Characteristic set algorithms for equation solving in finite fields
نویسندگان
چکیده
منابع مشابه
Characteristic set algorithms for equation solving in finite fields
Efficient characteristic set methods for computing solutions of a polynomial equation system in a finite field is proposed. We introduce the concept of proper triangular sets and prove that proper triangular sets are square-free in certain sense. We present an improved algorithm which can be used to reduce the zero set of an equation system in general form as the union of zero sets of proper tr...
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 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 کاملSolving Polynomial Systems over Finite Fields: Algorithms, Implementation and Applications
Polynomial systems can be used to formulate a large variety of non-linear problems. Polynomial systems over finite fields are of particular interest because of their applications in Cryptography, Coding Theory, and other areas of information science and technologies. Solving polynomial systems is a central topic in Computer Algebra and has stimulated the development in this area. In this thesis...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Journal of Symbolic Computation
سال: 2012
ISSN: 0747-7171
DOI: 10.1016/j.jsc.2011.12.025