Linear complexity of binary sequences derived from Euler quotients with prime-power modulus

We extend the definition of binary threshold sequences from Fermat quotients to Euler quotients modulo prpr with odd prime p   and r⩾1r⩾1. Under the condition of 2p−1≢1(modp2), we present exact values of the linear complexity by defining cyclotomic classes modulo pnpn for all 1⩽n⩽r1⩽n⩽r. The linear complexity is very close to the period and is of desired value for cryptographic purpose. We also present a lower bound on the linear complexity for the case of 2p−1≡1(modp2).

► Extend the definition of binary threshold sequences from Fermat quotients to Euler quotients.
► Determine the linear complexities by defining cyclotomic classes.
► The linear complexity is very close to the period if 2p−1≢1(modp2).
► Present a lower bound on the linear complexity for the case of 2p−1≡1(modp2).