Is it “safe” to release aggregate statistics from a database of sensitive information on individuals? Evidence suggests that even seemingly innocuous statistical releases can fatally compromise an individual’s privacy, especially in the presence of auxiliary information about the individual (see this paper by Homer et al. for a recent example). How might we then get … Continue reading Privacy-Preserving Data Analysis and Computational Learning: A Match made in Heaven

Part II. For Part I see here. Having largely reproduced the main results of the Lenstra et al. paper, the next research question became identifying the root cause or causes of this vulnerability. There was no shortage of explanations put forward shortly after the paper was released, and we were able to critically examine some of … Continue reading Factoring RSA Moduli. Part II.

In my first post on this blog I would like to expand its range of topics to applied cryptography and share some interesting new findings that so far have not been reported anywhere else except a Eurocrypt'12 rump session talk. On Valentine's Day earlier this year, the paper with a somewhat enigmatic title ``Ron was … Continue reading Factoring RSA Moduli. Part I.

The first question we'd like to answer is this: which is the monotone, balanced, transitive Boolean function which is least sensitive to bit-flips? We know that Majority is the worst possible with $latex NS( Maj) = \Theta(1/\sqrt{n})$. The new champion turns out to be the Tribes function first studied by Ben-Or and Linial. $latex Tribes_{s,w}$ … Continue reading When did Majority become the stablest? (Part 2)

The fireworks happening over at Ryan O'Donnell's blog reminded me of something that always puzzles me: Is Majority the Stablest? Or the Unstablest? Consider the class of all monotone, balanced Boolean functions $latex f:\{-1,1\}^n \rightarrow \{-1,1\}$. We define the noise sensitivity $latex NS(f)$ of a function $latex f$ as $latex NS(f) = P_{x,e}[f(x) \neq f( … Continue reading When did Majority become the stablest?

Every year the ACM gives out an award for the best doctoral dissertation, as well as up to 3 honorable mentions. This year, both honorable mentions were given to CS theorists: Aleksander Madry and David Steurer (the dissertation award was given to Seth Cooper for his work on protein folding games). Both Aleksander's and David's … Continue reading Aleksander Madry and David Steurer win ACM honorable mention

Guest post by Boaz Barak and Zvika Brakerski (part 2) In the previous post, we demonstrated the versatility of fully homomorphic encryption and its applicability for multiple applications. In this post we will demonstrate (not too painfully, we hope) how fully homomorphic encryption is constructed. Our goal is to present the simplest solution that (we … Continue reading Building the Swiss Army Knife

Guest post by Boaz Barak and Zvika Brakerski In 2009, Craig Gentry shook the world of cryptography by presenting a construction of a Fully Homomorphic Encryption Scheme (FHE). In this post and the next one, we will explain what FHE is, why cryptographers are so excited about it, and how its construction works. There is … Continue reading The Swiss Army Knife of Cryptography

This post has some tidbits regarding the problem of computing a 'fingerprint' of a long sequence of characters, often called 'string hashing'. Most of the results I will describe are quite old, but they are scattered upon several papers, so I think it is worthwhile to have a post where they are  put together. This … Continue reading How to collapse the universe?