**Abstract:** The collision-resistance of hash functions is an important foundation of many
cryptographic protocols. Formally, collision-resistance can only be expected if
the hash function in fact constitutes a parametrized family of functions, since
for a single function, the adversary could simply know a single hard-coded collision.
In practical applications, however, unkeyed hash functions are a common choice,
creating a gap between the practical application and the formal proof, and, even
more importantly, the concise mathematical definitions.

A pragmatic way out of this dilemma was recently formalized by Rogaway: instead of requiring that no adversary exists that breaks the protocol (existential security), one requires that given an adversary that breaks the protocol, we can efficiently construct a collision of the hash function using an explicitly given reduction (constructive security).

In this paper, we show the limits of this approach: We give a protocol that is existentially secure, but that provably cannot be proven secure using a constructive security proof.

Consequently, constructive security—albeit constituting a useful improvement over the state of the art—is not comprehensive enough to encompass all protocols that can be dealt with using existential security proofs.

**Permalink:** http://www.ut.ee/~unruh/publications/backes08limits.html