@inproceedings{1652,
abstract = {We develop new theoretical tools for proving lower-bounds on the (amortized) complexity of certain functions in models of parallel computation. We apply the tools to construct a class of functions with high amortized memory complexity in the parallel Random Oracle Model (pROM); a variant of the standard ROM allowing for batches of simultaneous queries. In particular we obtain a new, more robust, type of Memory-Hard Functions (MHF); a security primitive which has recently been gaining acceptance in practice as an effective means of countering brute-force attacks on security relevant functions. Along the way we also demonstrate an important shortcoming of previous definitions of MHFs and give a new definition addressing the problem. The tools we develop represent an adaptation of the powerful pebbling paradigm (initially introduced by Hewitt and Paterson [HP70] and Cook [Coo73]) to a simple and intuitive parallel setting. We define a simple pebbling game Gp over graphs which aims to abstract parallel computation in an intuitive way. As a conceptual contribution we define a measure of pebbling complexity for graphs called cumulative complexity (CC) and show how it overcomes a crucial shortcoming (in the parallel setting) exhibited by more traditional complexity measures used in the past. As a main technical contribution we give an explicit construction of a constant in-degree family of graphs whose CC in Gp approaches maximality to within a polylogarithmic factor for any graph of equal size (analogous to the graphs of Tarjan et. al. [PTC76, LT82] for sequential pebbling games). Finally, for a given graph G and related function fG, we derive a lower-bound on the amortized memory complexity of fG in the pROM in terms of the CC of G in the game Gp.},
author = {Alwen, Joel F and Serbinenko, Vladimir},
booktitle = {Proceedings of the 47th annual ACM symposium on Theory of computing},
location = {Portland, OR, United States},
pages = {595 -- 603},
publisher = {ACM},
title = {{High parallel complexity graphs and memory-hard functions}},
doi = {10.1145/2746539.2746622},
year = {2015},
}
@inproceedings{1654,
abstract = {HMAC and its variant NMAC are the most popular approaches to deriving a MAC (and more generally, a PRF) from a cryptographic hash function. Despite nearly two decades of research, their exact security still remains far from understood in many different contexts. Indeed, recent works have re-surfaced interest for {\em generic} attacks, i.e., attacks that treat the compression function of the underlying hash function as a black box.
Generic security can be proved in a model where the underlying compression function is modeled as a random function -- yet, to date, the question of proving tight, non-trivial bounds on the generic security of HMAC/NMAC even as a PRF remains a challenging open question.
In this paper, we ask the question of whether a small modification to HMAC and NMAC can allow us to exactly characterize the security of the resulting constructions, while only incurring little penalty with respect to efficiency. To this end, we present simple variants of NMAC and HMAC, for which we prove tight bounds on the generic PRF security, expressed in terms of numbers of construction and compression function queries necessary to break the construction. All of our constructions are obtained via a (near) {\em black-box} modification of NMAC and HMAC, which can be interpreted as an initial step of key-dependent message pre-processing.
While our focus is on PRF security, a further attractive feature of our new constructions is that they clearly defeat all recent generic attacks against properties such as state recovery and universal forgery. These exploit properties of the so-called ``functional graph'' which are not directly accessible in our new constructions. },
author = {Gazi, Peter and Pietrzak, Krzysztof Z and Tessaro, Stefano},
location = {Auckland, New Zealand},
pages = {85 -- 109},
publisher = {Springer},
title = {{Generic security of NMAC and HMAC with input whitening}},
doi = {10.1007/978-3-662-48800-3_4},
volume = {9453},
year = {2015},
}
@inproceedings{1668,
abstract = {We revisit the security (as a pseudorandom permutation) of cascading-based constructions for block-cipher key-length extension. Previous works typically considered the extreme case where the adversary is given the entire codebook of the construction, the only complexity measure being the number qe of queries to the underlying ideal block cipher, representing adversary’s secret-key-independent computation. Here, we initiate a systematic study of the more natural case of an adversary restricted to adaptively learning a number qc of plaintext/ciphertext pairs that is less than the entire codebook. For any such qc, we aim to determine the highest number of block-cipher queries qe the adversary can issue without being able to successfully distinguish the construction (under a secret key) from a random permutation.
More concretely, we show the following results for key-length extension schemes using a block cipher with n-bit blocks and κ-bit keys:
Plain cascades of length ℓ=2r+1 are secure whenever qcqre≪2r(κ+n), qc≪2κ and qe≪22κ. The bound for r=1 also applies to two-key triple encryption (as used within Triple DES).
The r-round XOR-cascade is secure as long as qcqre≪2r(κ+n), matching an attack by Gaži (CRYPTO 2013).
We fully characterize the security of Gaži and Tessaro’s two-call },
author = {Gazi, Peter and Lee, Jooyoung and Seurin, Yannick and Steinberger, John and Tessaro, Stefano},
location = {Istanbul, Turkey},
pages = {319 -- 341},
publisher = {Springer},
title = {{Relaxing full-codebook security: A refined analysis of key-length extension schemes}},
doi = {10.1007/978-3-662-48116-5_16},
volume = {9054},
year = {2015},
}
@inproceedings{1669,
abstract = {Computational notions of entropy (a.k.a. pseudoentropy) have found many applications, including leakage-resilient cryptography, deterministic encryption or memory delegation. The most important tools to argue about pseudoentropy are chain rules, which quantify by how much (in terms of quantity and quality) the pseudoentropy of a given random variable X decreases when conditioned on some other variable Z (think for example of X as a secret key and Z as information leaked by a side-channel). In this paper we give a very simple and modular proof of the chain rule for HILL pseudoentropy, improving best known parameters. Our version allows for increasing the acceptable length of leakage in applications up to a constant factor compared to the best previous bounds. As a contribution of independent interest, we provide a comprehensive study of all known versions of the chain rule, comparing their worst-case strength and limitations.},
author = {Pietrzak, Krzysztof Z and Skórski, Maciej},
location = {Guadalajara, Mexico},
pages = {81 -- 98},
publisher = {Springer},
title = {{The chain rule for HILL pseudoentropy, revisited}},
doi = {10.1007/978-3-319-22174-8_5},
volume = {9230},
year = {2015},
}
@inproceedings{1671,
abstract = {This paper studies the concrete security of PRFs and MACs obtained by keying hash functions based on the sponge paradigm. One such hash function is KECCAK, selected as NIST’s new SHA-3 standard. In contrast to other approaches like HMAC, the exact security of keyed sponges is not well understood. Indeed, recent security analyses delivered concrete security bounds which are far from existing attacks. This paper aims to close this gap. We prove (nearly) exact bounds on the concrete PRF security of keyed sponges using a random permutation. These bounds are tight for the most relevant ranges of parameters, i.e., for messages of length (roughly) l ≤ min{2n/4, 2r} blocks, where n is the state size and r is the desired output length; and for l ≤ q queries (to the construction or the underlying permutation). Moreover, we also improve standard-model bounds. As an intermediate step of independent interest, we prove tight bounds on the PRF security of the truncated CBC-MAC construction, which operates as plain CBC-MAC, but only returns a prefix of the output.},
author = {Gazi, Peter and Pietrzak, Krzysztof Z and Tessaro, Stefano},
location = {Santa Barbara, CA, United States},
pages = {368 -- 387},
publisher = {Springer},
title = {{The exact PRF security of truncation: Tight bounds for keyed sponges and truncated CBC}},
doi = {10.1007/978-3-662-47989-6_18},
volume = {9215},
year = {2015},
}
@inproceedings{1672,
abstract = {Composable notions of incoercibility aim to forbid a coercer from using anything beyond the coerced parties’ inputs and outputs to catch them when they try to deceive him. Existing definitions are restricted to weak coercion types, and/or are not universally composable. Furthermore, they often make too strong assumptions on the knowledge of coerced parties—e.g., they assume they known the identities and/or the strategies of other coerced parties, or those of corrupted parties— which makes them unsuitable for applications of incoercibility such as e-voting, where colluding adversarial parties may attempt to coerce honest voters, e.g., by offering them money for a promised vote, and use their own view to check that the voter keeps his end of the bargain. In this work we put forward the first universally composable notion of incoercible multi-party computation, which satisfies the above intuition and does not assume collusions among coerced parties or knowledge of the corrupted set. We define natural notions of UC incoercibility corresponding to standard coercion-types, i.e., receipt-freeness and resistance to full-active coercion. Importantly, our suggested notion has the unique property that it builds on top of the well studied UC framework by Canetti instead of modifying it. This guarantees backwards compatibility, and allows us to inherit results from the rich UC literature. We then present MPC protocols which realize our notions of UC incoercibility given access to an arguably minimal setup—namely honestly generate tamper-proof hardware performing a very simple cryptographic operation—e.g., a smart card. This is, to our knowledge, the first proposed construction of an MPC protocol (for more than two parties) that is incoercibly secure and universally composable, and therefore the first construction of a universally composable receipt-free e-voting protocol.},
author = {Alwen, Joel F and Ostrovsky, Rafail and Zhou, Hongsheng and Zikas, Vassilis},
location = {Santa Barbara, CA, United States},
pages = {763 -- 780},
publisher = {Springer},
title = {{Incoercible multi-party computation and universally composable receipt-free voting}},
doi = {10.1007/978-3-662-48000-7_37},
volume = {9216},
year = {2015},
}
@inproceedings{1675,
abstract = {Proofs of work (PoW) have been suggested by Dwork and Naor (Crypto’92) as protection to a shared resource. The basic idea is to ask the service requestor to dedicate some non-trivial amount of computational work to every request. The original applications included prevention of spam and protection against denial of service attacks. More recently, PoWs have been used to prevent double spending in the Bitcoin digital currency system. In this work, we put forward an alternative concept for PoWs - so-called proofs of space (PoS), where a service requestor must dedicate a significant amount of disk space as opposed to computation. We construct secure PoS schemes in the random oracle model (with one additional mild assumption required for the proof to go through), using graphs with high “pebbling complexity” and Merkle hash-trees. We discuss some applications, including follow-up work where a decentralized digital currency scheme called Spacecoin is constructed that uses PoS (instead of wasteful PoW like in Bitcoin) to prevent double spending. The main technical contribution of this work is the construction of (directed, loop-free) graphs on N vertices with in-degree O(log logN) such that even if one places Θ(N) pebbles on the nodes of the graph, there’s a constant fraction of nodes that needs Θ(N) steps to be pebbled (where in every step one can put a pebble on a node if all its parents have a pebble).},
author = {Dziembowski, Stefan and Faust, Sebastian and Kolmogorov, Vladimir and Pietrzak, Krzysztof Z},
location = {Santa Barbara, CA, United States},
pages = {585 -- 605},
publisher = {Springer},
title = {{Proofs of space}},
doi = {10.1007/978-3-662-48000-7_29},
volume = {9216},
year = {2015},
}
@inproceedings{1474,
abstract = {Cryptographic access control offers selective access to encrypted data via a combination of key management and functionality-rich cryptographic schemes, such as attribute-based encryption. Using this approach, publicly available meta-data may inadvertently leak information on the access policy that is enforced by cryptography, which renders cryptographic access control unusable in settings where this information is highly sensitive. We begin to address this problem by presenting rigorous definitions for policy privacy in cryptographic access control. For concreteness we set our results in the model of Role-Based Access Control (RBAC), where we identify and formalize several different flavors of privacy, however, our framework should serve as inspiration for other models of access control. Based on our insights we propose a new system which significantly improves on the privacy properties of state-of-the-art constructions. Our design is based on a novel type of privacy-preserving attribute-based encryption, which we introduce and show how to instantiate. We present our results in the context of a cryptographic RBAC system by Ferrara et al. (CSF'13), which uses cryptography to control read access to files, while write access is still delegated to trusted monitors. We give an extension of the construction that permits cryptographic control over write access. Our construction assumes that key management uses out-of-band channels between the policy enforcer and the users but eliminates completely the need for monitoring read/write access to the data.},
author = {Ferrara, Anna and Fuchsbauer, Georg and Liu, Bin and Warinschi, Bogdan},
location = {Verona, Italy},
pages = {46--60},
publisher = {IEEE},
title = {{Policy privacy in cryptographic access control}},
doi = {10.1109/CSF.2015.11},
year = {2015},
}
@inproceedings{2045,
abstract = {We introduce and study a new notion of enhanced chosen-ciphertext security (ECCA) for public-key encryption. Loosely speaking, in the ECCA security experiment, the decryption oracle provided to the adversary is augmented to return not only the output of the decryption algorithm on a queried ciphertext but also of a randomness-recovery algorithm associated to the scheme. Our results mainly concern the case where the randomness-recovery algorithm is efficient. We provide constructions of ECCA-secure encryption from adaptive trapdoor functions as defined by Kiltz et al. (EUROCRYPT 2010), resulting in ECCA encryption from standard number-theoretic assumptions. We then give two applications of ECCA-secure encryption: (1) We use it as a unifying concept in showing equivalence of adaptive trapdoor functions and tag-based adaptive trapdoor functions, resolving an open question of Kiltz et al. (2) We show that ECCA-secure encryption can be used to securely realize an approach to public-key encryption with non-interactive opening (PKENO) originally suggested by Damgård and Thorbek (EUROCRYPT 2007), resulting in new and practical PKENO schemes quite different from those in prior work. Our results demonstrate that ECCA security is of both practical and theoretical interest.},
author = {Dachman Soled, Dana and Fuchsbauer, Georg and Mohassel, Payman and O’Neill, Adam},
booktitle = {Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)},
editor = {Krawczyk, Hugo},
location = {Buenos Aires, Argentina},
pages = {329 -- 344},
publisher = {Springer},
title = {{Enhanced chosen-ciphertext security and applications}},
doi = {10.1007/978-3-642-54631-0_19},
volume = {8383},
year = {2014},
}
@inproceedings{2046,
abstract = {We introduce policy-based signatures (PBS), where a signer can only sign messages conforming to some authority-specified policy. The main requirements are unforgeability and privacy, the latter meaning that signatures not reveal the policy. PBS offers value along two fronts: (1) On the practical side, they allow a corporation to control what messages its employees can sign under the corporate key. (2) On the theoretical side, they unify existing work, capturing other forms of signatures as special cases or allowing them to be easily built. Our work focuses on definitions of PBS, proofs that this challenging primitive is realizable for arbitrary policies, efficient constructions for specific policies, and a few representative applications.},
author = {Bellare, Mihir and Fuchsbauer, Georg},
booktitle = {Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)},
editor = {Krawczyk, Hugo},
location = {Buenos Aires, Argentina},
pages = {520 -- 537},
publisher = {Springer},
title = {{Policy-based signatures}},
doi = {10.1007/978-3-642-54631-0_30},
volume = {8383},
year = {2014},
}
@inproceedings{2047,
abstract = {Following the publication of an attack on genome-wide association studies (GWAS) data proposed by Homer et al., considerable attention has been given to developing methods for releasing GWAS data in a privacy-preserving way. Here, we develop an end-to-end differentially private method for solving regression problems with convex penalty functions and selecting the penalty parameters by cross-validation. In particular, we focus on penalized logistic regression with elastic-net regularization, a method widely used to in GWAS analyses to identify disease-causing genes. We show how a differentially private procedure for penalized logistic regression with elastic-net regularization can be applied to the analysis of GWAS data and evaluate our method’s performance.},
author = {Yu, Fei and Rybar, Michal and Uhler, Caroline and Fienberg, Stephen},
booktitle = {Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)},
editor = {Domingo Ferrer, Josep},
location = {Ibiza, Spain},
pages = {170 -- 184},
publisher = {Springer},
title = {{Differentially-private logistic regression for detecting multiple-SNP association in GWAS databases}},
doi = {10.1007/978-3-319-11257-2_14},
volume = {8744},
year = {2014},
}
@inproceedings{2082,
abstract = {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). Security proofs and attacks for NMAC can typically be lifted to HMAC. 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, assuming that (1) f is a PRF and (2) the function we get when cascading f is weakly collision-resistant. Unfortunately, HMAC is typically instantiated with cryptographic hash functions like MD5 or SHA-1 for which (2) has been found to be wrong. To restore the provable guarantees for NMAC, Bellare [Crypto'06] showed its security based solely on the assumption that f is a PRF, albeit via a non-uniform reduction. - Our first contribution is a simpler and uniform proof for this fact: 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+ℓqδ)-secure PRF against q queries of length at most ℓ blocks each. - We then show that this ε+ℓqδ bound is basically tight. For the most interesting case where ℓqδ ≥ ε we prove this by constructing an f for which an attack with advantage ℓqδ exists. This also violates the bound O(ℓε) on the PRF-security of NMAC recently claimed by Koblitz and Menezes. - Finally, we analyze the PRF-security of a modification of NMAC called NI [An and Bellare, Crypto'99] that differs mainly by using a compression function with an additional keying input. This avoids the constant rekeying on multi-block messages in NMAC and allows for a security proof starting by the standard switch from a PRF to a random function, followed by an information-theoretic analysis. We carry out such an analysis, obtaining a tight ℓq2/2 c bound for this step, improving over the trivial bound of ℓ2q2/2c. The proof borrows combinatorial techniques originally developed for proving the security of CBC-MAC [Bellare et al., Crypto'05].},
author = {Gazi, Peter and Pietrzak, Krzysztof Z and Rybar, Michal},
editor = {Garay, Juan and Gennaro, Rosario},
location = {Santa Barbara, USA},
number = {1},
pages = {113 -- 130},
publisher = {Springer},
title = {{The exact PRF-security of NMAC and HMAC}},
doi = {10.1007/978-3-662-44371-2_7},
volume = {8616},
year = {2014},
}
@inproceedings{2185,
abstract = {We revisit the classical problem of converting an imperfect source of randomness into a usable cryptographic key. Assume that we have some cryptographic application P that expects a uniformly random m-bit key R and ensures that the best attack (in some complexity class) against P(R) has success probability at most δ. Our goal is to design a key-derivation function (KDF) h that converts any random source X of min-entropy k into a sufficiently "good" key h(X), guaranteeing that P(h(X)) has comparable security δ′ which is 'close' to δ. Seeded randomness extractors provide a generic way to solve this problem for all applications P, with resulting security δ′ = O(δ), provided that we start with entropy k ≥ m + 2 log (1/δ) - O(1). By a result of Radhakrishnan and Ta-Shma, this bound on k (called the "RT-bound") is also known to be tight in general. Unfortunately, in many situations the loss of 2 log (1/δ) bits of entropy is unacceptable. This motivates the study KDFs with less entropy waste by placing some restrictions on the source X or the application P. In this work we obtain the following new positive and negative results in this regard: - Efficient samplability of the source X does not help beat the RT-bound for general applications. This resolves the SRT (samplable RT) conjecture of Dachman-Soled et al. [DGKM12] in the affirmative, and also shows that the existence of computationally-secure extractors beating the RT-bound implies the existence of one-way functions. - We continue in the line of work initiated by Barak et al. [BDK+11] and construct new information-theoretic KDFs which beat the RT-bound for large but restricted classes of applications. Specifically, we design efficient KDFs that work for all unpredictability applications P (e.g., signatures, MACs, one-way functions, etc.) and can either: (1) extract all of the entropy k = m with a very modest security loss δ′ = O(δ·log (1/δ)), or alternatively, (2) achieve essentially optimal security δ′ = O(δ) with a very modest entropy loss k ≥ m + loglog (1/δ). In comparison, the best prior results from [BDK+11] for this class of applications would only guarantee δ′ = O(√δ) when k = m, and would need k ≥ m + log (1/δ) to get δ′ = O(δ). - The weaker bounds of [BDK+11] hold for a larger class of so-called "square- friendly" applications (which includes all unpredictability, but also some important indistinguishability, applications). Unfortunately, we show that these weaker bounds are tight for the larger class of applications. - We abstract out a clean, information-theoretic notion of (k,δ,δ′)- unpredictability extractors, which guarantee "induced" security δ′ for any δ-secure unpredictability application P, and characterize the parameters achievable for such unpredictability extractors. Of independent interest, we also relate this notion to the previously-known notion of (min-entropy) condensers, and improve the state-of-the-art parameters for such condensers.},
author = {Dodis, Yevgeniy and Pietrzak, Krzysztof Z and Wichs, Daniel},
editor = {Nguyen, Phong and Oswald, Elisabeth},
location = {Copenhagen, Denmark},
pages = {93 -- 110},
publisher = {Springer},
title = {{Key derivation without entropy waste}},
doi = {10.1007/978-3-642-55220-5_6},
volume = {8441},
year = {2014},
}
@inproceedings{2219,
abstract = {Recently, Döttling et al. (ASIACRYPT 2012) proposed the first chosen-ciphertext (IND-CCA) secure public-key encryption scheme from the learning parity with noise (LPN) assumption. In this work we give an alternative scheme which is conceptually simpler and more efficient. At the core of our construction is a trapdoor technique originally proposed for lattices by Micciancio and Peikert (EUROCRYPT 2012), which we adapt to the LPN setting. The main technical tool is a new double-trapdoor mechanism, together with a trapdoor switching lemma based on a computational variant of the leftover hash lemma.},
author = {Kiltz, Eike and Masny, Daniel and Pietrzak, Krzysztof Z},
isbn = {978-364254630-3},
pages = {1 -- 18},
publisher = {Springer},
title = {{Simple chosen-ciphertext security from low noise LPN}},
doi = {10.1007/978-3-642-54631-0_1},
volume = {8383},
year = {2014},
}
@inproceedings{2236,
abstract = {Consider a joint distribution (X,A) on a set. We show that for any family of distinguishers, there exists a simulator such that 1 no function in can distinguish (X,A) from (X,h(X)) with advantage ε, 2 h is only O(2 3ℓ ε -2) times less efficient than the functions in. For the most interesting settings of the parameters (in particular, the cryptographic case where X has superlogarithmic min-entropy, ε > 0 is negligible and consists of circuits of polynomial size), we can make the simulator h deterministic. As an illustrative application of our theorem, we give a new security proof for the leakage-resilient stream-cipher from Eurocrypt'09. Our proof is simpler and quantitatively much better than the original proof using the dense model theorem, giving meaningful security guarantees if instantiated with a standard blockcipher like AES. Subsequent to this work, Chung, Lui and Pass gave an interactive variant of our main theorem, and used it to investigate weak notions of Zero-Knowledge. Vadhan and Zheng give a more constructive version of our theorem using their new uniform min-max theorem.},
author = {Jetchev, Dimitar and Pietrzak, Krzysztof Z},
editor = {Lindell, Yehuda},
isbn = {978-364254241-1},
location = {San Diego, USA},
pages = {566 -- 590},
publisher = {Springer},
title = {{How to fake auxiliary input}},
doi = {10.1007/978-3-642-54242-8_24},
volume = {8349},
year = {2014},
}
@article{2852,
abstract = {A robust combiner for hash functions takes two candidate implementations and constructs a hash function which is secure as long as at least one of the candidates is secure. So far, hash function combiners only aim at preserving a single property such as collision-resistance or pseudorandomness. However, when hash functions are used in protocols like TLS they are often required to provide several properties simultaneously. We therefore put forward the notion of robust multi-property combiners and elaborate on different definitions for such combiners. We then propose a combiner that provably preserves (target) collision-resistance, pseudorandomness, and being a secure message authentication code. This combiner satisfies the strongest notion we propose, which requires that the combined function satisfies every security property which is satisfied by at least one of the underlying hash function. If the underlying hash functions have output length n, the combiner has output length 2 n. This basically matches a known lower bound for black-box combiners for collision-resistance only, thus the other properties can be achieved without penalizing the length of the hash values. We then propose a combiner which also preserves the property of being indifferentiable from a random oracle, slightly increasing the output length to 2 n+ω(log n). Moreover, we show how to augment our constructions in order to make them also robust for the one-wayness property, but in this case require an a priory upper bound on the input length.},
author = {Fischlin, Marc and Lehmann, Anja and Pietrzak, Krzysztof Z},
journal = {Journal of Cryptology},
number = {3},
pages = {397 -- 428},
publisher = {Springer},
title = {{Robust multi-property combiners for hash functions}},
doi = {10.1007/s00145-013-9148-7},
volume = {27},
year = {2014},
}
@inproceedings{1643,
abstract = {We extend the notion of verifiable random functions (VRF) to constrained VRFs, which generalize the concept of constrained pseudorandom functions, put forward by Boneh and Waters (Asiacrypt’13), and independently by Kiayias et al. (CCS’13) and Boyle et al. (PKC’14), who call them delegatable PRFs and functional PRFs, respectively. In a standard VRF the secret key sk allows one to evaluate a pseudorandom function at any point of its domain; in addition, it enables computation of a non-interactive proof that the function value was computed correctly. In a constrained VRF from the key sk one can derive constrained keys skS for subsets S of the domain, which allow computation of function values and proofs only at points in S. After formally defining constrained VRFs, we derive instantiations from the multilinear-maps-based constrained PRFs by Boneh and Waters, yielding a VRF with constrained keys for any set that can be decided by a polynomial-size circuit. Our VRFs have the same function values as the Boneh-Waters PRFs and are proved secure under the same hardness assumption, showing that verifiability comes at no cost. Constrained (functional) VRFs were stated as an open problem by Boyle et al.},
author = {Fuchsbauer, Georg},
booktitle = {SCN 2014},
editor = {Abdalla, Michel and De Prisco, Roberto},
location = {Amalfi, Italy},
pages = {95 -- 114},
publisher = {Springer},
title = {{Constrained Verifiable Random Functions }},
doi = {10.1007/978-3-319-10879-7_7},
volume = {8642},
year = {2014},
}
@inproceedings{1907,
abstract = {Most cryptographic security proofs require showing that two systems are indistinguishable. A central tool in such proofs is that of a game, where winning the game means provoking a certain condition, and it is shown that the two systems considered cannot be distinguished unless this condition is provoked. Upper bounding the probability of winning such a game, i.e., provoking this condition, for an arbitrary strategy is usually hard, except in the special case where the best strategy for winning such a game is known to be non-adaptive. A sufficient criterion for ensuring the optimality of non-adaptive strategies is that of conditional equivalence to a system, a notion introduced in [1]. In this paper, we show that this criterion is not necessary to ensure the optimality of non-adaptive strategies by giving two results of independent interest: 1) the optimality of non-adaptive strategies is not preserved under parallel composition; 2) in contrast, conditional equivalence is preserved under parallel composition.},
author = {Demay, Grégory and Gazi, Peter and Maurer, Ueli and Tackmann, Björn},
booktitle = {IEEE International Symposium on Information Theory},
location = {Honolulu, USA},
publisher = {IEEE},
title = {{Optimality of non-adaptive strategies: The case of parallel games}},
doi = {10.1109/ISIT.2014.6875125},
year = {2014},
}
@inproceedings{2258,
abstract = {In a digital signature scheme with message recovery, rather than transmitting the message m and its signature σ, a single enhanced signature τ is transmitted. The verifier is able to recover m from τ and at the same time verify its authenticity. The two most important parameters of such a scheme are its security and overhead |τ| − |m|. A simple argument shows that for any scheme with “n bits security” |τ| − |m| ≥ n, i.e., the overhead is lower bounded by the security parameter n. Currently, the best known constructions in the random oracle model are far from this lower bound requiring an overhead of n + logq h , where q h is the number of queries to the random oracle. In this paper we give a construction which basically matches the n bit lower bound. We propose a simple digital signature scheme with n + o(logq h ) bits overhead, where q h denotes the number of random oracle queries.
Our construction works in two steps. First, we propose a signature scheme with message recovery having optimal overhead in a new ideal model, the random invertible function model. Second, we show that a four-round Feistel network with random oracles as round functions is tightly “public-indifferentiable” from a random invertible function. At the core of our indifferentiability proof is an almost tight upper bound for the expected number of edges of the densest “small” subgraph of a random Cayley graph, which may be of independent interest.
},
author = {Kiltz, Eike and Pietrzak, Krzysztof Z and Szegedy, Mario},
location = {Santa Barbara, CA, United States},
pages = {571 -- 588},
publisher = {Springer},
title = {{Digital signatures with minimal overhead from indifferentiable random invertible functions}},
doi = {10.1007/978-3-642-40041-4_31},
volume = {8042},
year = {2013},
}
@inproceedings{2259,
abstract = {The learning with rounding (LWR) problem, introduced by Banerjee, Peikert and Rosen at EUROCRYPT ’12, is a variant of learning with errors (LWE), where one replaces random errors with deterministic rounding. The LWR problem was shown to be as hard as LWE for a setting of parameters where the modulus and modulus-to-error ratio are super-polynomial. In this work we resolve the main open problem and give a new reduction that works for a larger range of parameters, allowing for a polynomial modulus and modulus-to-error ratio. In particular, a smaller modulus gives us greater efficiency, and a smaller modulus-to-error ratio gives us greater security, which now follows from the worst-case hardness of GapSVP with polynomial (rather than super-polynomial) approximation factors.
As a tool in the reduction, we show that there is a “lossy mode” for the LWR problem, in which LWR samples only reveal partial information about the secret. This property gives us several interesting new applications, including a proof that LWR remains secure with weakly random secrets of sufficient min-entropy, and very simple constructions of deterministic encryption, lossy trapdoor functions and reusable extractors.
Our approach is inspired by a technique of Goldwasser et al. from ICS ’10, which implicitly showed the existence of a “lossy mode” for LWE. By refining this technique, we also improve on the parameters of that work to only requiring a polynomial (instead of super-polynomial) modulus and modulus-to-error ratio.
},
author = {Alwen, Joel F and Krenn, Stephan and Pietrzak, Krzysztof Z and Wichs, Daniel},
location = {Santa Barbara, CA, United States},
number = {1},
pages = {57 -- 74},
publisher = {Springer},
title = {{Learning with rounding, revisited: New reduction properties and applications}},
doi = {10.1007/978-3-642-40041-4_4},
volume = {8042},
year = {2013},
}