A Characteristic Set Method for Solving Boolean Equations and Applications in Cryptanalysis of Stream Ciphers1
نویسندگان
چکیده
We present a characteristic set method for solving Boolean equations, which is more efficient and has better properties than the general characteristic set method. In particular, we give a disjoint and monic zero decomposition algorithm for the zero set of a Boolean equation system and an explicit formula for the number of solutions of a Boolean equation system. We also prove that a characteristic set can be computed with a polynomial number of multiplications of Boolean polynomials in terms of the number of variables. As experiments, we use our method to solve equations from cryptanalysis of a class of stream ciphers based on nonlinear filter generators. Extensive experiments show that the method is quite effective.
منابع مشابه
A characteristic set method for solving boolean equations and applications in cryptanalysis of stream ciphers
This paper presents a characteristic set method for solving Boolean equations, which is more efficient and has better properties than the general characteristic set method. In particular, the authors give a disjoint and monic zero decomposition algorithm for the zero set of a Boolean equation system and an explicit formula for the number of solutions of a Boolean equation system. The authors al...
متن کاملA Characteristic Set Method for Equation Solving in F2 and Applications in Cryptanalysis of Stream Ciphers
In this paper, we present a characteristic set method to solve polynomial equation systems in the finite field F2. Due to the special property of F2, the given characteristic set methods are much more efficient and simpler than the general characteristic set method. We also use our methods to solve equations raised from cryptanalysis of stream ciphers based on nonlinear filter generators.
متن کاملEfficient Characteristic Set Algorithms for Equation Solving in Finite Fields and Applications in Cryptanalysis
Efficient characteristic set methods for computing solutions of polynomial equation systems in a finite field are proposed. The concept of proper triangular sets is introduced and an explicit formula for the number of solutions of a proper and monic (or regular) triangular set is given. An improved zero decomposition algorithm which can be used to reduce the zero set of an equation system in ge...
متن کاملEfficient Characteristic Set Algorithms for Equation Solving in Finite Fields and Application in Analysis of Stream Ciphers
Efficient characteristic set methods for computing solutions of a polynomial equation system in a finite field are proposed. We introduce the concept of proper triangular sets and prove that proper triangular sets are square-free and have solutions. We present an improved algorithm which can be used to reduce the zero set of an equation system in general form to the union of zero sets of proper...
متن کاملPolyhedrons over Finite Abelian Groups and Their Cryptographic Applications
The algebraic method for stream-cipher key recovering was developed in [5]. The essence of this method is in solving the system of nonlinear equations which are the simplified consequences of the enciphering equations. The different questions on this method were investigated in [5, 6, 7]. We are using the group-theory methods for justification of algebraic method in cryptanalysis. We are consid...
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:
دوره شماره
صفحات -
تاریخ انتشار 2008