Extended algebraic immunity of symmetric Boolean function
Boolean functions with optimal algebraic immunity play an important role in stream ciphers.Based on the univariate polynomial representation of Boolean functions,a construction of Boolean functions with maximum extended algebraic immunity (EAI) is proposed,some previous results are special cases of...
Saved in:
| Main Authors: | , , , |
|---|---|
| Format: | Article |
| Language: | zho |
| Published: |
Editorial Department of Journal on Communications
2014-11-01
|
| Series: | Tongxin xuebao |
| Subjects: | |
| Online Access: | http://www.joconline.com.cn/zh/article/doi/10.3969/j.issn.1000-436x.2014.z2.024/ |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1841539683771744256 |
|---|---|
| author | Gao-fei WU Xue-feng LIU Ye TIAN Yu-qing ZHANG |
| author_facet | Gao-fei WU Xue-feng LIU Ye TIAN Yu-qing ZHANG |
| author_sort | Gao-fei WU |
| collection | DOAJ |
| description | Boolean functions with optimal algebraic immunity play an important role in stream ciphers.Based on the univariate polynomial representation of Boolean functions,a construction of Boolean functions with maximum extended algebraic immunity (EAI) is proposed,some previous results are special cases of our construction.The EAI of symmetric Boolean functions which have maximum algebraic immunity (AI) are analyzed by using the properties of symmetric Boolean functions.The result shows that there are only <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML"> <msup> <mn>2</mn> <mrow> <mrow><mo>＆#x230A;</mo> <mrow> <mtext>lb</mtext><mo stretchy="false">(</mo><mi>n</mi><mo>/</mo><mn>2</mn><mo stretchy="false">)</mo></mrow> <mo>＆#x230B;</mo></mrow><mo>+</mo><mn>2</mn></mrow> </msup> </math></inline-formula> n-variable (n even) symmetric Boolean functions achieve maximum EAI. |
| format | Article |
| id | doaj-art-bfdb079da3c94d53a2e951c544023292 |
| institution | Kabale University |
| issn | 1000-436X |
| language | zho |
| publishDate | 2014-11-01 |
| publisher | Editorial Department of Journal on Communications |
| record_format | Article |
| series | Tongxin xuebao |
| spelling | doaj-art-bfdb079da3c94d53a2e951c5440232922025-01-14T06:45:13ZzhoEditorial Department of Journal on CommunicationsTongxin xuebao1000-436X2014-11-013517918359689309Extended algebraic immunity of symmetric Boolean functionGao-fei WUXue-feng LIUYe TIANYu-qing ZHANGBoolean functions with optimal algebraic immunity play an important role in stream ciphers.Based on the univariate polynomial representation of Boolean functions,a construction of Boolean functions with maximum extended algebraic immunity (EAI) is proposed,some previous results are special cases of our construction.The EAI of symmetric Boolean functions which have maximum algebraic immunity (AI) are analyzed by using the properties of symmetric Boolean functions.The result shows that there are only <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML"> <msup> <mn>2</mn> <mrow> <mrow><mo>＆#x230A;</mo> <mrow> <mtext>lb</mtext><mo stretchy="false">(</mo><mi>n</mi><mo>/</mo><mn>2</mn><mo stretchy="false">)</mo></mrow> <mo>＆#x230B;</mo></mrow><mo>+</mo><mn>2</mn></mrow> </msup> </math></inline-formula> n-variable (n even) symmetric Boolean functions achieve maximum EAI.http://www.joconline.com.cn/zh/article/doi/10.3969/j.issn.1000-436x.2014.z2.024/cryptographyBoolean functionssymmetric Boolean functionsalgebraic immunity annihilatorsextended algebraic immunity |
| spellingShingle | Gao-fei WU Xue-feng LIU Ye TIAN Yu-qing ZHANG Extended algebraic immunity of symmetric Boolean function Tongxin xuebao cryptography Boolean functions symmetric Boolean functions algebraic immunity annihilators extended algebraic immunity |
| title | Extended algebraic immunity of symmetric Boolean function |
| title_full | Extended algebraic immunity of symmetric Boolean function |
| title_fullStr | Extended algebraic immunity of symmetric Boolean function |
| title_full_unstemmed | Extended algebraic immunity of symmetric Boolean function |
| title_short | Extended algebraic immunity of symmetric Boolean function |
| title_sort | extended algebraic immunity of symmetric boolean function |
| topic | cryptography Boolean functions symmetric Boolean functions algebraic immunity annihilators extended algebraic immunity |
| url | http://www.joconline.com.cn/zh/article/doi/10.3969/j.issn.1000-436x.2014.z2.024/ |
| work_keys_str_mv | AT gaofeiwu extendedalgebraicimmunityofsymmetricbooleanfunction AT xuefengliu extendedalgebraicimmunityofsymmetricbooleanfunction AT yetian extendedalgebraicimmunityofsymmetricbooleanfunction AT yuqingzhang extendedalgebraicimmunityofsymmetricbooleanfunction |