  In this article, we propose a new construction of probabilistic
collusion-secure fingerprint codes against up to three pirates and give a
theoretical security evaluation. Our pirate tracing algorithm combines a
scoring method analogous to Tardos codes (J. ACM, 2008) with an extension of
parent search techniques of some preceding 2-secure codes. Numerical examples
show that our code lengths are significantly shorter than (about 30% to 40% of)
the shortest known c-secure codes by Nuida et al. (Des. Codes Cryptogr., 2009)
with c = 3. Some preliminary proposal for improving efficiency of our tracing
algorithm is also given.
