Fast algebraic immunity of Boolean functions
| Autor: | Sihem Mesnager, Gérard D. Cohen |
|---|---|
| Rok vydání: | 2017 |
| Předmět: |
Algebra and Number Theory
Computer Networks and Communications business.industry Applied Mathematics 020206 networking & telecommunications Cryptography 02 engineering and technology Microbiology Upper and lower bounds law.invention Algebra 020303 mechanical engineering & transports 0203 mechanical engineering law 0202 electrical engineering electronic engineering information engineering Discrete Mathematics and Combinatorics Cryptosystem Boolean expression Algebraic number Boolean function Cryptanalysis business Stream cipher Computer Science::Cryptography and Security Mathematics |
| Zdroj: | Advances in Mathematics of Communications. 11:373-377 |
| ISSN: | 1930-5338 |
| DOI: | 10.3934/amc.2017031 |
| Popis: | Since 1970, Boolean functions have been the focus of a lot of attention in cryptography. An important topic in symmetric ciphers concerns the cryptographic properties of Boolean functions and constructions of Boolean functions with good cryptographic properties, that is, good resistance to known attacks. An important progress in cryptanalysis areas made in 2003 was the introduction by Courtois and Meier of algebraic attacks and fast algebraic attacks which are very powerful analysis concepts and can be applied to almost all cryptographic algorithms. To study the resistance against algebraic attacks, the notion of algebraic immunity has been introduced. In this paper, we use a parameter introduced by Liu and al., called fast algebraic immunity, as a tool to measure the resistance of a cryptosystem (involving Boolean functions) to fast algebraic attacks. We prove an upper bound on the fast algebraic immunity. Using our upper bound, we establish the weakness of trace inverse functions against fast algebraic attacks confirming a recent result of Feng and Gong. |
| Databáze: | OpenAIRE |
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