@inproceedings{6526,
abstract = {This paper studies the complexity of estimating Rényi divergences of discrete distributions: p observed from samples and the baseline distribution q known a priori. Extending the results of Acharya et al. (SODA'15) on estimating Rényi entropy, we present improved estimation techniques together with upper and lower bounds on the sample complexity. We show that, contrarily to estimating Rényi entropy where a sublinear (in the alphabet size) number of samples suffices, the sample complexity is heavily dependent on events occurring unlikely in q, and is unbounded in general (no matter what an estimation technique is used). For any divergence of integer order bigger than 1, we provide upper and lower bounds on the number of samples dependent on probabilities of p and q (the lower bounds hold for non-integer orders as well). We conclude that the worst-case sample complexity is polynomial in the alphabet size if and only if the probabilities of q are non-negligible. This gives theoretical insights into heuristics used in the applied literature to handle numerical instability, which occurs for small probabilities of q. Our result shows that they should be handled with care not only because of numerical issues, but also because of a blow up in the sample complexity.},
author = {Skórski, Maciej},
booktitle = {2017 IEEE International Symposium on Information Theory (ISIT)},
isbn = {9781509040964},
location = {Aachen, Germany},
publisher = {IEEE},
title = {{On the complexity of estimating Rènyi divergences}},
doi = {10.1109/isit.2017.8006529},
year = {2017},
}
@inproceedings{6527,
abstract = {A memory-hard function (MHF) ƒn with parameter n can be computed in sequential time and space n. Simultaneously, a high amortized parallel area-time complexity (aAT) is incurred per evaluation. In practice, MHFs are used to limit the rate at which an adversary (using a custom computational device) can evaluate a security sensitive function that still occasionally needs to be evaluated by honest users (using an off-the-shelf general purpose device). The most prevalent examples of such sensitive functions are Key Derivation Functions (KDFs) and password hashing algorithms where rate limits help mitigate off-line dictionary attacks. As the honest users' inputs to these functions are often (low-entropy) passwords special attention is given to a class of side-channel resistant MHFs called iMHFs.
Essentially all iMHFs can be viewed as some mode of operation (making n calls to some round function) given by a directed acyclic graph (DAG) with very low indegree. Recently, a combinatorial property of a DAG has been identified (called "depth-robustness") which results in good provable security for an iMHF based on that DAG. Depth-robust DAGs have also proven useful in other cryptographic applications. Unfortunately, up till now, all known very depth-robust DAGs are impractically complicated and little is known about their exact (i.e. non-asymptotic) depth-robustness both in theory and in practice.
In this work we build and analyze (both formally and empirically) several exceedingly simple and efficient to navigate practical DAGs for use in iMHFs and other applications. For each DAG we:
*Prove that their depth-robustness is asymptotically maximal.
*Prove bounds of at least 3 orders of magnitude better on their exact depth-robustness compared to known bounds for other practical iMHF.
*Implement and empirically evaluate their depth-robustness and aAT against a variety of state-of-the art (and several new) depth-reduction and low aAT attacks.
We find that, against all attacks, the new DAGs perform significantly better in practice than Argon2i, the most widely deployed iMHF in practice.
Along the way we also improve the best known empirical attacks on the aAT of Argon2i by implementing and testing several heuristic versions of a (hitherto purely theoretical) depth-reduction attack. Finally, we demonstrate practicality of our constructions by modifying the Argon2i code base to use one of the new high aAT DAGs. Experimental benchmarks on a standard off-the-shelf CPU show that the new modifications do not adversely affect the impressive throughput of Argon2i (despite seemingly enjoying significantly higher aAT).
},
author = {Alwen, Joel F and Blocki, Jeremiah and Harsha, Ben},
booktitle = {Proceedings of the 2017 ACM SIGSAC Conference on Computer and Communications Security},
isbn = {9781450349468},
location = {Dallas, TX, USA},
pages = {1001--1017},
publisher = {ACM Press},
title = {{Practical graphs for optimal side-channel resistant memory-hard functions}},
doi = {10.1145/3133956.3134031},
year = {2017},
}
@inproceedings{697,
abstract = {De, Trevisan and Tulsiani [CRYPTO 2010] show that every distribution over n-bit strings which has constant statistical distance to uniform (e.g., the output of a pseudorandom generator mapping n-1 to n bit strings), can be distinguished from the uniform distribution with advantage epsilon by a circuit of size O( 2^n epsilon^2). We generalize this result, showing that a distribution which has less than k bits of min-entropy, can be distinguished from any distribution with k bits of delta-smooth min-entropy with advantage epsilon by a circuit of size O(2^k epsilon^2/delta^2). As a special case, this implies that any distribution with support at most 2^k (e.g., the output of a pseudoentropy generator mapping k to n bit strings) can be distinguished from any given distribution with min-entropy k+1 with advantage epsilon by a circuit of size O(2^k epsilon^2). Our result thus shows that pseudoentropy distributions face basically the same non-uniform attacks as pseudorandom distributions. },
author = {Pietrzak, Krzysztof Z and Skórski, Maciej},
issn = {18688969},
location = {Warsaw, Poland},
publisher = {Schloss Dagstuhl - Leibniz-Zentrum für Informatik},
title = {{Non uniform attacks against pseudoentropy}},
doi = {10.4230/LIPIcs.ICALP.2017.39},
volume = {80},
year = {2017},
}
@inproceedings{710,
abstract = {We revisit the problem of estimating entropy of discrete distributions from independent samples, studied recently by Acharya, Orlitsky, Suresh and Tyagi (SODA 2015), improving their upper and lower bounds on the necessary sample size n. For estimating Renyi entropy of order alpha, up to constant accuracy and error probability, we show the following * Upper bounds n = O(1) 2^{(1-1/alpha)H_alpha} for integer alpha>1, as the worst case over distributions with Renyi entropy equal to H_alpha. * Lower bounds n = Omega(1) K^{1-1/alpha} for any real alpha>1, with the constant being an inverse polynomial of the accuracy, as the worst case over all distributions on K elements. Our upper bounds essentially replace the alphabet size by a factor exponential in the entropy, which offers improvements especially in low or medium entropy regimes (interesting for example in anomaly detection). As for the lower bounds, our proof explicitly shows how the complexity depends on both alphabet and accuracy, partially solving the open problem posted in previous works. The argument for upper bounds derives a clean identity for the variance of falling-power sum of a multinomial distribution. Our approach for lower bounds utilizes convex optimization to find a distribution with possibly worse estimation performance, and may be of independent interest as a tool to work with Le Cam’s two point method. },
author = {Obremski, Maciej and Skórski, Maciej},
issn = {18688969},
location = {Berkeley, USA},
publisher = {Schloss Dagstuhl - Leibniz-Zentrum für Informatik},
title = {{Renyi entropy estimation revisited}},
doi = {10.4230/LIPIcs.APPROX-RANDOM.2017.20},
volume = {81},
year = {2017},
}
@phdthesis{838,
abstract = {In this thesis we discuss the exact security of message authentications codes HMAC , NMAC , and PMAC . NMAC is a mode of operation which turns a fixed input-length keyed hash function f into a variable input-length function. A practical single-key variant of NMAC called HMAC is a very popular and widely deployed message authentication code (MAC). PMAC is a block-cipher based mode of operation, which also happens to be the most famous fully parallel MAC. NMAC was introduced by Bellare, Canetti and Krawczyk Crypto’96, who proved it to be a secure pseudorandom function (PRF), and thus also a MAC, under two assumptions. Unfortunately, for many instantiations of HMAC one of them has been found to be wrong. To restore the provable guarantees for NMAC , Bellare [Crypto’06] showed its security without this assumption. PMAC was introduced by Black and Rogaway at Eurocrypt 2002. If instantiated with a pseudorandom permutation over n -bit strings, PMAC constitutes a provably secure variable input-length PRF. For adversaries making q queries, each of length at most ` (in n -bit blocks), and of total length σ ≤ q` , the original paper proves an upper bound on the distinguishing advantage of O ( σ 2 / 2 n ), while the currently best bound is O ( qσ/ 2 n ). In this work we show that this bound is tight by giving an attack with advantage Ω( q 2 `/ 2 n ). In the PMAC construction one initially XORs a mask to every message block, where the mask for the i th block is computed as τ i := γ i · L , where L is a (secret) random value, and γ i is the i -th codeword of the Gray code. Our attack applies more generally to any sequence of γ i ’s which contains a large coset of a subgroup of GF (2 n ). As for NMAC , our first contribution is a simpler and uniform proof: If f is an ε -secure PRF (against q queries) and a δ - non-adaptively secure PRF (against q queries), then NMAC f is an ( ε + `qδ )-secure PRF against q queries of length at most ` blocks each. We also show that this ε + `qδ bound is basically tight by constructing an f for which an attack with advantage `qδ exists. Moreover, we analyze the PRF-security of a modification of NMAC called NI by An and Bellare that avoids the constant rekeying on multi-block messages in NMAC and allows for an information-theoretic analysis. We carry out such an analysis, obtaining a tight `q 2 / 2 c bound for this step, improving over the trivial bound of ` 2 q 2 / 2 c . Finally, we investigate, if the security of PMAC can be further improved by using τ i ’s that are k -wise independent, for k > 1 (the original has k = 1). We observe that the security of PMAC will not increase in general if k = 2, and then prove that the security increases to O ( q 2 / 2 n ), if the k = 4. Due to simple extension attacks, this is the best bound one can hope for, using any distribution on the masks. Whether k = 3 is already sufficient to get this level of security is left as an open problem. Keywords: Message authentication codes, Pseudorandom functions, HMAC, PMAC. },
author = {Rybar, Michal},
pages = {86},
publisher = {IST Austria},
title = {{(The exact security of) Message authentication codes}},
doi = {10.15479/AT:ISTA:th_828},
year = {2017},
}
@article{1187,
abstract = {We construct efficient authentication protocols and message authentication codes (MACs) whose security can be reduced to the learning parity with noise (LPN) problem. Despite a large body of work—starting with the (Formula presented.) protocol of Hopper and Blum in 2001—until now it was not even known how to construct an efficient authentication protocol from LPN which is secure against man-in-the-middle attacks. A MAC implies such a (two-round) protocol.},
author = {Kiltz, Eike and Pietrzak, Krzysztof Z and Venturi, Daniele and Cash, David and Jain, Abhishek},
journal = {Journal of Cryptology},
number = {4},
pages = {1238 -- 1275},
publisher = {Springer},
title = {{Efficient authentication from hard learning problems}},
doi = {10.1007/s00145-016-9247-3},
volume = {30},
year = {2017},
}
@inproceedings{1174,
abstract = {Security of cryptographic applications is typically defined by security games. The adversary, within certain resources, cannot win with probability much better than 0 (for unpredictability applications, like one-way functions) or much better than 1/2 (indistinguishability applications for instance encryption schemes). In so called squared-friendly applications the winning probability of the adversary, for different values of the application secret randomness, is not only close to 0 or 1/2 on average, but also concentrated in the sense that its second central moment is small. The class of squared-friendly applications, which contains all unpredictability applications and many indistinguishability applications, is particularly important for key derivation. Barak et al. observed that for square-friendly applications one can beat the "RT-bound", extracting secure keys with significantly smaller entropy loss. In turn Dodis and Yu showed that in squared-friendly applications one can directly use a "weak" key, which has only high entropy, as a secure key. In this paper we give sharp lower bounds on square security assuming security for "weak" keys. We show that any application which is either (a) secure with weak keys or (b) allows for entropy savings for keys derived by universal hashing, must be square-friendly. Quantitatively, our lower bounds match the positive results of Dodis and Yu and Barak et al. (TCC\'13, CRYPTO\'11) Hence, they can be understood as a general characterization of squared-friendly applications. While the positive results on squared-friendly applications where derived by one clever application of the Cauchy-Schwarz Inequality, for tight lower bounds we need more machinery. In our approach we use convex optimization techniques and some theory of circular matrices.},
author = {Skórski, Maciej},
issn = {18688969},
location = {Hannover, Germany},
publisher = {Schloss Dagstuhl - Leibniz-Zentrum für Informatik},
title = {{Lower bounds on key derivation for square-friendly applications}},
doi = {10.4230/LIPIcs.STACS.2017.57},
volume = {66},
year = {2017},
}
@inproceedings{1175,
abstract = {We study space complexity and time-space trade-offs with a focus not on peak memory usage but on overall memory consumption throughout the computation. Such a cumulative space measure was introduced for the computational model of parallel black pebbling by [Alwen and Serbinenko ’15] as a tool for obtaining results in cryptography. We consider instead the non- deterministic black-white pebble game and prove optimal cumulative space lower bounds and trade-offs, where in order to minimize pebbling time the space has to remain large during a significant fraction of the pebbling. We also initiate the study of cumulative space in proof complexity, an area where other space complexity measures have been extensively studied during the last 10–15 years. Using and extending the connection between proof complexity and pebble games in [Ben-Sasson and Nordström ’08, ’11] we obtain several strong cumulative space results for (even parallel versions of) the resolution proof system, and outline some possible future directions of study of this, in our opinion, natural and interesting space measure.},
author = {Alwen, Joel F and De Rezende, Susanna and Nordstrom, Jakob and Vinyals, Marc},
editor = {Papadimitriou, Christos},
issn = {18688969},
location = {Berkeley, CA, United States},
pages = {38:1--38--21},
publisher = {Schloss Dagstuhl - Leibniz-Zentrum für Informatik},
title = {{Cumulative space in black-white pebbling and resolution}},
doi = {10.4230/LIPIcs.ITCS.2017.38},
volume = {67},
year = {2017},
}
@inproceedings{1176,
abstract = {The algorithm Argon2i-B of Biryukov, Dinu and Khovratovich is currently being considered by the IRTF (Internet Research Task Force) as a new de-facto standard for password hashing. An older version (Argon2i-A) of the same algorithm was chosen as the winner of the recent Password Hashing Competition. An important competitor to Argon2i-B is the recently introduced Balloon Hashing (BH) algorithm of Corrigan-Gibs, Boneh and Schechter. A key security desiderata for any such algorithm is that evaluating it (even using a custom device) requires a large amount of memory amortized across multiple instances. Alwen and Blocki (CRYPTO 2016) introduced a class of theoretical attacks against Argon2i-A and BH. While these attacks yield large asymptotic reductions in the amount of memory, it was not, a priori, clear if (1) they can be extended to the newer Argon2i-B, (2) the attacks are effective on any algorithm for practical parameter ranges (e.g., 1GB of memory) and (3) if they can be effectively instantiated against any algorithm under realistic hardware constrains. In this work we answer all three of these questions in the affirmative for all three algorithms. This is also the first work to analyze the security of Argon2i-B. In more detail, we extend the theoretical attacks of Alwen and Blocki (CRYPTO 2016) to the recent Argon2i-B proposal demonstrating severe asymptotic deficiencies in its security. Next we introduce several novel heuristics for improving the attack's concrete memory efficiency even when on-chip memory bandwidth is bounded. We then simulate our attacks on randomly sampled Argon2i-A, Argon2i-B and BH instances and measure the resulting memory consumption for various practical parameter ranges and for a variety of upperbounds on the amount of parallelism available to the attacker. Finally we describe, implement, and test a new heuristic for applying the Alwen-Blocki attack to functions employing a technique developed by Corrigan-Gibs et al. for improving concrete security of memory-hard functions. We analyze the collected data and show the effects various parameters have on the memory consumption of the attack. In particular, we can draw several interesting conclusions about the level of security provided by these functions. · For the Alwen-Blocki attack to fail against practical memory parameters, Argon2i-B must be instantiated with more than 10 passes on memory - beyond the "paranoid" parameter setting in the current IRTF proposal. · The technique of Corrigan-Gibs for improving security can also be overcome by the Alwen-Blocki attack under realistic hardware constraints. · On a positive note, both the asymptotic and concrete security of Argon2i-B seem to improve on that of Argon2i-A.},
author = {Alwen, Joel F and Blocki, Jeremiah},
isbn = {978-150905761-0},
location = {Paris, France},
publisher = {IEEE},
title = {{Towards practical attacks on Argon2i and balloon hashing}},
doi = {10.1109/EuroSP.2017.47},
year = {2017},
}
@article{1592,
abstract = {A modular approach to constructing cryptographic protocols leads to simple designs but often inefficient instantiations. On the other hand, ad hoc constructions may yield efficient protocols at the cost of losing conceptual simplicity. We suggest a new design paradigm, structure-preserving cryptography, that provides a way to construct modular protocols with reasonable efficiency while retaining conceptual simplicity. A cryptographic scheme over a bilinear group is called structure-preserving if its public inputs and outputs consist of elements from the bilinear groups and their consistency can be verified by evaluating pairing-product equations. As structure-preserving schemes smoothly interoperate with each other, they are useful as building blocks in modular design of cryptographic applications. This paper introduces structure-preserving commitment and signature schemes over bilinear groups with several desirable properties. The commitment schemes include homomorphic, trapdoor and length-reducing commitments to group elements, and the structure-preserving signature schemes are the first ones that yield constant-size signatures on multiple group elements. A structure-preserving signature scheme is called automorphic if the public keys lie in the message space, which cannot be achieved by compressing inputs via a cryptographic hash function, as this would destroy the mathematical structure we are trying to preserve. Automorphic signatures can be used for building certification chains underlying privacy-preserving protocols. Among a vast number of applications of structure-preserving protocols, we present an efficient round-optimal blind-signature scheme and a group signature scheme with an efficient and concurrently secure protocol for enrolling new members.},
author = {Abe, Masayuki and Fuchsbauer, Georg and Groth, Jens and Haralambiev, Kristiyan and Ohkubo, Miyako},
journal = {Journal of Cryptology},
number = {2},
pages = {363 -- 421},
publisher = {Springer},
title = {{Structure preserving signatures and commitments to group elements}},
doi = {10.1007/s00145-014-9196-7},
volume = {29},
year = {2016},
}