数学
素数(序理论)
发电机(电路理论)
组合数学
质数
二进制数
主电源
时间复杂性
价值(数学)
离散数学
算术
功率(物理)
统计
物理
量子力学
作者
Vladimir Edemskiy,Zhixiong Chen
标识
DOI:10.1007/s12190-022-01740-z
摘要
R. Hofer and A. Winterhof proved that the 2-adic complexity of the two-prime (binary) generator of period pq with two odd primes $$p\ne q$$ is close to its period and it can attain the maximum in many cases. When the two-prime generator is applied to producing quaternary sequences, we need to determine the 4-adic complexity. It is proved that there are only two possible values of the 4-adic complexity for the two-prime quaternary generator, which are at least $$pq-1-\max \{\log _4(pq^2),\log _4(p^2q)\}$$ . Examples for primes p and q with $$5\le p, q <10000$$ illustrate that the 4-adic complexity only takes one value larger than $$pq-\max \{\log _4(p),\log _4(q)\}$$ , which is close to its period. So it is good enough to resist the attack of the rational approximation algorithm.
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