Verified Indifferentiable Hashing into Elliptic Curves

Gilles Barthe (1) , Benjamin Grégoire (2) , Sylvain Heraud (2) , Federico Olmedo (1) , Santiago Zanella-Béguelin (3)

1 Institute IMDEA Software [Madrid]
2 MARELLE - Mathematical, Reasoning and Software
3 Microsoft - Microsoft Research [Cambridge]

Many cryptographic systems based on elliptic curves are proven secure in the Random Oracle Model, assuming there exist probabilistic functions that map elements in some domain (e.g. bitstrings) onto uniformly and independently distributed points in a curve. When implementing such systems, and in order for the proof to carry over to the implementation, those mappings must be instantiated with concrete constructions whose behavior does not deviate significantly from random oracles. In contrast to other approaches to public-key cryptography, where candidates to instantiate random oracles have been known for some time, the first generic construction for hashing into ordinary elliptic curves indifferentiable from a random oracle was put forward only recently by Brier et al. We present a machine-checked proof of this construction. The proof is based on an extension of the CertiCrypt framework with logics and mechanized tools for reasoning about approximate forms of observational equivalence, and integrates mathematical libraries of group theory and elliptic curves.

Domaines: Cryptographie et sécurité [cs.CR]

Gilles Barthe, Benjamin Grégoire, Sylvain Heraud, Federico Olmedo, Santiago Zanella-Béguelin. Verified Indifferentiable Hashing into Elliptic Curves. Principles of Security and Trust - First International Conference, POST 2012, Held as Part of the European Joint Conferences on Theory and Practice of Software, ETAPS 2012, Mar 2012, Tallinn, Estonia. pp.209-228, ⟨10.1007/978-3-642-28641-4_12⟩. ⟨hal-00765874⟩