Publications: Abstract

# Optimal Tree-based One-time Digital Signature Schemes

## Daniel Bleichenbacher and Ueli Maurer

 A minimal cutset of a tree directed from the leaves to the root is a minimal set of vertices such that every path from a leaf to the root meets at least one of these vertices. An order relation on the set of minmal cutsets can be defined: $U\leq V$ if and only if every vertex of $U$ is on the path from some vertex in $V$ to the root. Motivated by the design of efficient cryptographic digital signature schemes, the problem of constructing trees with a large number of pairwise incomparable minimal cutsets or, equivalently, with a large antichain in the poset of minimal cutsets, is considered. Keywords: Cryptography, digital signature schemes, trees, partially ordered sets.