> <mn>2</mn><mi>n</mi></mrow> </msup> </mrow> </msub> </math></inline-formula>.By generalizing the idea of changing 2-1 functions to 1-1 functions over finite fields with odd characteristics,methods to change 3-1 functions over finite fields with even characteristics into permutations were obtained and permutations from APN power functions over <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML"> <msub> <mi>F</mi> <mrow> <msup> <mn>2</mn> <mrow> <mn>2</mn><mi>n</mi></mrow> </msup> </mrow> </msub> </math></inline-formula> were constructed.According to the construction,the differential properties of permutations obtained by this method were discussed. |
| format | Article |
| id | doaj-art-32d2b1dc9ee34125be185871568bf269 |
| institution | Kabale University |
| issn | 2096-109X |
| language | English |
| publishDate | 2017-10-01 |
| publisher | POSTS&TELECOM PRESS Co., LTD |
| record_format | Article |
| series | 网络与信息安全学报 |
| spelling | doaj-art-32d2b1dc9ee34125be185871568bf2692025-01-15T03:06:09ZengPOSTS&TELECOM PRESS Co., LTD网络与信息安全学报2096-109X2017-10-013727659551719Permutations from APN power functions over <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML"> <msub> <mi>F</mi> <mrow> <msup> <mn>2</mn> <mrow> <mn>2</mn><mi>n</mi></mrow> </msup> </mrow> </msub> </math></inline-formula>Shi-zhu TIANAPN functions have the lowest differential uniform over finite fields with characteristic 2 and the APN power functions are the most classical ones.APN power functions are all 3-1 functions over <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML"> <msub> <mi>F</mi> <mrow> <msup> <mn>2</mn> <mrow> <mn>2</mn><mi>n</mi></mrow> </msup> </mrow> </msub> </math></inline-formula>.By generalizing the idea of changing 2-1 functions to 1-1 functions over finite fields with odd characteristics,methods to change 3-1 functions over finite fields with even characteristics into permutations were obtained and permutations from APN power functions over <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML"> <msub> <mi>F</mi> <mrow> <msup> <mn>2</mn> <mrow> <mn>2</mn><mi>n</mi></mrow> </msup> </mrow> </msub> </math></inline-formula> were constructed.According to the construction,the differential properties of permutations obtained by this method were discussed.http://www.cjnis.com.cn/thesisDetails#10.11959/j.issn.2096-109x.2017.00203finite fieldspermutation polynomialsAPNpower functions |
| spellingShingle | Shi-zhu TIAN Permutations from APN power functions over <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML"> <msub> <mi>F</mi> <mrow> <msup> <mn>2</mn> <mrow> <mn>2</mn><mi>n</mi></mrow> </msup> </mrow> </msub> </math></inline-formula> 网络与信息安全学报 finite fields permutation polynomials APN power functions |
| title | Permutations from APN power functions over <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML"> <msub> <mi>F</mi> <mrow> <msup> <mn>2</mn> <mrow> <mn>2</mn><mi>n</mi></mrow> </msup> </mrow> </msub> </math></inline-formula> |
| title_full | Permutations from APN power functions over <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML"> <msub> <mi>F</mi> <mrow> <msup> <mn>2</mn> <mrow> <mn>2</mn><mi>n</mi></mrow> </msup> </mrow> </msub> </math></inline-formula> |
| title_fullStr | Permutations from APN power functions over <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML"> <msub> <mi>F</mi> <mrow> <msup> <mn>2</mn> <mrow> <mn>2</mn><mi>n</mi></mrow> </msup> </mrow> </msub> </math></inline-formula> |
| title_full_unstemmed | Permutations from APN power functions over <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML"> <msub> <mi>F</mi> <mrow> <msup> <mn>2</mn> <mrow> <mn>2</mn><mi>n</mi></mrow> </msup> </mrow> </msub> </math></inline-formula> |
| title_short | Permutations from APN power functions over <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML"> <msub> <mi>F</mi> <mrow> <msup> <mn>2</mn> <mrow> <mn>2</mn><mi>n</mi></mrow> </msup> </mrow> </msub> </math></inline-formula> |
| title_sort | permutations from apn power functions over inline formula math xmlns http www w3 org 1998 math mathml msub mi f mi mrow msup mn 2 mn mrow mn 2 mn mi n mi mrow msup mrow msub math inline formula |
| topic | finite fields permutation polynomials APN power functions |
| url | http://www.cjnis.com.cn/thesisDetails#10.11959/j.issn.2096-109x.2017.00203 |
| work_keys_str_mv | AT shizhutian permutationsfromapnpowerfunctionsoverinlineformulamathxmlnshttpwwww3org1998mathmathmlmsubmifmimrowmsupmn2mnmrowmn2mnminmimrowmsupmrowmsubmathinlineformula |