Generalization and Application of Fermat Quotients
Chenhuang Wu · Journal of Putian University · 2011
Let p be an odd prime and integers μ be prime to ρ.Define generalized Fermat quotients as Hρ(μ)≡μλ-1/p(modρ),where λμ is the multiplicative order of μ(modρ).Some arithmetic properties are studied.Two families of pseudorandom binary sequences are constructed by using the generalized Fermat quotients.The linear complexities are determined in terms of linear recurrence relations.The results indicate that such sequences possess high linear complexities,and hence have potential applications in stream ciphers.