【摘要】 二元域上n数组空间上的非线性置换在分组码，杂凑函数与流密码等密码学领域中有重要应用.域GF（2n）上的幂函数提供了二元域上n数组空间上的一类非线性置换．本文着重研究幂函数的强完全性、完全性与非线性度等密码学性质．作为结果，本文证明了幂函数具有完全性；证明了具有强完全性的函数必有较高的拓扑非线性度；木文找到一类具有强完全性的幂函数；周时也定出了幂函数的代数非线性度．更多还原

【Abstract】 Nonlinear permutations on linear spaces with finite dimensions over the binary field GF(2), with proper cryptographic properties, have important applications in cryptology such as DES-like block ciphers, Hush functions and stream ciphers.In this paper, we study some cryptographic properties of exponential functions over the finite field GF(2n), which provide permutations on n-dimensional linear space and can be implemented easily. We concentrate on the properties such as strict avanlanche criterion (SAC,or called strict completeness), completeness and nonlinear degrees of exponential functions. As results, we prove that the exponential functions have the property of completeness. We also find a class of exponential functions satisfying SAC, and prove that functions satisfying SAC do have high topological nonlinear degrees. Finally the algebraic nonlinear degrees of the exponential functions are determined.更多还原