A construction of traceability set systems with polynomial tracing algorithm

Abstract

A family F of w-subsets of a finite set X is called a set system with the identifiable parent property if for any w-subset contained in the union of some t sets, called traitors, of F at least one of these sets can be uniquely determined, i.e. traced. A set system with traceability property (TSS, for short) allows to trace at least one traitor by minimal distance decoding of the corresponding binary code, and hence the complexity of tracing procedure is of order O(M), where M is the number of users or the code's cardinality. We propose a new construction of TSS which is based on the old Kautz-Singleton concatenated construction with algebraic-geometry codes as the outer code and Guruswami-Sudan decoding algorithm. The resulting codes (set systems) have exponentially many users (codevectors) M and polylog(M) complexity of code construction and decoding, i.e. tracing traitors. This is the first construction of traceability set systems with such properties.