Some Improved Bounds for Secure Frameproof Codes and Related Separating Hash Families

We present some improved bounds on necessary conditions for separating hash families of type {w, w} and type {w, w - 1}. In particular, these bounds apply to secure frame- proof codes, which are equivalent to separating hash families of type {w, w}. We also consider existence results for separating hash families of type {w, w₂} that can be obtained from the probabilistic method. The asymptotic behavior of these bounds is analyzed.