Akshay Degwekar

Multi-Collision Resistant Hash Functions and Their Applications

Collision resistant hash functions are functions that shrink their input, but for which it is computationally infeasible to find a collision, namely two strings that hash to the same value (although collisions are abundant).

Structure vs. Hardness Through the Obfuscation Lens

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 \({\textsf {NP}} \cap {\textsf {coNP}}\) or statistical zero-knowledge (SZK).

Fine-Grained Cryptography

Fine-grained cryptographic primitives are ones that are secure against adversaries with an a-priori bounded polynomial amount of resources time, space or parallel-time, where the honest algorithms use less resources than the adversaries they are designed to fool. Such primitives were previously studied in the context of time-bounded adversaries Merkle, CACM 1978, space-bounded adversaries Cachin and Maurer, CRYPTO 1997 and parallel-time-bounded adversaries Hastad, IPL 1987. Our goal is come up with fine-grained primitives in the setting of parallel-time-bounded adversaries and to show unconditional security of these constructions when possible, or base security on widely believed separation of worst-case complexity classes. We show:1.

From Laconic Zero-Knowledge to Public-Key Cryptography

{\textsf {NC}^{1}}

Multi Collision Resistant Hash Functions and their Applications.

-cryptography: Under the assumption that [InlineEquation not available: see fulltext.], we construct one-way functions, pseudo-random generators with sub-linear stretch, collision-resistant hash functions and most importantly, public-key encryption schemes, all computable in