Constructing Two Classes of Boolean Functions With Good Cryptographic Properties
Wu et al. proposed a generalized Tu-Deng conjecture over <inline-formula> <tex-math notation="LaTeX">$\mathbb {F}_{2^{rm}}\times {\mathbb {F}_{2^{m}}}$ </tex-math></inline-formula>, and constructed Boolean functions with good properties. However the proof of the gen...
| Main Authors: | , , , |
|---|---|
| Format: | Article |
| Language: | English |
| Published: |
IEEE
2019-01-01
|
| Series: | IEEE Access |
| Subjects: | |
| Online Access: | https://ieeexplore.ieee.org/document/8868156/ |
| _version_ | 1798001982406918144 |
|---|---|
| author | Yindong Chen Liu Zhang Zhangquan Gong Weihong Cai |
| author_facet | Yindong Chen Liu Zhang Zhangquan Gong Weihong Cai |
| author_sort | Yindong Chen |
| collection | DOAJ |
| description | Wu et al. proposed a generalized Tu-Deng conjecture over <inline-formula> <tex-math notation="LaTeX">$\mathbb {F}_{2^{rm}}\times {\mathbb {F}_{2^{m}}}$ </tex-math></inline-formula>, and constructed Boolean functions with good properties. However the proof of the generalized conjecture is still open. Based on Wu’s work and assuming that the conjecture is true, we come up with a new class of balanced Boolean functions which has optimal algebraic degree, high nonlinearity and optimal algebraic immunity. The Boolean function also behaves well against fast algebraic attacks. Meanwhile we construct another class of Boolean functions by concatenation, which is 1-resilient and also has other good cryptographic properties. |
| first_indexed | 2024-04-11T11:44:51Z |
| format | Article |
| id | doaj.art-d0776ac2d1a24334a7438bc287495300 |
| institution | Directory Open Access Journal |
| issn | 2169-3536 |
| language | English |
| last_indexed | 2024-04-11T11:44:51Z |
| publishDate | 2019-01-01 |
| publisher | IEEE |
| record_format | Article |
| series | IEEE Access |
| spelling | doaj.art-d0776ac2d1a24334a7438bc2874953002022-12-22T04:25:40ZengIEEEIEEE Access2169-35362019-01-01714965714966510.1109/ACCESS.2019.29473678868156Constructing Two Classes of Boolean Functions With Good Cryptographic PropertiesYindong Chen0https://orcid.org/0000-0001-8849-6087Liu Zhang1Zhangquan Gong2Weihong Cai3Department of Computer Science, Shantou University, Shantou, ChinaDepartment of Computer Science, Shantou University, Shantou, ChinaDepartment of Computer Science, Shantou University, Shantou, ChinaDepartment of Computer Science, Shantou University, Shantou, ChinaWu et al. proposed a generalized Tu-Deng conjecture over <inline-formula> <tex-math notation="LaTeX">$\mathbb {F}_{2^{rm}}\times {\mathbb {F}_{2^{m}}}$ </tex-math></inline-formula>, and constructed Boolean functions with good properties. However the proof of the generalized conjecture is still open. Based on Wu’s work and assuming that the conjecture is true, we come up with a new class of balanced Boolean functions which has optimal algebraic degree, high nonlinearity and optimal algebraic immunity. The Boolean function also behaves well against fast algebraic attacks. Meanwhile we construct another class of Boolean functions by concatenation, which is 1-resilient and also has other good cryptographic properties.https://ieeexplore.ieee.org/document/8868156/Algebraic immunity1-resilientnonlinearityfast algebraic attacksTu-Deng conjectureBoolean function |
| spellingShingle | Yindong Chen Liu Zhang Zhangquan Gong Weihong Cai Constructing Two Classes of Boolean Functions With Good Cryptographic Properties IEEE Access Algebraic immunity 1-resilient nonlinearity fast algebraic attacks Tu-Deng conjecture Boolean function |
| title | Constructing Two Classes of Boolean Functions With Good Cryptographic Properties |
| title_full | Constructing Two Classes of Boolean Functions With Good Cryptographic Properties |
| title_fullStr | Constructing Two Classes of Boolean Functions With Good Cryptographic Properties |
| title_full_unstemmed | Constructing Two Classes of Boolean Functions With Good Cryptographic Properties |
| title_short | Constructing Two Classes of Boolean Functions With Good Cryptographic Properties |
| title_sort | constructing two classes of boolean functions with good cryptographic properties |
| topic | Algebraic immunity 1-resilient nonlinearity fast algebraic attacks Tu-Deng conjecture Boolean function |
| url | https://ieeexplore.ieee.org/document/8868156/ |
| work_keys_str_mv | AT yindongchen constructingtwoclassesofbooleanfunctionswithgoodcryptographicproperties AT liuzhang constructingtwoclassesofbooleanfunctionswithgoodcryptographicproperties AT zhangquangong constructingtwoclassesofbooleanfunctionswithgoodcryptographicproperties AT weihongcai constructingtwoclassesofbooleanfunctionswithgoodcryptographicproperties |