Linear Complexity of Binary Sequences Derived from Euler Quotients Modulo 2p^m

Families of pseudorandom sequences derived from Euler quotients modulo odd prime power possess sound cryptographic properties. In this paper, according to the theory of residue class ring, a new classes of binary sequences with period $2{p^{m + 1}}$ is constructed using Euler quotients modulo $2{p^m},$ where $p$ is an odd prime and integer $m \ge 1.$ Under the condition of ${2^{p - 1}}\not \equiv 1 ({od}\,{p^2})$, the linear complexity of the sequence is examined with the method of determining the roots of polynomial over finite field ${F_2}$. The results show that the linear complexity of the sequence takes the value $2({p^{m + 1}} - p)$ or $2({p^{m + 1}} - 1)$, which is larger than half of its period and can resist the attack of Berlekamp-Massey (B-M) algorithm. It is a good sequence from the viewpoint of cryptography.