TY - GEN

T1 - The magic of ELFs

AU - Zhandry, Mark

N1 - Funding Information:
M. Zhandry—This work was sponsored by the Defense Advanced Research Projects Agency (DARPA) and the U.S. Army Research Office under contract number W911NF-15-C-0226.
Publisher Copyright:
© International Association for Cryptologic Research 2016.

PY - 2016

Y1 - 2016

N2 - 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 polynomiallymany hardcore bits for any one-way function. Such applications were previously known from strong knowledge assumptions — for example polynomiallymany hardcore bits were only know from differing inputs obfuscation, a notion whose plausibility has been seriously challenged. We also use ELFs to build a simple hash function with output intractability, a new notion we define that may be useful for generating common reference strings. Next, we give a construction of ELFs relying on the exponential hardness of the decisional Diffie-Hellman problem, which is plausible in pairing-based groups. Combining with the applications above, our work gives several practical constructions relying on qualitatively different — and arguably better — assumptions than prior works.

AB - 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 polynomiallymany hardcore bits for any one-way function. Such applications were previously known from strong knowledge assumptions — for example polynomiallymany hardcore bits were only know from differing inputs obfuscation, a notion whose plausibility has been seriously challenged. We also use ELFs to build a simple hash function with output intractability, a new notion we define that may be useful for generating common reference strings. Next, we give a construction of ELFs relying on the exponential hardness of the decisional Diffie-Hellman problem, which is plausible in pairing-based groups. Combining with the applications above, our work gives several practical constructions relying on qualitatively different — and arguably better — assumptions than prior works.

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U2 - 10.1007/978-3-662-53018-4_18

DO - 10.1007/978-3-662-53018-4_18

M3 - Conference contribution

AN - SCOPUS:84979590784

SN - 9783662530177

T3 - Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)

SP - 479

EP - 508

BT - Advances in Cryptology - 36th Annual International Cryptology Conference, CRYPTO 2016, Proceedings

A2 - Robshaw, Matthew

A2 - Katz, Jonathan

PB - Springer Verlag

T2 - 36th Annual International Cryptology Conference, CRYPTO 2016

Y2 - 14 August 2016 through 18 August 2016

ER -