Towards a Theory of Extractable Functions

Extractable functions are functions where any adversary that outputs a point in the range of the function is guaranteed to "know" a corresponding preimage. Here, knowledge is captured by the existence of an efficient extractor that recovers the preimage from the internal state of the adversary. Extractability of functions was defined by the authors (ICALP'08) in the context of perfectly functions. It can be regarded as an abstraction from specific knowledge assumptions, such as the Knowledge of Exponent assumption (Hada and Tanaka, Crypto 1998). We initiate a more general study of extractable functions. We explore two different approaches. The first approach is aimed at understanding the concept of extractability in of itself; in particular we demonstrate that a weak notion of extraction implies a strong one, and make rigorous the intuition that extraction and obfuscation are complementary notions. In the second approach, we study the possibility of constructing cryptogr...

• Type: Conference
• Year: 2009
• Where: TCC
• Authors: Ran Canetti, Ronny Ramzi Dakdouk
• Keywords: Cryptography, Extractable One-way Functions, Extractable Pseudorandom Functions, TCC 2009, Weak One-way Functions