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

Abstract

We extend the definition of binary threshold sequences from Fermat quotients to Euler quotients modulo pr with odd prime p and r⩾1. Under the condition of 2p−1≢1(modp2), we present exact values of the linear complexity by defining cyclotomic classes modulo pn for all 1⩽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).