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Electronic Colloquium on Computational Complexity

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REPORTS > AUTHORS > ZVIKA BRAKERSKI:
All reports by Author Zvika Brakerski:

TR18-125 | 7th July 2018
Zvika Brakerski

Fundamentals of Fully Homomorphic Encryption – A Survey

A homomorphic encryption scheme is one that allows computing on encrypted data without decrypting it first. In fully homomorphic encryption it is possible to apply any efficiently computable function to encrypted data. We provide a survey on the origins, definitions, properties, constructions and uses of fully homomorphic encryption.

more >>>

TR18-056 | 20th March 2018
Zvika Brakerski, Vadim Lyubashevsky, Vinod Vaikuntanathan, Daniel Wichs

Worst-Case Hardness for LPN and Cryptographic Hashing via Code Smoothing

We present a worst case decoding problem whose hardness reduces to that of solving the Learning Parity with Noise (LPN) problem, in some parameter regime. Prior to this work, no worst case hardness result was known for LPN (as opposed to syntactically similar problems such as Learning with Errors). The ... more >>>


TR17-060 | 9th April 2017
Boaz Barak, Zvika Brakerski, Ilan Komargodski, Pravesh Kothari

Limits on Low-Degree Pseudorandom Generators (Or: Sum-of-Squares Meets Program Obfuscation)

Revisions: 1

We prove that for every function $G\colon\{0,1\}^n \rightarrow \mathbb{R}^m$, if every output of $G$ is a polynomial (over $\mathbb{R}$) of degree at most $d$ of at most $s$ monomials and $m > \widetilde{O}(sn^{\lceil d/2 \rceil})$, then there is a polynomial time algorithm that can distinguish a vector of the form ... more >>>


TR16-077 | 12th May 2016
Zvika Brakerski, Justin Holmgren, Yael Tauman Kalai

Non-Interactive RAM and Batch NP Delegation from any PIR

Revisions: 1

We present an adaptive and non-interactive protocol for verifying arbitrary efficient computations in fixed polynomial time. Our protocol is computationally sound and can be based on any computational PIR scheme, which in turn can be based on standard polynomial-time cryptographic assumptions (e.g. the worst case hardness of polynomial-factor approximation of ... more >>>


TR13-014 | 11th January 2013
Zvika Brakerski, Moni Naor

Fast Algorithms for Interactive Coding

Consider two parties who wish to communicate in order to execute some interactive protocol $\pi$. However, the communication channel between them is noisy: An adversary sees everything that is transmitted over the channel and can change a constant fraction of the bits as he pleases, thus interrupting the execution of ... more >>>


TR12-043 | 16th April 2012
Zvika Brakerski, Yael Tauman Kalai

Efficient Interactive Coding Against Adversarial Noise

Revisions: 1

In this work, we study the fundamental problem of constructing interactive protocols that are robust to noise, a problem that was originally considered in the seminal works of Schulman (FOCS '92, STOC '93), and has recently regained popularity. Robust interactive communication is the interactive analogue of error correcting codes: Given ... more >>>


TR11-111 | 10th August 2011
Zvika Brakerski, Craig Gentry, Vinod Vaikuntanathan

Fully Homomorphic Encryption without Bootstrapping

We present a radically new approach to fully homomorphic encryption (FHE) that dramatically improves performance and bases security on weaker assumptions. A central conceptual contribution in our work is a new way of constructing leveled fully homomorphic encryption schemes (capable of evaluating arbitrary polynomial-size circuits), {\em without Gentry's bootstrapping procedure}.

... more >>>

TR11-109 | 9th August 2011
Zvika Brakerski, Vinod Vaikuntanathan

Efficient Fully Homomorphic Encryption from (Standard) LWE

We present a fully homomorphic encryption scheme that is based solely on the (standard) learning with errors (LWE) assumption. Applying known results on LWE, the security of our scheme is based on the worst-case hardness of ``short vector problems'' on arbitrary lattices.

Our construction improves on previous works in two ... more >>>


TR09-031 | 6th April 2009
Zvika Brakerski, Oded Goldreich

From absolute distinguishability to positive distinguishability


We study methods of converting algorithms that distinguish pairs
of distributions with a gap that has an absolute value that is noticeable
into corresponding algorithms in which the gap is always positive.
Our focus is on designing algorithms that, in addition to the tested string,
obtain a ... more >>>




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