Abstract
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, w <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sub> } that can be obtained from the probabilistic method. The asymptotic behavior of these bounds is analyzed.
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