Algebraic attacks on stream ciphers: recent developments and new results

The security of stream ciphers against algebraic attacks is studied in this paper. Emphasis is given on analysing the properties of the underlying Boolean functions that need to be satisfied, such as the algebraic and the fast algebraic immunity. We present an overview of the constructions of functions with maximum algebraic immunity discovered recently, whereas known relationships with other cryptographic criteria are also reviewed. Moreover, we investigate the link between the fast algebraic immunity and the correlation immunity of Boolean functions. where a trade-off between resistance to correlation and fast algebraic attacks is proved. It is also shown that a known construction of cryptographic functions does not behave well with respect to (fast) algebraic- attacks. [PUBLICATION ABSTRACT]