论文标题
布尔功能和LCD代码的快速代数免疫力
Fast algebraic immunity of Boolean functions and LCD codes
论文作者
论文摘要
如今，对代数攻击和快速代数攻击的阻力被认为是流媒体中使用的布尔功能的重要加密特性。两种攻击都是非常有力的分析概念，可以应用于流密码中使用的对称加密算法。代数免疫的概念引起了广泛的关注，因为它是测量布尔功能对标准代数攻击的阻力的强大工具。然而，文献中尚未清楚地识别出处理对快速代数攻击的阻力的代数工具。在当前论文中，我们提出了一个新参数，以测量布尔函数对快速代数攻击的电阻。我们还介绍了快速免疫力概况的概念，并表明它既可以告知对标准和快速代数攻击的阻力。此外，我们评估了布尔函数的两个二级结构的参数。此外，提出了一种编码理论的方法来表征完美的代数免疫功能。通过这种表征，从完美的代数免疫功能获得了二元线性互补双码代码（或简称LCD代码）的无限家族。本文介绍的二进制LCD代码除了在通信和数据存储系统中的应用外，还针对所谓的侧通道攻击（SCA）和故障非侵入攻击还具有应用程序。
Nowadays, the resistance against algebraic attacks and fast algebraic attacks are considered as an important cryptographic property for Boolean functions used in stream ciphers. Both attacks are very powerful analysis concepts and can be applied to symmetric cryptographic algorithms used in stream ciphers. The notion of algebraic immunity has received wide attention since it is a powerful tool to measure the resistance of a Boolean function to standard algebraic attacks. Nevertheless, an algebraic tool to handle the resistance to fast algebraic attacks is not clearly identified in the literature. In the current paper, we propose a new parameter to measure the resistance of a Boolean function to fast algebraic attack. We also introduce the notion of fast immunity profile and show that it informs both on the resistance to standard and fast algebraic attacks. Further, we evaluate our parameter for two secondary constructions of Boolean functions. Moreover, A coding-theory approach to the characterization of perfect algebraic immune functions is presented. Via this characterization, infinite families of binary linear complementary dual codes (or LCD codes for short) are obtained from perfect algebraic immune functions. The binary LCD codes presented in this paper have applications in armoring implementations against so-called side-channel attacks (SCA) and fault non-invasive attacks, in addition to their applications in communication and data storage systems.
