Efficient Indifferentiable Hashing into Ordinary Elliptic Curves
- Cite this paper as:
- Brier E., Coron JS., Icart T., Madore D., Randriam H., Tibouchi M. (2010) Efficient Indifferentiable Hashing into Ordinary Elliptic Curves. In: Rabin T. (eds) Advances in Cryptology – CRYPTO 2010. CRYPTO 2010. Lecture Notes in Computer Science, vol 6223. Springer, Berlin, Heidelberg
We provide the first construction of a hash function into ordinary elliptic curves that is indifferentiable from a random oracle, based on Icart’s deterministic encoding from Crypto 2009. While almost as efficient as Icart’s encoding, this hash function can be plugged into any cryptosystem that requires hashing into elliptic curves, while not compromising proofs of security in the random oracle model.
We also describe a more general (but less efficient) construction that works for a large class of encodings into elliptic curves, for example the Shallue-Woestijne-Ulas (SWU) algorithm. Finally we describe the first deterministic encoding algorithm into elliptic curves in characteristic 3.