In this paper we give nearly tight reductions for modern implicitly authenticated Diffie-Hellman protocols in the style of the Signal and Noise protocols, which are extremely simple and efficient. Unlike previous approaches, the combination of nearly tight proofs and efficient protocols enables the first real-world instantiations for which the parameters can be chosen in a theoretically sound manner, i.e., according to the bounds of the reductions. Specifically, our reductions have a security loss which is only linear in the number of users μ and constant in the number of sessions per user ℓ. This is much better than most other key exchange proofs which are typically quadratic in the product μℓ. Combined with the simplicity of our protocols, this implies that our protocols are more efficient than the state of the art when soundly instantiated.
We also prove that our security proofs are optimal: a linear loss in the number of users is unavoidable for our protocols for a large and natural class of reductions.
Human dignity demands that personal information, like medical and forensic data, be hidden from the public. But veils of secrecy designed to preserve privacy may also be abused to cover up lies and deceit by parties entrusted with Data, unjustly harming citizens and eroding trust in central institutions.
Zero knowledge (ZK) proof systems are an ingenious cryptographic solution to the tension between the ideals of personal privacy and institutional integrity, enforcing the latter in a way that does not compromise the former. Public trust demands transparency from ZK systems, meaning they be set up with no reliance on any trusted party, and have no trapdoors that could be exploited by powerful parties to bear false witness. For ZK systems to be used with Big Data, it is imperative that the public verification process scale sublinearly in data size. Transparent ZK proofs that can be verified exponentially faster than data size were first described in the 1990s but early constructions were impractical, and no ZK system realized thus far in code (including that used by crypto-currencies like Zcash) has achieved both transparency and exponential verification speedup, simultaneously, for general computations.
Here we report the first realization of a transparent ZK system (ZK-STARK) in which verification scales exponentially faster than database size, and moreover, this exponential speedup in verification is observed concretely for meaningful and sequential computations, described next. Our system uses several recent advances on interactive oracle proofs (IOP), such as a “fast” (linear time) IOP system for error correcting codes.
Our proof-of-concept system allows the Police to prove to the public that the DNA profile of a Presidential Candidate does not appear in the forensic DNA profile database maintained by the Police. The proof, which is generated by the Police, relies on no external trusted party, and reveals no further information about the contents of the database, nor about the candidate’s profile; in particular, no DNA information is disclosed to any party outside the Police. The proof is shorter than the size of the DNA database, and verified faster than the time needed to examine that database naively.
We present Libra, the first zero-knowledge proof system that has both optimal prover time and succinct proof size/verification time. In particular, if C is the size of the circuit being proved (i) the prover time is O(C) irrespective of the circuit type; (ii) the proof size and verification time are both O(d log C) for d-depth log-space uniform circuits (such as RAM programs). In addition Libra features an one-time trusted setup that depends only on the size of the input to the circuit and not on the circuit logic. Underlying Libra is a new linear-time algorithm for the prover of the interactive proof protocol by Goldwasser, Kalai and Rothblum (also known as GKR protocol), as well as an efficient approach to turn the GKR protocol to zero-knowledge using small masking polynomials. Not only does Libra have excellent asymptotics, but it is also efficient in practice. For example, our implementation shows that it takes 200 seconds to generate a proof for constructing a SHA2-based Merkle tree root on 256 leaves, outperforming all existing zero-knowledge proof systems. Proof size and verification time of Libra are also competitive.
Secure multiparty computation (MPC) often relies on sources of correlated randomness for better efficiency and simplicity. This is particularly useful for MPC with no honest majority, where input-independent correlated randomness enables a lightweight “non-cryptographic” online phase once the inputs are known. However, since the amount of correlated randomness typically scales with the circuit size of the function being computed, securely generating correlated randomness forms an efficiency bottleneck, involving a large amount of communication and storage. A natural tool for addressing the above limitations is a pseudorandom correlation generator (PCG). A PCG allows two or more parties to securely generate long sources of useful correlated randomness via a local expansion of correlated short seeds and no interaction. PCGs enable MPC with silent preprocessing, where a small amount of interaction used for securely sampling the seeds is followed by silent local generation of correlated pseudorandomness. A concretely efficient PCG for Vector-OLE correlations was recently obtained by Boyle et al. (CCS 2018) based on variants of the learning parity with noise (LPN) assumption over large fields. In this work, we initiate a systematic study of PCGs and present concretely efficient constructions for several types of useful MPC correlations. We obtain the following main contributions:
– PCG foundations. We give a general security definition for PCGs. Our definition suffices for any MPC protocol satisfying a stronger security requirement that is met by existing protocols. We prove that a stronger security requirement is indeed necessary, and justify our PCG definition by ruling out a stronger and more natural definition.
– Silent OT extension. We present the first concretely efficient PCG for oblivious transfer correlations. Its security is based on a variant of the binary LPN assumption and any correlation-robust hash function. We expect it to provide a faster alternative to the IKNP OT extension protocol (Crypto ’03) when communication is the bottleneck. We present several applications, including protocols for non-interactive zero-knowledge with bounded-reusable preprocessing from binary LPN, and concretely efficient related-key oblivious pseudorandom functions.
– PCGs for simple 2-party correlations. We obtain PCGs for several other types of useful 2-party correlations, including (authenticated) one-time truth-tables and Beaver triples. While the latter PCGs are slower than our PCG for OT, they are still practically feasible. These PCGs are based on a host of assumptions and techniques, including specialized homomorphic secret sharing schemes and pseudorandom generators tailored to their structure.
– Multiparty correlations. We obtain PCGs for multiparty correlations that can be used to make the circuit-dependent communication of MPC protocols scale linearly (instead of quadratically) with the number of parties.
We describe a novel approach for two-party private set intersection (PSI) with semi-honest security. Compared to existing PSI protocols, ours has a more favorable balance between communication and computation. Specifically, our protocol has the lowest monetary cost of any known PSI protocol, when run over the Internet using cloud-based computing services (taking into account current rates for CPU + data). On slow networks (e.g., 10Mbps) our protocol is actually the fastest.
Our novel underlying technique is a variant of oblivious transfer (OT) extension that we call sparse OT extension. Conceptually it can be thought of as a communication-efficient multipoint oblivious PRF evaluation. Our sparse OT technique relies heavily on manipulating high-degree polynomials over large finite fields (i.e. elements whose representation requires hundreds of bits). We introduce extensive algorithmic and engineering improvements for interpolation and multi-point evaluation of such polynomials, which we believe will be of independent interest.
Finally, we present an extensive empirical comparison of state-of-the- art PSI protocols in several application scenarios and along several dimensions of measurement: running time, communication, peak memory consumption, and — arguably the most relevant metric for practice — monetary cost
Content moderation is crucial for stopping abuse and harassment via messaging on online platforms. Existing moderation mechanisms, such as message franking, require platform providers to see user identifiers on encrypted traffic. These mechanisms cannot be used in messaging systems in which users can hide their identities, such as Signal. The key technical challenge preventing moderation is in simultaneously achieving cryptographic accountability while preserving deniability. In this work, we resolve this tension with a new cryptographic primitive: asymmetric message franking schemes (AMFs). We define strong security notions for AMFs, including the first formal treatment of deniability in moderation settings. We then construct, analyze, and implement an AMF scheme that is fast enough for deployment. We detail how to use AMFs to build content moderation for metadata-private messaging.
ECDSA is a widely adopted digital signature standard. Unfortunately, efficient distributed variants of this primitive are notoriously hard to achieve and known solutions often require expensive zero knowledge proofs to deal with malicious adversaries. For the two party case, Lindell [Lin17] recently managed to get an efficient solution which, to achieve simulation-based security, relies on an interactive, non standard, assumption on Paillier’s cryptosystem.
In this paper we generalize Lindell’s solution using hash proof systems. The main advantage of our generic method is that it results in a simulation-based security proof without resorting to non-standard interactive assumptions.
Moving to concrete constructions, we show how to instantiate our framework using class groups of imaginary quadratic fields. Our implementations show that the practical impact of dropping such interactive assumptions is minimal. Indeed, while for 128-bit security our scheme is marginally slower than Lindell’s, for 256-bit security it turns out to be better both in key generation and signing time. Moreover, in terms of communication cost, our implementation significantly reduces both the number of rounds and the transmitted bits without exception.
We introduce a new form of encryption that we name matchmaking encryption (ME). Using ME, sender S and receiver R (each with its own attributes) can both specify policies the other party must satisfy in order for the message to be revealed. The main security guarantee is that of privacy-preserving policy matching: During decryption nothing is leaked beyond the fact that a match occurred/did not occur. ME opens up new ways of secretly communicating, and enables several new applications where both participants can specify fine-grained access policies to encrypted data. For instance, in social matchmaking, S can encrypt a file containing his/her personal details and specify a policy so that the file can be decrypted only by his/her ideal partner. On the other end, a receiver R will be able to decrypt the file only if S corresponds to his/her ideal partner defined through a policy. On the theoretical side, we define security for ME, as well as provide generic frameworks for constructing ME from functional encryption. These constructions need to face the technical challenge of simultaneously checking the policies chosen by S and R, to avoid any leakage. On the practical side, we construct an efficient identity-based scheme for equality policies, with provable security in the random oracle model under the standard BDH assumption. We implement and evaluate our scheme and provide experimental evidence that our construction is practical. We also apply identity-based ME to a concrete use case, in particular for creating an anonymous bulletin board over a Tor network.
We devise new techniques for design and analysis of efficient lattice-based zero-knowledge proofs (ZKP). First, we introduce one-shot proof techniques for non-linear polynomial relations of degree k≥2, where the protocol achieves a negligible soundness error in a single execution, and thus performs significantly better in both computation and communication compared to prior protocols requiring multiple repetitions. Such proofs with degree k≥2 have been crucial ingredients for important privacy-preserving protocols in the discrete logarithm setting, such as Bulletproofs (IEEE S&P ’18) and arithmetic circuit arguments (EUROCRYPT ’16). In contrast, one-shot proofs in lattice-based cryptography have previously only been shown for the linear case (k=1) and a very specific quadratic case (k=2), which are obtained as a special case of our technique.
Moreover, we introduce two speedup techniques for lattice-based ZKPs: a CRT-packing technique supporting “inter-slot’’ operations, and “NTT-friendly’’ tools that permit the use of fully-splitting rings. The former technique comes at almost no cost to the proof length, and the latter one barely increases it, which can be compensated for by tweaking the rejection sampling parameters while still having faster computation overall.
To illustrate the utility of our techniques, we show how to use them to build efficient relaxed proofs for important relations, namely proof of commitment to bits, one-out-of-many proof, range proof and set membership proof. Despite their relaxed nature, we further show how our proof systems can be used as building blocks for advanced cryptographic tools such as ring signatures.
Our ring signature achieves a dramatic improvement in length over all the existing proposals from lattices at the same security level. The computational evaluation also shows that our construction is highly likely to outperform all the relevant works in running times. Being efficient in both aspects, our ring signature is particularly suitable for both small-scale and large-scale applications such as cryptocurrencies and e-voting systems. No trusted setup is required for any of our proposals.
We provide new zero-knowledge argument of knowledge systems that work directly for a wide class of language, namely, ones involving the satisfiability of matrix-vector relations and integer relations commonly found in constructions of lattice-based cryptography. Prior to this work, practical arguments for lattice-based relations either have a constant soundness error ( 2/3 ), or consider a weaker form of soundness, namely, extraction only guarantees that the prover is in possession of a witness that “approximates” the actual witness. Our systems do not suffer from these limitations.
The core of our new argument systems is an efficient zero-knowledge argument of knowledge of a solution to a system of linear equations, where variables of this solution satisfy a set of quadratic constraints. This argument enjoys standard soundness, a small soundness error ( 1/poly ), and a complexity linear in the size of the solution. Using our core argument system, we construct highly efficient argument systems for a variety of statements relevant to lattices, including linear equations with short solutions and matrix-vector relations with hidden matrices.
Based on our argument systems, we present several new constructions of common privacy-preserving primitives in the standard lattice setting, including a group signature, a ring signature, an electronic cash system, and a range proof protocol. Our new constructions are one to three orders of magnitude more efficient than the state of the art (in standard lattice). This illustrates the efficiency and expressiveness of our argument system.
We present two new, highly efficient, protocols for securely generating a distributed RSA key pair in the two-party setting. One protocol is semi-honestly secure and the other maliciously secure. Both are constant round and do not rely on any specific number-theoretic assumptions and improve significantly over the state-of-the-art by allowing a slight leakage (which we show to not affect security).
For our maliciously secure protocol our most significant improvement comes from executing most of the protocol in a ``strong’’ semi-honest manner and then doing a single, light, zero-knowledge argument of correct execution. We introduce other significant improvements as well. One such improvement arrives in showing that certain, limited leakage does not compromise security, which allows us to use lightweight subprotocols. Another improvement, which may be of independent interest, comes in our approach for multiplying two large integers using OT, in the malicious setting, without being susceptible to a selective-failure attack. Finally, we implement our malicious protocol and show that its performance is an order of magnitude better than the best previous protocol, which provided only semi-honest security.
The rise of machine learning as a service multiplies scenarios where one faces a privacy dilemma: either sensitive user data must be revealed to the entity that evaluates the cognitive model (e.g., in the Cloud), or the model itself must be revealed to the user so that the evaluation can take place locally. Fully Homomorphic Encryption (FHE) offers an elegant way to reconcile these conflicting interests in the Cloud-based scenario and also preserve non-interactivity. However, due to the inefficiency of existing FHE schemes, most applications prefer to use Somewhat Homomorphic Encryption (SHE), where the complexity of the computation to be performed has to be known in advance, and the efficiency of the scheme depends on this global complexity.
In this paper, we present a new framework for homomorphic evaluation of neural networks, that we call FHE-DiNN, whose complexity is strictly linear in the depth of the network and whose parameters can be set beforehand. To obtain this scale-invariance property, we rely heavily on the bootstrapping procedure. We refine the recent FHE construction by Chillotti et al. (ASIACRYPT 2016) in order to increase the message space and apply the sign function (that we use to activate the neurons in the network) during the bootstrapping. We derive some empirical results, using TFHE library as a starting point, and classify encrypted images from the MNIST dataset with more than 96% accuracy in less than 1.7 seconds.
Finally, as a side contribution, we analyze and introduce some variations to the bootstrapping technique of Chillotti et al. that offer an improvement in efficiency at the cost of increasing the storage requirements.
Tight security is increasingly gaining importance in real-world cryptography, as it allows to choose cryptographic parameters in a way that is supported by a security proof, without the need to sacrifice efficiency by compensating the security loss of a reduction with larger parameters. However, for many important cryptographic primitives, including digital signatures and authenticated key exchange (AKE), we are still lacking constructions that are suitable for real-world deployment.
We construct the first truly practical signature scheme with tight security in a real-world multi-user setting with adaptive corruptions. The scheme is based on a new way of applying the Fiat-Shamir approach to construct tightly-secure signatures from certain identification schemes.
Then we use this scheme as a building block to construct the first practical AKE protocol with tight security. It allows the establishment of a key within 1 RTT in a practical client-server setting, provides forward security, is simple and easy to implement, and thus very suitable for practical deployment. It is essentially the ``signed Diffie-Hellman’’ protocol, but with an additional message, which is crucial to achieve tight security. This additional message is used to overcome a technical difficulty in constructing tightly-secure AKE protocols.
For a theoretically-sound choice of parameters and a moderate number of users and sessions, our protocol has comparable computational efficiency to the simple signed Diffie-Hellman protocol with EC-DSA, while for large-scale settings our protocol has even better computational performance, at moderately increased communication complexity.
Wang et al. (CCS 2017) recently proposed a protocol for malicious secure two-party computation that represents the state-of-the- art with regard to concrete efficiency in both the single-execution and amortized settings, with or without preprocessing. We show here several optimizations of their protocol that result in a significant improvement in the overall communication and running time. Specifically:
We show how to make the “authenticated garbling” at the heart of their protocol compatible with the half-gate optimization of Zahur et al. (Eurocrypt 2015). We also show how to avoid sending an information-theoretic MAC for each garbled row. These two optimizations give up to a 2.6x improvement in communication, and make the communication of the online phase essentially equivalent to that of state-of-the-art semi-honest secure computation.
We show various optimizations to their protocol for generating AND triples that, overall, result in a 1.5x improvement in the communication and a 2x improvement in the computation for that step.
Protocols for secure multiparty computation enable a set of parties to compute a function of their inputs without revealing anything but the output. The security properties of the protocol must be preserved in the presence of adversarial behavior. The two classic adversary models considered are semi-honest (where the adversary follows the protocol specification but tries to learn more than allowed by examining the protocol transcript) and malicious (where the adversary may follow any arbitrary attack strategy). Protocols for semi-honest adversaries are often far more efficient, but in many cases the security guarantees are not strong enough.
In this paper, we present new protocols for securely computing any functionality represented by an arithmetic circuit. We utilize a new method for verifying that the adversary does not cheat, that yields a cost of just twice that of semi-honest protocols in some settings. Our protocols are information-theoretically secure in the presence of a malicious adversaries, assuming an honest majority. We present protocol variants for small and large fields, and show how to efficiently instantiate them based on replicated secret sharing and Shamir sharing. As with previous works in this area aiming to achieve high efficiency, our protocol is secure with abort and does not achieve fairness, meaning that the adversary may receive output while the honest parties do not.
We implemented our protocol and ran experiments for different numbers of parties, different network configurations and different circuit depths. Our protocol significantly outperforms the previous best for this setting (Lindell and Nof, CCS 2017); for a large number of parties, our implementation runs almost an order of magnitude faster than theirs.
We present a new approach to designing concretely efficient MPC protocols with semi-honest security in the dishonest majority setting. Motivated by the fact that within the dishonest majority setting the efficiency of most practical protocols does not depend on the number of honest parties, we investigate how to construct protocols which improve in efficiency as the number of honest parties increases. Our central idea is to take a protocol which is secure for n−1 corruptions and modify it to use short symmetric keys, with the aim of basing security on the concatenation of all honest parties’ keys. This results in a more efficient protocol tolerating fewer corruptions, whilst also introducing an LPN-style syndrome decoding assumption.
We first apply this technique to a modified version of the semi-honest GMW protocol, using OT extension with short keys, to improve the efficiency of standard GMW with fewer corruptions. We also obtain more efficient constant-round MPC, using BMR-style garbled circuits with short keys, and present an implementation of the online phase of this protocol. Our techniques start to improve upon existing protocols when there are around n=20
parties with h=6 honest parties, and as these increase we obtain up to a 13 times reduction (for n=400,h=120) in communication complexity for our GMW variant, compared with the best-known GMW-based protocol modified to use the same threshold.
Most multi-party computation protocols allow secure computation of arithmetic circuits over a finite field, such as the integers modulo a prime. In the more natural setting of integer computations modulo 2^k, which are useful for simplifying implementations and applications, no solutions with active security are known unless the majority of the participants are honest.
We present a new scheme for information-theoretic MACs that are homomorphic modulo 2^k, and are as efficient as the well-known standard solutions that are homomorphic over fields. We apply this to construct an MPC protocol for dishonest majority in the preprocessing model that has efficiency comparable to the well-known SPDZ protocol (Damgård et al., CRYPTO 2012), with operations modulo 2^k instead of over a field. We also construct a matching preprocessing protocol based on oblivious transfer, which is in the style of the MASCOT protocol (Keller et al., CCS 2016) and almost as efficient.
Message franking enables cryptographically verifiable reporting of abusive content in end-to-end encrypted messaging. Grubbs, Lu, and Ristenpart recently formalized the needed underlying primitive, what they call compactly committing authenticated encryption (AE), and analyzed the security of a number of approaches. But all known secure schemes are still slow compared to the fastest standard AE schemes. For this reason Facebook Messenger uses AES-GCM for franking of attachments such as images or videos. We show how to break Facebook’s attachment franking scheme: a malicious user can send an objectionable image to a recipient but that recipient cannot report it as abuse. The core problem stems from use of fast but non-committing AE, and so we build the fastest compactly committing AE schemes to date. To do so we introduce a new primitive, called encryptment, which captures the essential properties needed. We prove that, unfortunately, schemes with performance profile similar to AES-GCM won’t work. Instead, we show how to efficiently transform Merkle-Damgärd-style hash functions into secure encryptments, and how to efficiently build compactly committing AE from encryptment. Ultimately our main construction allows franking using just a single computation of SHA-256 or SHA-3. Encryptment proves useful for a variety of other applications, such as remotely keyed AE and concealments, and our results imply the first single-pass schemes in these settings as well.
In this paper we introduce two things: On one hand we introduce the Tile-Probe-and-Fault model, a model generalising the wire-probe model of Ishai et al. extending it to cover both more realistic side-channel leakage scenarios on a chip and also to cover fault and combined attacks. Secondly we introduce CAPA: a combined Countermeasure Against Physical Attacks. Our countermeasure is motivated by our model, and aims to provide security against higher-order SCA, multiple-shot FA and combined attacks. The tile-probe-and-fault model leads one to naturally look (by analogy) at actively secure multi-party computation protocols. Indeed, CAPA draws much inspiration from the MPC protocol SPDZ. So as to demonstrate that the model, and the CAPA countermeasure, are not just theoretical constructions, but could also serve to build practical countermeasures, we present initial experiments of proof-of-concept designs using the CAPA methodology. Namely, a hardware implementation of the KATAN and AES block ciphers, as well as a software bitsliced AES S-box implementation. We demonstrate experimentally that the design can resist second-order DPA attacks, even when the attacker is presented with many hundreds of thousands of traces. In addition our proof-of-concept can also detect faults within our model with high probability in accordance to the methodology.
HElib is a software library that implements homomorphic encryption (HE), with a focus on effective use of “packed” ciphertexts. An important operation (which is used in bootstrapping, as well as in other applications) is applying a known linear map to a vector of encrypted data. In this paper, we describe several algorithmic improvements that significantly speed up this operation: in our experiments, our new algorithms were 30-75 times faster than those currently implemented in HElib for typical parameters.
Our techniques also reduce the size of the large public evaluation key, often using 33%-50% less space than the previous HElib implementation. We also implemented a new tradeoff that enables a drastic reduction in size, maybe a 25x factor or more for some parameters, paying only a 2-4x factor in runtime (and giving up some parallelization opportunities).
Extensive efforts are currently put into securing messaging platforms, where a key challenge is that of protecting against man-in-the-middle attacks when setting up secure end-to-end channels. The vast majority of these efforts, however, have so far focused on securing user-to-user messaging, and recent attacks indicate that the security of group messaging is still quite fragile.
We initiate the study of out-of-band authentication in the group setting, extending the user-to-user setting where messaging platforms (e.g., Telegram and WhatsApp) protect against man-in-the-middle attacks by assuming that users have access to an external channel for authenticating one short value (e.g., two users who recognize each other’s voice can compare a short value). Inspired by the frameworks of Vaudenay (CRYPTO ’05) and Naor et al. (CRYPTO ’06) in the user-to-user setting, we assume that users communicate over a completely-insecure channel, and that a group administrator can out-of-band authenticate one short message to all users. An adversary may read, remove, or delay this message (for all or for some of the users), but cannot undetectably modify it.
Within our framework we establish tight bounds on the tradeoff between the adversary’s success probability and the length of the out-of-band authenticated message (which is a crucial bottleneck given that the out-of-band channel is of low bandwidth). We consider both computationally-secure and statistically-secure protocols, and for each flavor of security we construct an authentication protocol and prove a lower bound showing that our protocol achieves essentially the best possible tradeoff.
In particular, considering groups that consist of an administrator and k
additional users, for statistically-secure protocols we show that at least (k+1)⋅(log(1/ϵ)−Θ(1)) bits must be out-of-band authenticated, whereas for computationally-secure ones log(1/ϵ)+logk bits suffice, where ϵ is the adversary’s success probability. Moreover, instantiating our computationally-secure protocol in the random-oracle model yields an efficient and practically-relevant protocol (which, alternatively, can also be based on any one-way function in the standard model).
We aim to understand the best possible security of a (bidirectional) cryptographic channel against an adversary that may arbitrarily and repeatedly learn the secret state of either communicating party. We give a formal security definition and a proven-secure construction. This construction provides better security against state compromise than the Signal Double Ratchet Algorithm or any other known channel construction. To facilitate this we define and construct new forms of public-key encryption and digital signatures that update their keys over time.
Ratcheted key exchange (RKE) is a cryptographic technique used in instant messaging systems like Signal and the WhatsApp messenger for attaining strong security in the face of state exposure attacks. RKE received academic attention in the recent works of Cohn-Gordon et al. (EuroS&P 2017) and Bellare et al. (CRYPTO 2017). While the former is analytical in the sense that it aims primarily at assessing the security that one particular protocol does achieve (which might be weaker than the notion that it should achieve), the authors of the latter develop and instantiate a notion of security from scratch, independently of existing implementations. Unfortunately, however, their model is quite restricted, e.g. for considering only unidirectional communication and the exposure of only one of the two parties.
In this article we resolve the limitations of prior work by developing alternative security definitions, for unidirectional RKE as well as for RKE where both parties contribute. We follow a purist approach, aiming at finding strong yet convincing notions that cover a realistic communication model with fully concurrent operation of both participants. We further propose secure instantiations (as the protocols analyzed or proposed by Cohn-Gordon et al. and Bellare et al. turn out to be weak in our models). While our scheme for the unidirectional case builds on a generic KEM as the main building block (differently to prior work that requires explicitly Diffie–Hellman), our schemes for bidirectional RKE require a stronger, HIBE-like component.
Motivated by typo correction in password authentication, we investigate cryptographic error-correction of secrets in settings where the distribution of secrets is a priori (approximately) known. We refer to this as the distribution-sensitive setting.
We design a new secure sketch called the layer-hiding hash (LHH) that offers the best security to date. Roughly speaking, we show that LHH saves an additional log H_0(W) bits of entropy compared to the recent layered sketch construction due to Fuller, Reyzin, and Smith (FRS). Here H_0(W) is the size of the support of the distribution W. When supports are large, as with passwords, our new construction offers a substantial security improvement.
We provide two new constructions of typo-tolerant password-based authentication schemes. The first combines a LHH or FRS sketch with a standard slow-to-compute hash function, and the second avoids secure sketches entirely, correcting typos instead by checking all nearby passwords. Unlike the previous such brute-force-checking construction, due to Chatterjee et al., our new construction uses a hash function whose run-time is proportional to the popularity of the password (forcing a longer hashing time on more popular, lower entropy passwords). We refer to this as popularity-proportional hashing (PPH). We then introduce a frame-work for comparing different typo-tolerant authentication approaches. We show that PPH always offers a better time / security trade-off than the LHH and FRS constructions, and for certain distributions outperforms the Chatterjee et al. construction. Elsewhere, this latter construction offers the best trade-off. In aggregate our results suggest that the best known secure sketches are still inferior to simpler brute-force based approaches.
The pseudorandom-function oracle-Diffie–Hellman (PRF-ODH) assumption has been introduced recently to analyze a variety of DH-based key exchange protocols, including TLS 1.2 and the TLS 1.3 candidates, as well as the extended access control (EAC) protocol. Remarkably, the assumption comes in different flavors in these settings and none of them has been scrutinized comprehensively yet. In this paper here we therefore present a systematic study of the different PRF-ODH variants in the literature. In particular, we analyze their strengths relative to each other, carving out that the variants form a hierarchy. We further investigate the boundaries between instantiating the assumptions in the standard model and the random oracle model. While we show that even the strongest variant is achievable in the random oracle model under the strong Diffie–Hellman assumption, we provide a negative result showing that it is implausible to instantiate even the weaker variants in the standard model via algebraic black-box reductions to common cryptographic problems.