Does Secure Time-Stamping Imply Collision-Free Hash Functions?

Abstract

We prove that there are no black-box reductions from Collision-Free Hash Functions to secure time-stamping schemes, which means that in principle secure time-stamping schemes may exist even if there exist no collision-resistant hash functions. We show that there is an oracle relative to which there exist secure time-stamping schemes but no hash function is collision-free. The oracle we use is not new — a similar idea was already used by Simon in 1998 to show that collision-free hash functions cannot be constructed from one-way permutations in a black-box way. Our oracle contains a random hash function family f and a universal collision-finder A. We show that hash-tree time-stamping schemes that use f as a hash function remain secure even in the presence of A. From more practical view, our result is an implicit confirmation that collision-finding attacks against hash functions will tell us quite little about the security of hash-tree time-stamping schemes and that we need more dedicated research about back-dating attacks against practical hash functions.KeywordsHash FunctionTuring MachineCompression PropertySecurity ProofOblivious TransferThese keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.