Linear Complexity of Binary Sequences Derived from Euler Quotients Modulo 2pm

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 2p(m+1) is constructed using Euler quotients modulo 2p(m), where p is an odd prime and integer m >= 1. Under the condition of 2(p)(-1)not equivalent to( )( mod 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.