On pseudorandomness of families of binary sequences

In cryptography one needs large families of binary sequences with strong pseudorandom properties. In the last decades many families of this type have been constructed. However, in many applications it is not enough if our family of “good” sequences is large, it is more important to know that it has a rich, complex structure, and the sequences in the family are “independent”, and they are “far apart”. Thus various measures have been introduced and applied for studying pseudorandomness of families of binary sequences: family complexity, collision, distance minimum, avalanche effect and cross-correlation measure. In this paper a survey of all these definitions and results will be presented.