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Title:
The Encrypted Elliptic Curve Hash
Authors: Daniel R. L. Brown
Abstract:Bellare and Micciancio’s MuHASH applies a pre-existing hash function to map indexed message blocks into a secure group. The resulting hash is the product. Bellare and Micciancio proved, in the random oracle model, that MuHASH is collision-resistant if the group’s discrete logarithm problem is infeasible. MuHASH, however, relies on a pre-existing hash being collision resistant. In this paper, we remove such a reliance by replacing the pre-existing hash with a block cipher under a fixed key. We adapt Bellare and Micciancio’s collision-resistance proof to the ideal cipher model. Preimage resistance requires us to add a further modification.
ePrint: https://eprint.iacr.org/2008/012
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