Akshayaram Srinivasan

Breaking the Sub-Exponential Barrier in Obfustopia

Indistinguishability obfuscation (\(i\mathcal {O}\)) has emerged as a surprisingly powerful notion. Almost all known cryptographic primitives can be constructed from general purpose \(i\mathcal {O}\) and other minimalistic assumptions such as one-way functions. A major challenge in this direction of research is to develop novel techniques for using \(i\mathcal {O}\) since \(i\mathcal {O}\) by itself offers virtually no protection for secret information in the underlying programs. When dealing with complex situations, often these techniques have to consider an exponential number of hybrids (usually one per input) in the security proof. This results in a sub-exponential loss in the security reduction. Unfortunately, this scenario is becoming more and more common and appears to be a fundamental barrier to many current techniques.

Revisiting the Cryptographic Hardness of Finding a Nash Equilibrium

The exact hardness of computing a Nash equilibrium is a fundamental open question in algorithmic game theory. This problem is complete for the complexity class PPAD. It is well known that problems in PPAD cannot be

Two-Round Multiparty Secure Computation from Minimal Assumptions

\mathrm {NP}

Certificateless Proxy Re-Encryption Without Pairing: Revisited

-complete unless

Two-Round Multiparty Secure Computation Minimizing Public Key Operations

\mathrm {NP}=\mathrm {coNP}

Efficiently Obfuscating Re-Encryption Program Under DDH Assumption

. Therefore, a natural direction is to reduce the hardness of PPAD to the hardness of problems used in cryptography. Bitansky, Paneth, and Rosen [FOCS 2015] prove the hardness of PPAD assuming the existence of quasi-polynomially hard indistinguishability obfuscation and sub-exponentially hard one-way functions. This leaves open the possibility of basing PPAD hardness on simpler, polynomially hard, computational assumptions. We make further progress in this direction and reduce PPAD hardness directly to polynomially hard assumptions. Our first result proves hardness of PPAD assuming the existence of polynomially hard indistinguishability obfuscation