Limits of Constructive Security Proofs

  • Michael Backes
  • Dominique Unruh
Part of the Lecture Notes in Computer Science book series (LNCS, volume 5350)


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.

Copyright information

© Springer-Verlag Berlin Heidelberg 2008

Authors and Affiliations

  • Michael Backes
    • 1
    • 2
  • Dominique Unruh
    • 1
  1. 1.Saarland UniversitySaarbrückenGermany
  2. 2.Max-Planck-Institute for Software SystemsSaarbrückenGermany

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