The Magic of ELFs

We introduce the notion of an Extremely Lossy Function (ELF). An ELF is a family of functions with an image size that is tunable anywhere from injective to having a polynomial-sized image. Moreover, for any efficient adversary, for a sufficiently large polynomial r (necessarily chosen to be larger than the running time of the adversary), the adversary cannot distinguish the injective case from the case of image size r. We develop a handful of techniques for using ELFs, and show that such extreme lossiness is useful for instantiating random oracles in several settings. In particular, we show how to use ELFs to build secure point function obfuscation with auxiliary input, as well as polynomially-many hardcore bits for any one-way function. Such applications were previously known from strong knowledge assumptions — for example polynomially-many hardcore bits were only know from differing inputs obfuscation, a notion whose plausibility has been seriously challenged. We also use ELFs to...

• Type: Journal
• Year: 2016
• Where: IACR
• Authors: Mark Zhandry
• Keywords: Biometrics, IACR 2016