Some words on linearisation attacks on FCSR-based stream ciphers

Abstract

Linearisation attacks are effective against those stream ciphers whose analysis theory depends on the properties of 2-adic numbers. This paper discuses these attacks in the context of Feedback with Carry Shift Register (FCSR) based stream ciphers. In this context, linearisation attacks build upon the theory of linearisation intervals of the FCSR state update function. The paper presents detailed theoretical results on FCSRs, which describe various operational aspects of the FCSR state update function in relation to the linearisation intervals. Linearisation attacks combine these theoretical results on FCSRs with the concepts of well-known techniques of cryptanalysis, which depends upon the structures of specific ciphers to be analysed such as linear cryptanalysis, correlation attacks, guess-and-determine attacks, and algebraic attacks. In the context of FCSR-based stream ciphers, the paper describes three variants of linearisation attacks. These variants are named as “Conventional Linearisation Attacks”, “Fast Linearisation Attacks” and “Improved Linearisation Attacks”. These variants of linearisation attacks provide trade-offs between data, time and memory complexities with respect to each other. Moreover this paper also presents a detailed comparison of linearisation attacks with other well-known techniques of cryptanalysis.