All reports by Author Akshay Degwekar:

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TR19-038
| 7th March 2019
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Itay Berman, Akshay Degwekar, Ron D. Rothblum, Prashant Nalini Vasudevan#### Statistical Difference Beyond the Polarizing Regime

Revisions: 1

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TR17-172
| 3rd November 2017
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Itay Berman, Akshay Degwekar, Ron Rothblum, Prashant Nalini Vasudevan#### From Laconic Zero-Knowledge to Public-Key Cryptography

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TR17-097
| 31st May 2017
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Itay Berman, Akshay Degwekar, Ron Rothblum, Prashant Nalini Vasudevan#### Multi Collision Resistant Hash Functions and their Applications

Revisions: 1

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TR16-091
| 3rd June 2016
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Nir Bitansky, Akshay Degwekar, Vinod Vaikuntanathan#### Structure vs Hardness through the Obfuscation Lens

Revisions: 3

Itay Berman, Akshay Degwekar, Ron D. Rothblum, Prashant Nalini Vasudevan

The polarization lemma for statistical distance ($\mathrm{SD}$), due to Sahai and Vadhan (JACM, 2003), is an efficient transformation taking as input a pair of circuits $(C_0,C_1)$ and an integer $k$ and outputting a new pair of circuits $(D_0,D_1)$ such that if $\mathrm{SD}(C_0,C_1)\geq\alpha$ then $\mathrm{SD}(D_0,D_1) \geq 1-2^{-k}$ and if $\mathrm{SD}(C_0,C_1) \leq ... more >>>

Itay Berman, Akshay Degwekar, Ron Rothblum, Prashant Nalini Vasudevan

Since its inception, public-key encryption (PKE) has been one of the main cornerstones of cryptography. A central goal in cryptographic research is to understand the foundations of public-key encryption and in particular, base its existence on a natural and generic complexity-theoretic assumption. An intriguing candidate for such an assumption is ... more >>>

Itay Berman, Akshay Degwekar, Ron Rothblum, Prashant Nalini Vasudevan

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).

In this work we study multi-collision resistant hash functions (MCRH) a natural relaxation of collision resistant ... more >>>

Nir Bitansky, Akshay Degwekar, Vinod Vaikuntanathan

Cryptography relies on the computational hardness of structured problems. While one-way functions, the most basic cryptographic object, do not seem to require much structure, as we advance up the ranks into public-key cryptography and beyond, we seem to require that certain structured problems are hard. For example, factoring, quadratic residuosity, ... more >>>