TY - GEN

T1 - Structure vs. Hardness through the obfuscation lens

AU - Bitansky, Nir

AU - Degwekar, Akshay

AU - Vaikuntanathan, Vinod

N1 - Publisher Copyright:
© International Association for Cryptologic Research 2017.

PY - 2017

Y1 - 2017

N2 - Much of modern cryptography, starting from public-key encryption and going beyond, is based on the hardness of structured (mostly algebraic) problems like factoring, discrete log or finding short lattice vectors. While structure is perhaps what enables advanced applications, it also puts the hardness of these problems in question. In particular, this structure often puts them in low complexity classes such as NP ∩ coNP or statistical zero-knowledge (SZK). Is this structure really necessary? For some cryptographic primitives, such as one-way permutations and homomorphic encryption, we know that the answer is yes—they imply hard problems in NP ∩ coNP and SZK, respectively. In contrast, one-way functions do not imply such hard problems, at least not by fully black-box reductions. Yet, for many basic primitives such as public-key encryption, oblivious transfer, and functional encryption, we do not have any answer. We show that the above primitives, and many others, do not imply hard problems in NP ∩ coNP or SZK via fully black-box reductions. In fact, we first show that even the very powerful notion of Indistinguishability Obfuscation (IO) does not imply such hard problems, and then deduce the same for a large class of primitives that can be constructed from IO.

AB - Much of modern cryptography, starting from public-key encryption and going beyond, is based on the hardness of structured (mostly algebraic) problems like factoring, discrete log or finding short lattice vectors. While structure is perhaps what enables advanced applications, it also puts the hardness of these problems in question. In particular, this structure often puts them in low complexity classes such as NP ∩ coNP or statistical zero-knowledge (SZK). Is this structure really necessary? For some cryptographic primitives, such as one-way permutations and homomorphic encryption, we know that the answer is yes—they imply hard problems in NP ∩ coNP and SZK, respectively. In contrast, one-way functions do not imply such hard problems, at least not by fully black-box reductions. Yet, for many basic primitives such as public-key encryption, oblivious transfer, and functional encryption, we do not have any answer. We show that the above primitives, and many others, do not imply hard problems in NP ∩ coNP or SZK via fully black-box reductions. In fact, we first show that even the very powerful notion of Indistinguishability Obfuscation (IO) does not imply such hard problems, and then deduce the same for a large class of primitives that can be constructed from IO.

KW - Collision-resistant hashing

KW - Indistinguishability obfuscation

KW - NP ∩ coNP

KW - Statistical zero-knowledge

KW - Structured hardness

UR - http://www.scopus.com/inward/record.url?scp=85028461652&partnerID=8YFLogxK

U2 - 10.1007/978-3-319-63688-7_23

DO - 10.1007/978-3-319-63688-7_23

M3 - פרסום בספר כנס

AN - SCOPUS:85028461652

SN - 9783319636870

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

SP - 696

EP - 723

BT - Advances in Cryptology – CRYPTO 2017 - 37th Annual International Cryptology Conference, Proceedings

A2 - Shacham, Hovav

A2 - Katz, Jonathan

PB - Springer Verlag

Y2 - 20 August 2017 through 24 August 2017

ER -