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中文摘要：
设p为奇素数,整数u与p互素,定义广义费马商为：Hp（u）≡u^λu-1/p（modp）,其中λu为u（modp）的乘法阶。讨论了广义费马商的若干算术性质,并利用广义费马商构造两类伪随机二元序列,通过线性递归关系确定了序列的线性复杂度。结论表明,这两类序列具有高的线性复杂度,在序列密码中具有潜在的应用。
英文摘要：
Let p be an odd prime and integers u be prime to p.Define generalized Fermat quotients as Hρ（u）≡u^λu-1/p（modp）,where λu is the multiplicative order of u（modp）.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.
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