@inproceedings{6677, abstract = {The Fiat-Shamir heuristic transforms a public-coin interactive proof into a non-interactive argument, by replacing the verifier with a cryptographic hash function that is applied to the protocol’s transcript. Constructing hash functions for which this transformation is sound is a central and long-standing open question in cryptography. We show that solving the END−OF−METERED−LINE problem is no easier than breaking the soundness of the Fiat-Shamir transformation when applied to the sumcheck protocol. In particular, if the transformed protocol is sound, then any hard problem in #P gives rise to a hard distribution in the class CLS, which is contained in PPAD. Our result opens up the possibility of sampling moderately-sized games for which it is hard to find a Nash equilibrium, by reducing the inversion of appropriately chosen one-way functions to #SAT. Our main technical contribution is a stateful incrementally verifiable procedure that, given a SAT instance over n variables, counts the number of satisfying assignments. This is accomplished via an exponential sequence of small steps, each computable in time poly(n). Incremental verifiability means that each intermediate state includes a sumcheck-based proof of its correctness, and the proof can be updated and verified in time poly(n).}, author = {Choudhuri, Arka Rai and Hubáček, Pavel and Kamath Hosdurg, Chethan and Pietrzak, Krzysztof Z and Rosen, Alon and Rothblum, Guy N.}, booktitle = {Proceedings of the 51st Annual ACM SIGACT Symposium on Theory of Computing - STOC 2019}, isbn = {9781450367059}, location = {Phoenix, AZ, United States}, pages = {1103--1114}, publisher = {ACM Press}, title = {{Finding a Nash equilibrium is no easier than breaking Fiat-Shamir}}, doi = {10.1145/3313276.3316400}, year = {2019}, } @inbook{6726, abstract = {Randomness is an essential part of any secure cryptosystem, but many constructions rely on distributions that are not uniform. This is particularly true for lattice based cryptosystems, which more often than not make use of discrete Gaussian distributions over the integers. For practical purposes it is crucial to evaluate the impact that approximation errors have on the security of a scheme to provide the best possible trade-off between security and performance. Recent years have seen surprising results allowing to use relatively low precision while maintaining high levels of security. A key insight in these results is that sampling a distribution with low relative error can provide very strong security guarantees. Since floating point numbers provide guarantees on the relative approximation error, they seem a suitable tool in this setting, but it is not obvious which sampling algorithms can actually profit from them. While previous works have shown that inversion sampling can be adapted to provide a low relative error (Pöppelmann et al., CHES 2014; Prest, ASIACRYPT 2017), other works have called into question if this is possible for other sampling techniques (Zheng et al., Eprint report 2018/309). In this work, we consider all sampling algorithms that are popular in the cryptographic setting and analyze the relationship of floating point precision and the resulting relative error. We show that all of the algorithms either natively achieve a low relative error or can be adapted to do so.}, author = {Walter, Michael}, booktitle = {Progress in Cryptology – AFRICACRYPT 2019}, editor = {Buchmann, J and Nitaj, A and Rachidi, T}, isbn = {978-3-0302-3695-3}, issn = {0302-9743}, location = {Rabat, Morocco}, pages = {157--180}, publisher = {Springer Nature}, title = {{Sampling the integers with low relative error}}, doi = {10.1007/978-3-030-23696-0_9}, volume = {11627}, year = {2019}, } @phdthesis{83, abstract = {A proof system is a protocol between a prover and a verifier over a common input in which an honest prover convinces the verifier of the validity of true statements. Motivated by the success of decentralized cryptocurrencies, exemplified by Bitcoin, the focus of this thesis will be on proof systems which found applications in some sustainable alternatives to Bitcoin, such as the Spacemint and Chia cryptocurrencies. In particular, we focus on proofs of space and proofs of sequential work. Proofs of space (PoSpace) were suggested as more ecological, economical, and egalitarian alternative to the energy-wasteful proof-of-work mining of Bitcoin. However, the state-of-the-art constructions of PoSpace are based on sophisticated graph pebbling lower bounds, and are therefore complex. Moreover, when these PoSpace are used in cryptocurrencies like Spacemint, miners can only start mining after ensuring that a commitment to their space is already added in a special transaction to the blockchain. Proofs of sequential work (PoSW) are proof systems in which a prover, upon receiving a statement x and a time parameter T, computes a proof which convinces the verifier that T time units had passed since x was received. Whereas Spacemint assumes synchrony to retain some interesting Bitcoin dynamics, Chia requires PoSW with unique proofs, i.e., PoSW in which it is hard to come up with more than one accepting proof for any true statement. In this thesis we construct simple and practically-efficient PoSpace and PoSW. When using our PoSpace in cryptocurrencies, miners can start mining on the fly, like in Bitcoin, and unlike current constructions of PoSW, which either achieve efficient verification of sequential work, or faster-than-recomputing verification of correctness of proofs, but not both at the same time, ours achieve the best of these two worlds.}, author = {Abusalah, Hamza M}, issn = {2663-337X}, pages = {59}, publisher = {Institute of Science and Technology Austria}, title = {{Proof systems for sustainable decentralized cryptocurrencies}}, doi = {10.15479/AT:ISTA:TH_1046}, year = {2018}, } @inproceedings{6941, abstract = {Bitcoin has become the most successful cryptocurrency ever deployed, and its most distinctive feature is that it is decentralized. Its underlying protocol (Nakamoto consensus) achieves this by using proof of work, which has the drawback that it causes the consumption of vast amounts of energy to maintain the ledger. Moreover, Bitcoin mining dynamics have become less distributed over time. Towards addressing these issues, we propose SpaceMint, a cryptocurrency based on proofs of space instead of proofs of work. Miners in SpaceMint dedicate disk space rather than computation. We argue that SpaceMint’s design solves or alleviates several of Bitcoin’s issues: most notably, its large energy consumption. SpaceMint also rewards smaller miners fairly according to their contribution to the network, thus incentivizing more distributed participation. This paper adapts proof of space to enable its use in cryptocurrency, studies the attacks that can arise against a Bitcoin-like blockchain that uses proof of space, and proposes a new blockchain format and transaction types to address these attacks. Our prototype shows that initializing 1 TB for mining takes about a day (a one-off setup cost), and miners spend on average just a fraction of a second per block mined. Finally, we provide a game-theoretic analysis modeling SpaceMint as an extensive game (the canonical game-theoretic notion for games that take place over time) and show that this stylized game satisfies a strong equilibrium notion, thereby arguing for SpaceMint ’s stability and consensus.}, author = {Park, Sunoo and Kwon, Albert and Fuchsbauer, Georg and Gazi, Peter and Alwen, Joel F and Pietrzak, Krzysztof Z}, booktitle = {22nd International Conference on Financial Cryptography and Data Security}, isbn = {9783662583869}, issn = {1611-3349}, location = {Nieuwpoort, Curacao}, pages = {480--499}, publisher = {Springer Nature}, title = {{SpaceMint: A cryptocurrency based on proofs of space}}, doi = {10.1007/978-3-662-58387-6_26}, volume = {10957}, year = {2018}, } @inproceedings{7407, abstract = {Proofs of space (PoS) [Dziembowski et al., CRYPTO'15] are proof systems where a prover can convince a verifier that he "wastes" disk space. PoS were introduced as a more ecological and economical replacement for proofs of work which are currently used to secure blockchains like Bitcoin. In this work we investigate extensions of PoS which allow the prover to embed useful data into the dedicated space, which later can be recovered. Our first contribution is a security proof for the original PoS from CRYPTO'15 in the random oracle model (the original proof only applied to a restricted class of adversaries which can store a subset of the data an honest prover would store). When this PoS is instantiated with recent constructions of maximally depth robust graphs, our proof implies basically optimal security. As a second contribution we show three different extensions of this PoS where useful data can be embedded into the space required by the prover. Our security proof for the PoS extends (non-trivially) to these constructions. We discuss how some of these variants can be used as proofs of catalytic space (PoCS), a notion we put forward in this work, and which basically is a PoS where most of the space required by the prover can be used to backup useful data. Finally we discuss how one of the extensions is a candidate construction for a proof of replication (PoR), a proof system recently suggested in the Filecoin whitepaper. }, author = {Pietrzak, Krzysztof Z}, booktitle = {10th Innovations in Theoretical Computer Science Conference (ITCS 2019)}, isbn = {978-3-95977-095-8}, issn = {1868-8969}, location = {San Diego, CA, United States}, pages = {59:1--59:25}, publisher = {Schloss Dagstuhl - Leibniz-Zentrum für Informatik}, title = {{Proofs of catalytic space}}, doi = {10.4230/LIPICS.ITCS.2019.59}, volume = {124}, year = {2018}, } @inproceedings{193, abstract = {We show attacks on five data-independent memory-hard functions (iMHF) that were submitted to the password hashing competition (PHC). Informally, an MHF is a function which cannot be evaluated on dedicated hardware, like ASICs, at significantly lower hardware and/or energy cost than evaluating a single instance on a standard single-core architecture. Data-independent means the memory access pattern of the function is independent of the input; this makes iMHFs harder to construct than data-dependent ones, but the latter can be attacked by various side-channel attacks. Following [Alwen-Blocki'16], we capture the evaluation of an iMHF as a directed acyclic graph (DAG). The cumulative parallel pebbling complexity of this DAG is a measure for the hardware cost of evaluating the iMHF on an ASIC. Ideally, one would like the complexity of a DAG underlying an iMHF to be as close to quadratic in the number of nodes of the graph as possible. Instead, we show that (the DAGs underlying) the following iMHFs are far from this bound: Rig.v2, TwoCats and Gambit each having an exponent no more than 1.75. Moreover, we show that the complexity of the iMHF modes of the PHC finalists Pomelo and Lyra2 have exponents at most 1.83 and 1.67 respectively. To show this we investigate a combinatorial property of each underlying DAG (called its depth-robustness. By establishing upper bounds on this property we are then able to apply the general technique of [Alwen-Block'16] for analyzing the hardware costs of an iMHF.}, author = {Alwen, Joel F and Gazi, Peter and Kamath Hosdurg, Chethan and Klein, Karen and Osang, Georg F and Pietrzak, Krzysztof Z and Reyzin, Lenoid and Rolinek, Michal and Rybar, Michal}, booktitle = {Proceedings of the 2018 on Asia Conference on Computer and Communication Security}, location = {Incheon, Republic of Korea}, pages = {51 -- 65}, publisher = {ACM}, title = {{On the memory hardness of data independent password hashing functions}}, doi = {10.1145/3196494.3196534}, year = {2018}, } @article{5980, abstract = {The problem of private set-intersection (PSI) has been traditionally treated as an instance of the more general problem of multi-party computation (MPC). Consequently, in order to argue security, or compose these protocols one has to rely on the general theory that was developed for the purpose of MPC. The pursuit of efficient protocols, however, has resulted in designs that exploit properties pertaining to PSI. In almost all practical applications where a PSI protocol is deployed, it is expected to be executed multiple times, possibly on related inputs. In this work we initiate a dedicated study of PSI in the multi-interaction (MI) setting. In this model a server sets up the common system parameters and executes set-intersection multiple times with potentially different clients. We discuss a few attacks that arise when protocols are naïvely composed in this manner and, accordingly, craft security definitions for the MI setting and study their inter-relation. Finally, we suggest a set of protocols that are MI-secure, at the same time almost as efficient as their parent, stand-alone, protocols.}, author = {Chatterjee, Sanjit and Kamath Hosdurg, Chethan and Kumar, Vikas}, journal = {American Institute of Mathematical Sciences}, number = {1}, pages = {17--47}, publisher = {AIMS}, title = {{Private set-intersection with common set-up}}, doi = {10.3934/amc.2018002}, volume = {12}, year = {2018}, } @article{10286, abstract = {In this paper, we evaluate clock signals generated in ring oscillators and self-timed rings and the way their jitter can be transformed into random numbers. We show that counting the periods of the jittery clock signal produces random numbers of significantly better quality than the methods in which the jittery signal is simply sampled (the case in almost all current methods). Moreover, we use the counter values to characterize and continuously monitor the source of randomness. However, instead of using the widely used statistical variance, we propose to use Allan variance to do so. There are two main advantages: Allan variance is insensitive to low frequency noises such as flicker noise that are known to be autocorrelated and significantly less circuitry is required for its computation than that used to compute commonly used variance. We also show that it is essential to use a differential principle of randomness extraction from the jitter based on the use of two identical oscillators to avoid autocorrelations originating from external and internal global jitter sources and that this fact is valid for both kinds of rings. Last but not least, we propose a method of statistical testing based on high order Markov model to show the reduced dependencies when the proposed randomness extraction is applied.}, author = {Allini, Elie Noumon and Skórski, Maciej and Petura, Oto and Bernard, Florent and Laban, Marek and Fischer, Viktor}, issn = {2569-2925}, journal = {IACR Transactions on Cryptographic Hardware and Embedded Systems}, number = {3}, pages = {214--242}, publisher = {International Association for Cryptologic Research}, title = {{Evaluation and monitoring of free running oscillators serving as source of randomness}}, doi = {10.13154/tches.v2018.i3.214-242}, volume = {2018}, year = {2018}, } @article{107, abstract = {We introduce the notion of “non-malleable codes” which relaxes the notion of error correction and error detection. Informally, a code is non-malleable if the message contained in a modified codeword is either the original message, or a completely unrelated value. In contrast to error correction and error detection, non-malleability can be achieved for very rich classes of modifications. We construct an efficient code that is non-malleable with respect to modifications that affect each bit of the codeword arbitrarily (i.e., leave it untouched, flip it, or set it to either 0 or 1), but independently of the value of the other bits of the codeword. Using the probabilistic method, we also show a very strong and general statement: there exists a non-malleable code for every “small enough” family F of functions via which codewords can be modified. Although this probabilistic method argument does not directly yield efficient constructions, it gives us efficient non-malleable codes in the random-oracle model for very general classes of tampering functions—e.g., functions where every bit in the tampered codeword can depend arbitrarily on any 99% of the bits in the original codeword. As an application of non-malleable codes, we show that they provide an elegant algorithmic solution to the task of protecting functionalities implemented in hardware (e.g., signature cards) against “tampering attacks.” In such attacks, the secret state of a physical system is tampered, in the hopes that future interaction with the modified system will reveal some secret information. This problem was previously studied in the work of Gennaro et al. in 2004 under the name “algorithmic tamper proof security” (ATP). We show that non-malleable codes can be used to achieve important improvements over the prior work. In particular, we show that any functionality can be made secure against a large class of tampering attacks, simply by encoding the secret state with a non-malleable code while it is stored in memory.}, author = {Dziembowski, Stefan and Pietrzak, Krzysztof Z and Wichs, Daniel}, journal = {Journal of the ACM}, number = {4}, publisher = {ACM}, title = {{Non-malleable codes}}, doi = {10.1145/3178432}, volume = {65}, year = {2018}, } @inproceedings{108, abstract = {Universal hashing found a lot of applications in computer science. In cryptography the most important fact about universal families is the so called Leftover Hash Lemma, proved by Impagliazzo, Levin and Luby. In the language of modern cryptography it states that almost universal families are good extractors. In this work we provide a somewhat surprising characterization in the opposite direction. Namely, every extractor with sufficiently good parameters yields a universal family on a noticeable fraction of its inputs. Our proof technique is based on tools from extremal graph theory applied to the \'collision graph\' induced by the extractor, and may be of independent interest. We discuss possible applications to the theory of randomness extractors and non-malleable codes.}, author = {Obremski, Marciej and Skorski, Maciej}, location = {Vail, CO, USA}, publisher = {IEEE}, title = {{Inverted leftover hash lemma}}, doi = {10.1109/ISIT.2018.8437654}, volume = {2018}, year = {2018}, } @inproceedings{298, abstract = {Memory-hard functions (MHF) are functions whose evaluation cost is dominated by memory cost. MHFs are egalitarian, in the sense that evaluating them on dedicated hardware (like FPGAs or ASICs) is not much cheaper than on off-the-shelf hardware (like x86 CPUs). MHFs have interesting cryptographic applications, most notably to password hashing and securing blockchains. Alwen and Serbinenko [STOC’15] define the cumulative memory complexity (cmc) of a function as the sum (over all time-steps) of the amount of memory required to compute the function. They advocate that a good MHF must have high cmc. Unlike previous notions, cmc takes into account that dedicated hardware might exploit amortization and parallelism. Still, cmc has been critizised as insufficient, as it fails to capture possible time-memory trade-offs; as memory cost doesn’t scale linearly, functions with the same cmc could still have very different actual hardware cost. In this work we address this problem, and introduce the notion of sustained-memory complexity, which requires that any algorithm evaluating the function must use a large amount of memory for many steps. We construct functions (in the parallel random oracle model) whose sustained-memory complexity is almost optimal: our function can be evaluated using n steps and O(n/log(n)) memory, in each step making one query to the (fixed-input length) random oracle, while any algorithm that can make arbitrary many parallel queries to the random oracle, still needs Ω(n/log(n)) memory for Ω(n) steps. As has been done for various notions (including cmc) before, we reduce the task of constructing an MHFs with high sustained-memory complexity to proving pebbling lower bounds on DAGs. Our main technical contribution is the construction is a family of DAGs on n nodes with constant indegree with high “sustained-space complexity”, meaning that any parallel black-pebbling strategy requires Ω(n/log(n)) pebbles for at least Ω(n) steps. Along the way we construct a family of maximally “depth-robust” DAGs with maximum indegree O(logn) , improving upon the construction of Mahmoody et al. [ITCS’13] which had maximum indegree O(log2n⋅}, author = {Alwen, Joel F and Blocki, Jeremiah and Pietrzak, Krzysztof Z}, location = {Tel Aviv, Israel}, pages = {99 -- 130}, publisher = {Springer}, title = {{Sustained space complexity}}, doi = {10.1007/978-3-319-78375-8_4}, volume = {10821}, year = {2018}, } @inproceedings{300, abstract = {We introduce a formal quantitative notion of “bit security” for a general type of cryptographic games (capturing both decision and search problems), aimed at capturing the intuition that a cryptographic primitive with k-bit security is as hard to break as an ideal cryptographic function requiring a brute force attack on a k-bit key space. Our new definition matches the notion of bit security commonly used by cryptographers and cryptanalysts when studying search (e.g., key recovery) problems, where the use of the traditional definition is well established. However, it produces a quantitatively different metric in the case of decision (indistinguishability) problems, where the use of (a straightforward generalization of) the traditional definition is more problematic and leads to a number of paradoxical situations or mismatches between theoretical/provable security and practical/common sense intuition. Key to our new definition is to consider adversaries that may explicitly declare failure of the attack. We support and justify the new definition by proving a number of technical results, including tight reductions between several standard cryptographic problems, a new hybrid theorem that preserves bit security, and an application to the security analysis of indistinguishability primitives making use of (approximate) floating point numbers. This is the first result showing that (standard precision) 53-bit floating point numbers can be used to achieve 100-bit security in the context of cryptographic primitives with general indistinguishability-based security definitions. Previous results of this type applied only to search problems, or special types of decision problems.}, author = {Micciancio, Daniele and Walter, Michael}, location = {Tel Aviv, Israel}, pages = {3 -- 28}, publisher = {Springer}, title = {{On the bit security of cryptographic primitives}}, doi = {10.1007/978-3-319-78381-9_1}, volume = {10820}, year = {2018}, } @inproceedings{302, abstract = {At ITCS 2013, Mahmoody, Moran and Vadhan [MMV13] introduce and construct publicly verifiable proofs of sequential work, which is a protocol for proving that one spent sequential computational work related to some statement. The original motivation for such proofs included non-interactive time-stamping and universally verifiable CPU benchmarks. A more recent application, and our main motivation, are blockchain designs, where proofs of sequential work can be used – in combination with proofs of space – as a more ecological and economical substitute for proofs of work which are currently used to secure Bitcoin and other cryptocurrencies. The construction proposed by [MMV13] is based on a hash function and can be proven secure in the random oracle model, or assuming inherently sequential hash-functions, which is a new standard model assumption introduced in their work. In a proof of sequential work, a prover gets a “statement” χ, a time parameter N and access to a hash-function H, which for the security proof is modelled as a random oracle. Correctness requires that an honest prover can make a verifier accept making only N queries to H, while soundness requires that any prover who makes the verifier accept must have made (almost) N sequential queries to H. Thus a solution constitutes a proof that N time passed since χ was received. Solutions must be publicly verifiable in time at most polylogarithmic in N. The construction of [MMV13] is based on “depth-robust” graphs, and as a consequence has rather poor concrete parameters. But the major drawback is that the prover needs not just N time, but also N space to compute a proof. In this work we propose a proof of sequential work which is much simpler, more efficient and achieves much better concrete bounds. Most importantly, the space required can be as small as log (N) (but we get better soundness using slightly more memory than that). An open problem stated by [MMV13] that our construction does not solve either is achieving a “unique” proof, where even a cheating prover can only generate a single accepting proof. This property would be extremely useful for applications to blockchains.}, author = {Cohen, Bram and Pietrzak, Krzysztof Z}, location = {Tel Aviv, Israel}, pages = {451 -- 467}, publisher = {Springer}, title = {{Simple proofs of sequential work}}, doi = {10.1007/978-3-319-78375-8_15}, volume = {10821}, year = {2018}, } @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}, issn = {2663-337X}, pages = {86}, publisher = {Institute of Science and Technology Austria}, title = {{(The exact security of) Message authentication codes}}, doi = {10.15479/AT:ISTA:th_828}, 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}, } @inproceedings{559, abstract = {Proofs of space (PoS) were suggested as more ecological and economical alternative to proofs of work, which are currently used in blockchain designs like Bitcoin. The existing PoS are based on rather sophisticated graph pebbling lower bounds. Much simpler and in several aspects more efficient schemes based on inverting random functions have been suggested, but they don’t give meaningful security guarantees due to existing time-memory trade-offs. In particular, Hellman showed that any permutation over a domain of size N can be inverted in time T by an algorithm that is given S bits of auxiliary information whenever (Formula presented). For functions Hellman gives a weaker attack with S2· T≈ N2 (e.g., S= T≈ N2/3). To prove lower bounds, one considers an adversary who has access to an oracle f: [ N] → [N] and can make T oracle queries. The best known lower bound is S· T∈ Ω(N) and holds for random functions and permutations. We construct functions that provably require more time and/or space to invert. Specifically, for any constant k we construct a function [N] → [N] that cannot be inverted unless Sk· T∈ Ω(Nk) (in particular, S= T≈ (Formula presented). Our construction does not contradict Hellman’s time-memory trade-off, because it cannot be efficiently evaluated in forward direction. However, its entire function table can be computed in time quasilinear in N, which is sufficient for the PoS application. Our simplest construction is built from a random function oracle g: [N] × [N] → [ N] and a random permutation oracle f: [N] → N] and is defined as h(x) = g(x, x′) where f(x) = π(f(x′)) with π being any involution without a fixed point, e.g. flipping all the bits. For this function we prove that any adversary who gets S bits of auxiliary information, makes at most T oracle queries, and inverts h on an ϵ fraction of outputs must satisfy S2· T∈ Ω(ϵ2N2).}, author = {Abusalah, Hamza M and Alwen, Joel F and Cohen, Bram and Khilko, Danylo and Pietrzak, Krzysztof Z and Reyzin, Leonid}, isbn = {978-331970696-2}, location = {Hong Kong, China}, pages = {357 -- 379}, publisher = {Springer}, title = {{Beyond Hellman’s time-memory trade-offs with applications to proofs of space}}, doi = {10.1007/978-3-319-70697-9_13}, volume = {10625}, year = {2017}, } @inproceedings{605, abstract = {Position based cryptography (PBC), proposed in the seminal work of Chandran, Goyal, Moriarty, and Ostrovsky (SIAM J. Computing, 2014), aims at constructing cryptographic schemes in which the identity of the user is his geographic position. Chandran et al. construct PBC schemes for secure positioning and position-based key agreement in the bounded-storage model (Maurer, J. Cryptology, 1992). Apart from bounded memory, their security proofs need a strong additional restriction on the power of the adversary: he cannot compute joint functions of his inputs. Removing this assumption is left as an open problem. We show that an answer to this question would resolve a long standing open problem in multiparty communication complexity: finding a function that is hard to compute with low communication complexity in the simultaneous message model, but easy to compute in the fully adaptive model. On a more positive side: we also show some implications in the other direction, i.e.: we prove that lower bounds on the communication complexity of certain multiparty problems imply existence of PBC primitives. Using this result we then show two attractive ways to “bypass” our hardness result: the first uses the random oracle model, the second weakens the locality requirement in the bounded-storage model to online computability. The random oracle construction is arguably one of the simplest proposed so far in this area. Our results indicate that constructing improved provably secure protocols for PBC requires a better understanding of multiparty communication complexity. This is yet another example where negative results in one area (in our case: lower bounds in multiparty communication complexity) can be used to construct secure cryptographic schemes.}, author = {Brody, Joshua and Dziembowski, Stefan and Faust, Sebastian and Pietrzak, Krzysztof Z}, editor = {Kalai, Yael and Reyzin, Leonid}, isbn = {978-331970499-9}, location = {Baltimore, MD, United States}, pages = {56 -- 81}, publisher = {Springer}, title = {{Position based cryptography and multiparty communication complexity}}, doi = {10.1007/978-3-319-70500-2_3}, volume = {10677}, year = {2017}, } @inproceedings{609, abstract = {Several cryptographic schemes and applications are based on functions that are both reasonably efficient to compute and moderately hard to invert, including client puzzles for Denial-of-Service protection, password protection via salted hashes, or recent proof-of-work blockchain systems. Despite their wide use, a definition of this concept has not yet been distilled and formalized explicitly. Instead, either the applications are proven directly based on the assumptions underlying the function, or some property of the function is proven, but the security of the application is argued only informally. The goal of this work is to provide a (universal) definition that decouples the efforts of designing new moderately hard functions and of building protocols based on them, serving as an interface between the two. On a technical level, beyond the mentioned definitions, we instantiate the model for four different notions of hardness. We extend the work of Alwen and Serbinenko (STOC 2015) by providing a general tool for proving security for the first notion of memory-hard functions that allows for provably secure applications. The tool allows us to recover all of the graph-theoretic techniques developed for proving security under the older, non-composable, notion of security used by Alwen and Serbinenko. As an application of our definition of moderately hard functions, we prove the security of two different schemes for proofs of effort (PoE). We also formalize and instantiate the concept of a non-interactive proof of effort (niPoE), in which the proof is not bound to a particular communication context but rather any bit-string chosen by the prover.}, author = {Alwen, Joel F and Tackmann, Björn}, editor = {Kalai, Yael and Reyzin, Leonid}, isbn = {978-331970499-9}, location = {Baltimore, MD, United States}, pages = {493 -- 526}, publisher = {Springer}, title = {{Moderately hard functions: Definition, instantiations, and applications}}, doi = {10.1007/978-3-319-70500-2_17}, volume = {10677}, year = {2017}, } @article{6196, abstract = {PMAC is a simple and parallel block-cipher mode of operation, which was introduced by Black and Rogaway at Eurocrypt 2002. If instantiated with a (pseudo)random permutation over n-bit strings, PMAC constitutes a provably secure variable input-length (pseudo)random function. For adversaries making q queries, each of length at most l (in n-bit blocks), and of total length σ ≤ ql, the original paper proves an upper bound on the distinguishing advantage of Ο(σ2/2n), while the currently best bound is Ο (qσ/2n).In this work we show that this bound is tight by giving an attack with advantage Ω (q2l/2n). In the PMAC construction one initially XORs a mask to every message block, where the mask for the ith block is computed as τi := γi·L, where L is a (secret) random value, and γi is the i-th codeword of the Gray code. Our attack applies more generally to any sequence of γi’s which contains a large coset of a subgroup of GF(2n). We then investigate if the security of PMAC can be further improved by using τi’s that are k-wise independent, for k > 1 (the original distribution is only 1-wise independent). We observe that the security of PMAC will not increase in general, even if the masks are chosen from a 2-wise independent distribution, and then prove that the security increases to O(q<2/2n), if the τi are 4-wise independent. Due to simple extension attacks, this is the best bound one can hope for, using any distribution on the masks. Whether 3-wise independence is already sufficient to get this level of security is left as an open problem.}, author = {Gazi, Peter and Pietrzak, Krzysztof Z and Rybar, Michal}, issn = {2519-173X}, journal = {IACR Transactions on Symmetric Cryptology}, number = {2}, pages = {145--161}, publisher = {Ruhr University Bochum}, title = {{The exact security of PMAC}}, doi = {10.13154/TOSC.V2016.I2.145-161}, volume = {2016}, year = {2017}, }