Nonlinear permutations of GF(2n) with strong cryptographic properties have important applications in cryptology such as DES-like block ciphers, hush functions and stream ciphers. In paPer [1], we proved that the expon...Nonlinear permutations of GF(2n) with strong cryptographic properties have important applications in cryptology such as DES-like block ciphers, hush functions and stream ciphers. In paPer [1], we proved that the exponential function can provide a class of permutations satisfying the Strict Avalanche Criterion (SAC permutations) with algebraic nonlinear degree 2. In this paper, we further construct three classes of SAC permutations that are derived from the Dickson polynomials, GMW functions and the exponential functions with maximal algebraic nonlinear degree, respectively.展开更多
In this paper, a recursion is derived to compute the linear span of the p-ary cascaded GMW sequences. It is the first time to determine the linear span of the p-ary cascaded GMW sequence without any restriction on the...In this paper, a recursion is derived to compute the linear span of the p-ary cascaded GMW sequences. It is the first time to determine the linear span of the p-ary cascaded GMW sequence without any restriction on the parameters completely. Whereas, the known result on the p-ary cascaded GMW sequence with the specific parameters in the literature could be viewed as a special case of the new result.展开更多
A new family of GMW sequences over an arbitrary Galois ring was defined by using the trace functions and permutations.This generalizes the concept of GMW sequences over finite fields.Utilizing the Fourier representati...A new family of GMW sequences over an arbitrary Galois ring was defined by using the trace functions and permutations.This generalizes the concept of GMW sequences over finite fields.Utilizing the Fourier representation,we derived an estimate of the linear complexities of this family of GMW sequences.And the result shows that such sequences have large linear complexities.展开更多
文摘Nonlinear permutations of GF(2n) with strong cryptographic properties have important applications in cryptology such as DES-like block ciphers, hush functions and stream ciphers. In paPer [1], we proved that the exponential function can provide a class of permutations satisfying the Strict Avalanche Criterion (SAC permutations) with algebraic nonlinear degree 2. In this paper, we further construct three classes of SAC permutations that are derived from the Dickson polynomials, GMW functions and the exponential functions with maximal algebraic nonlinear degree, respectively.
基金the National Natural Science Foundation of China (Grant No. 60302015)the Foundation for the Author of National Excellent Doctoral Dissertation of China (Grant No. 200341)Sichuan Youth Science Foundation (Grant No. 04ZQ026-048)
文摘In this paper, a recursion is derived to compute the linear span of the p-ary cascaded GMW sequences. It is the first time to determine the linear span of the p-ary cascaded GMW sequence without any restriction on the parameters completely. Whereas, the known result on the p-ary cascaded GMW sequence with the specific parameters in the literature could be viewed as a special case of the new result.
文摘A new family of GMW sequences over an arbitrary Galois ring was defined by using the trace functions and permutations.This generalizes the concept of GMW sequences over finite fields.Utilizing the Fourier representation,we derived an estimate of the linear complexities of this family of GMW sequences.And the result shows that such sequences have large linear complexities.
