Boolean functions with all main cryptographic properties
نویسندگان
چکیده
In this paper, we propose a class of 2k-variable Boolean functions which have optimal algebraic degree, very high nonlinearity, and are 1-resilient. Based on our newly proposed conjecture, it can be shown that the algebraic immunity of our functions is at least suboptimal. Moreover, when k is odd, the algebraic immunity is actually optimal, and for even k, we find that the algebraic immunity is optimal at least for k 6 28.
منابع مشابه
Structures of Highly Nonlinear Cryptographic Functions
This paper studies the properties and constructions of nonlinear Boolean functions, which are a core component of cryptographic primitives including data encryption algorithms and one-way hash functions. A main contribution of this paper is to completely characterise the structures of cryptographic functions that satisfy the propagation criterion with respect to all but six or less vectors.
متن کاملBoolean Functions: Cryptography and Applications
With cryptographic investigations, the design of Boolean functions is a wide area. The Boolean functions play important role in the construction of a symmetric cryptosystem. In this paper the modified hill climbing method is considered. The method allows using hill climbing techniques to modify bent functions used to design balanced, highly nonlinear Boolean functions with high algebraic degree...
متن کاملOn Cryptographic Properties of Random Boolean Functions
Boolean functions used in cryptographic applications have to satisfy various cryptographic criteria. Although the choice of the criteria depends on the cryptosystem in which they are used, there are some properties (balancedness, nonlinearity, high algebraic degree, correlation immunity, propagation criteria) which a cryptographically strong Boolean function ought to have. We study the above me...
متن کاملCryptographic Boolean Functions with R
A Boolean function is a mapping {0,1}n → {0,1}. Those mappings are of much interest in the design of cryptographic algorithms such as secure pseudorandom number generators (for the design of stream ciphers among other applications), hash functions and block ciphers. The lack of open source software to assess cryptographic properties of Boolean functions and the increasing interest for statistic...
متن کاملHeuristic Optimization of Boolean Functions and Substitution Boxes for Cryptography
Fundamental to the electronic security of information and communication systems, is the correct use and application of appropriate ciphers. The strength of these ciphers, particularly in their ability to resist cryptanalytic attacks, directly influences the overall strength of the entire system. The strength of the underlying cipher is reliant upon a robust structure and the carefully designed ...
متن کاملOn Boolean Functions with Generalized Cryptographic Properties
By considering a new metric, we generalize cryptographic properties of Boolean functions such as resiliency and propagation characteristics. These new definitions result in a better understanding of the properties of Boolean functions and provide a better insight in the space defined by this metric. This approach leads to the construction of “handmade” Boolean functions, i.e., functions for whi...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
عنوان ژورنال:
- IACR Cryptology ePrint Archive
دوره 2010 شماره
صفحات -
تاریخ انتشار 2010