arXiv subjects

Maciej Skorski

Publications and source records attributed to Maciej Skorski.

42 records · Page 3Linked to original sources

arXiv2016

Simulating Auxiliary Inputs, Revisited

For any pair $(X,Z)$ of correlated random variables we can think of $Z$ as a randomized function of $X$. Provided that $Z$ is short, one can make this function computationally efficient by allowing it to be only approximately correct. In folklore this problem is known as \emph{simulating auxiliary inputs}. This idea of simulating auxiliary information turns out to be a powerful tool in computer science, finding applications in complexity theory, cryptography, pseudorandomness and zero-knowledge. In this paper we revisit this problem, achieving the following results: \begin{enumerate}[(a)] We discuss and compare efficiency of known results, finding the flaw in the best known bound claimed in the TCC'14 paper "How to Fake Auxiliary Inputs". We present a novel boosting algorithm for constructing the simulator. Our technique essentially fixes the flaw. This boosting proof is of independent interest, as it shows how to handle "negative mass" issues when constructing probability measures in descent algorithms. Our bounds are much better than bounds known so far. To make the simulator $(s,ε)$-indistinguishable we need the complexity $O\left(s\cdot 2^{5\ell}ε^{-2}\right)$ in time/circuit size, which is better by a factor $ε^{-2}$ compared to previous bounds. In particular, with our technique we (finally) get meaningful provable security for the EUROCRYPT'09 leakage-resilient stream cipher instantiated with a standard 256-bit block cipher, like $\mathsf{AES256}$.

cs.CR↗

arXiv2015

A New Approximate Min-Max Theorem with Applications in Cryptography

We propose a novel proof technique that can be applied to attack a broad class of problems in computational complexity, when switching the order of universal and existential quantifiers is helpful. Our approach combines the standard min-max theorem and convex approximation techniques, offering quantitative improvements over the standard way of using min-max theorems as well as more concise and elegant proofs.

cs.CR↗

arXiv2015

A Time-Success Ratio Analysis of wPRF-based Leakage-Resilient Stream Ciphers

Weak pseudorandom functions (wPRFs) found an important application as main building blocks for leakage-resilient ciphers (EUROCRYPT'09). Several security bounds, based on different techniques, were given to these stream ciphers. The security loss in these reduction-based proofs is always polynomial, but has not been studied in detail. The aim of this paper is twofold. First, we present a clear comparison of quantitatively different security bounds in the literature. Second, we revisit the current proof techniques and answer the natural question of how far we are from meaningful and provable security guarantees, when instantiating weak PRFs with standard primitives (block ciphers or hash functions). In particular, we demonstrate a flaw in the recent (TCC'14) analysis of the EUROCRYPT'09 stream cipher, which means that we still don't know if it offers provable security when instantiated with a standard block cipher. Our approach is a \emph{time-to-success Ratio} analysis, a universal measure introduced by Luby, which allow us to compare different security bounds.

cs.CR↗

arXiv2015

Condensed Unpredictability

We consider the task of deriving a key with high HILL entropy from an unpredictable source. Previous to this work, the only known way to transform unpredictability into a key that was $\eps$ indistinguishable from having min-entropy was via pseudorandomness, for example by Goldreich-Levin (GL) hardcore bits. This approach has the inherent limitation that from a source with $k$ bits of unpredictability entropy one can derive a key of length (and thus HILL entropy) at most $k-2\log(1/ε)$ bits. In many settings, e.g. when dealing with biometric data, such a $2\log(1/ε)$ bit entropy loss in not an option. Our main technical contribution is a theorem that states that in the high entropy regime, unpredictability implies HILL entropy. The loss in circuit size in this argument is exponential in the entropy gap $d$. To overcome the above restriction, we investigate if it's possible to first "condense" unpredictability entropy and make the entropy gap small. We show that any source with $k$ bits of unpredictability can be condensed into a source of length $k$ with $k-3$ bits of unpredictability entropy. Our condenser simply "abuses" the GL construction and derives a $k$ bit key from a source with $k$ bits of unpredicatibily. The original GL theorem implies nothing when extracting that many bits, but we show that in this regime, GL still behaves like a "condenser" for unpredictability. This result comes with two caveats (1) the loss in circuit size is exponential in $k$ and (2) we require that the source we start with has \emph{no} HILL entropy (equivalently, one can efficiently check if a guess is correct). We leave it as an intriguing open problem to overcome these restrictions or to prove they're inherent.

cs.CR↗

arXiv2015

Lower bounds on $q$-wise independence tails and applications to min-entropy condensers

We present novel and sharp lower bounds for higher load moments in the classical problem of mapping $M$ balls into $N$ bins by $q$-universal hashing, specialized to the case when $M=N$. As a corollary we prove a tight counterpart for the result about min-entropy condensers due to Dodis, Pietrzak and Wichs (CRYPTO'14), which has found important applications in key derivation. It states that condensing $k$ bits of min-entropy into a $k$-bit string $ε$-close to almost full min-entropy (precisely $ k-\log\log(1/ε)$ bits of entropy) can be achieved by the use of $q$-independent hashing with $q= \log(1/ε)$. We prove that when given a source of min-entropy $k$ and aiming at entropy loss $\ell = \log\log (1/ε) - 3$, the independence level $q=(1-o(1))\log(1/ε)$ is necessary (for small values of $ε$), which almost matches the positive result. Besides these asymptotic bounds, we provide clear hard bounds in terms of Bell numbers and some numerical examples. Our technique is based on an explicit representation of the load moments in terms of Stirling numbers, some asymptotic estimates on Stirling numbers and a tricky application of the Paley-Zygmund inequality. \keywords{ min-entropy condensers, key derivation, balls and bins hashing, anti-concentration inequalities }

cs.CR↗

arXiv2013

Modulus Computational Entropy

The so-called {\em leakage-chain rule} is a very important tool used in many security proofs. It gives an upper bound on the entropy loss of a random variable $X$ in case the adversary who having already learned some random variables $Z_{1},\ldots,Z_{\ell}$ correlated with $X$, obtains some further information $Z_{\ell+1}$ about $X$. Analogously to the information-theoretic case, one might expect that also for the \emph{computational} variants of entropy the loss depends only on the actual leakage, i.e. on $Z_{\ell+1}$. Surprisingly, Krenn et al.\ have shown recently that for the most commonly used definitions of computational entropy this holds only if the computational quality of the entropy deteriorates exponentially in $|(Z_{1},\ldots,Z_{\ell})|$. This means that the current standard definitions of computational entropy do not allow to fully capture leakage that occurred "in the past", which severely limits the applicability of this notion. As a remedy for this problem we propose a slightly stronger definition of the computational entropy, which we call the \emph{modulus computational entropy}, and use it as a technical tool that allows us to prove a desired chain rule that depends only on the actual leakage and not on its history. Moreover, we show that the modulus computational entropy unifies other,sometimes seemingly unrelated, notions already studied in the literature in the context of information leakage and chain rules. Our results indicate that the modulus entropy is, up to now, the weakest restriction that guarantees that the chain rule for the computational entropy works. As an example of application we demonstrate a few interesting cases where our restricted definition is fulfilled and the chain rule holds.

cs.IT↗