Robust parent-identifying codes

Codes with the identifiable parent property (IPP codes) are used in traitor tracing schemes that protect data broadcast by the publisher from unauthorized access or distribution. An n-word y over a finite alphabet is called a descendant of a set of t words x
¹
, ..., x
^t
if y
_i
ϵ {x
¹
_i
, ..., x
^t
_i
} for all i = 1, ... n. A code C = {x
¹
, ..., x
^M
} is said to have the i-IPP property if for any n-word y that is a descendant of at most t parents belonging to the code it is possible to identify at least one of them. The existence of good i-IPP codes is known from earlier works. We introduce a robust version of IPP codes which allows unconditional identification of parents even if some of the coordinates in y can break away from the descent rule, i.e., can take arbitrary values from the alphabet, or become completely unreadable. By linking this problem to perfect hash functions and, more generally, to hash distances of a code, we prove initial results on the proportion of such coordinates that can be tolerated under the unconditional recovery requirement.