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From Indifferentiability to Constructive Cryptography (and Back)

Ueli Maurer and Renato Renner

The concept of indifferentiability of systems, a generalized form of indistinguishability, was proposed in 2004 to provide a simplified and generalized explanation of impossibility results like the non-instantiability of random oracles by hash functions due to Canetti, Goldreich, and Halevi (STOC 1998). But indifferentiability is actually a constructive notion, leading to possibility results. For example, Coron et al. (Crypto 2005) argued that the soundness of the construction $C(f)$ of a hash function from a compression function $f$ can be demonstrated by proving that $C(R)$ is indifferentiable from a random oracle if $R$ is an ideal random compression function.

The purpose of this short paper is to describe how the indifferentiability notion was a precursor to the theory of constructive cryptography and thereby to provide a simplified and generalized treatment of indifferentiability as a special type of constructive statement.