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Given a directed acyclic graph (DAG) G=(V,E), we say that G is (e,d)depthrobust (resp. (e,d)edgedepthrobust) if for any set S⊆V (resp. S⊆E) of at most S≤e nodes (resp. edges) the graph G−S contains a directed path of length d. While edgedepthrobust graphs are potentially easier to construct, many applications in cryptography require node depthrobust graphs with small indegree. We create a graph reduction that transforms an (e,d)edgedepthrobust graph with m edges into a (e/2,d)depthrobust graph with O(m) nodes and constant indegree. One immediate consequence of this result is the first construction of a provably (nloglognlogn,nlogn(logn)loglogn)depthrobust graph with constant indegree. Ourmore »