Spectral Orbits and Peak-to-Average Power Ratio of Boolean Functions with respect to the {I,H,N}^n Transform
Lars Eirik Danielsen, Matthew G. Parker
备注：
Presented at Sequences and Their Applications, SETA'04, Seoul, South Korea, October 2004. 17 pages, 10 figures
发表信息：
In Sequences and Their Applications -- SETA 2004, edited by T. Helleseth, D. Sarwate, H.-Y. Song, and K. Yang, Lecture Notes in Comput. Sci., volume 3486, pp. 373--388, Springer-Verlag, Berlin, May 2005.
本文列举了GF（4）上块长为n的非等价自对偶加性码，从而将The On-Line Encyclopedia of Sequences中的序列A090899从n = 9推广到n = 12.这些代码有一个众所周知的量子代码的解释。它们也可以用图来表示，其中一个简单的图操作生成等价代码的轨道。我们突出的规则性和结构的一些图，对应于高距离的代码。这些代码也可以被解释为二次布尔函数，其中不等价具有谱意义。在此上下文中，我们定义PAR_IHN，相对于{I，H，N}^n变换集的峰均功率比。证明了布尔函数的PAR_IHN等价于图的相伴轨道上的最大独立集的大小。最后，我们提出了一种构造技术，以产生低PAR_IHN和代数次数高于2的布尔函数。
英文摘要：
We enumerate the inequivalent self-dual additive codes over GF(4) of blocklength n, thereby extending the sequence A090899 in The On-Line Encyclopedia of Integer Sequences from n = 9 to n = 12. These codes have a well-known interpretation as quantum codes. They can also be represented by graphs, where a simple graph operation generates the orbits of equivalent codes. We highlight the regularity and structure of some graphs that correspond to codes with high distance. The codes can also be interpreted as quadratic Boolean functions, where inequivalence takes on a spectral meaning. In this context we define PAR_IHN, peak-to-average power ratio with respect to the {I,H,N}^n transform set. We prove that PAR_IHN of a Boolean function is equivalent to the the size of the maximum independent set over the associated orbit of graphs. Finally we propose a construction technique to generate Boolean functions with low PAR_IHN and algebraic degree higher than 2.
The Maximum Nonlinearity of 8-variable Balanced Boolean Functions is 116
School of Computer and Electronic Information/School of Artificial Intelligence, Nanjing Normal University（南京师范大学计算机与电子信息学院/人工智能学院）；China Telecom Corporation Limited, Huaibei Branch（中国电信股份有限公司淮北分公司）
On the Differential Linear Connectivity Table of Vectorial Boolean Functions
Vectorial Boolean functions are crucial building blocks in symmetric ciphers. Different known attacks on block ciphers have resulted in diverse cryptographic criteria of vectorial Boolean functions,such as differential distribution table and nonlinearity. Very recently, Bar-On et al. introduced at Eurocrypt'19 a new tool, called the Differential-Linear Connectivity Table (DLCT).This paper is a follow-up work, which presents further theoretical characterization of the DLCT of vectorial Boolean functions and also investigates this new criterion of functions with certain forms. In this paper we i…
On the Differential-Linear Connectivity Table of Vectorial Boolean Functions
Vectorial Boolean functions are crucial building-blocks in symmetric ciphers. Different known attacks on block ciphers have resulted in diverse cryptographic criteria for vectorial Boolean functions, such as differential uniformity and nonlinearity. Very recently, Bar-On et al. introduced at Eurocrypt'19 a new tool, called the differential-linear connectivity table (DLCT), which allows for taking into account the dependency between the two subciphers $E_0$ and $E_1$ involved in differential-linear attacks. This new notion leads to significant improvements of differential-linear attacks on seve…
