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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| Main Author: | |
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| Format: | Article |
| Language: | English |
| Published: |
POSTS&TELECOM PRESS Co., LTD
2017-10-01
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| Series: | 网络与信息安全学报 |
| Subjects: | |
| Online Access: | http://www.cjnis.com.cn/thesisDetails#10.11959/j.issn.2096-109x.2017.00203 |
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| Summary: | 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. |
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| ISSN: | 2096-109X |