Periodic sequences with maximal [formula omitted]-adic complexity and large [formula omitted]-error [formula omitted]-adic complexity over [formula omitted

Abstract

Complexity measures for keystream sequences over Z/(N) play a crucial role in designing good stream cipher systems. This correspondence shows a general upper bound on k-error N-adic complexity of periodic sequences over Z/(N), and establishes the existence of periodic sequences over Z/(N) which simultaneously possess maximal N-adic complexity and large k-error N-adic complexity. Under some conditions the overwhelming majority of all T-periodic sequences over Z/(N) with maximal N-adic complexity logN(NT−1) have a k-error N-adic complexity close to logN(NT−1). The existence of many such sequences thwarts attacks against the keystreams by exhaustive search.