International Association for Cryptologic Research (IACR)
Abstract
Bernstein et al. recently introduced a system ``Elligator\u27\u27 for steganographic key distribution. At the heart of their construction are invertible maps between a finite field F and an elliptic curve E over F. There are two such maps, called ϕ in the ``Elligator 1\u27\u27 system, and ψ in the ``Elligator 2\u27\u27 system.
Here we show two ways to construct hash functions from ψ which are indifferentiable from a random oracle. Because ψ is relatively simple, our analyses are also simple. One of our constructions uses a novel ``wallpapering\u27\u27 approach, whereas the other uses the hash-twice-and-add approach of Brier et al