RiffleScrambler - a memory-hard password storing function

We introduce RiffleScrambler: a new family of directed acyclic graphs and a corresponding data-independent memory hard function with password independent memory access. We prove its memory hardness in the random oracle model. RiffleScrambler is similar to Catena -- updates of hashes are determined by a graph (bit-reversal or double-butterfly graph in Catena). The advantage of the RiffleScrambler over Catena is that the underlying graphs are not predefined but are generated per salt, as in Balloon Hashing. Such an approach leads to higher immunity against practical parallel attacks. RiffleScrambler offers better efficiency than Balloon Hashing since the in-degree of the underlying graph is equal to 3 (and is much smaller than in Ballon Hashing). At the same time, because the underlying graph is an instance of a Superconcentrator, our construction achieves the same time-memory trade-offs.Comment: Accepted to ESORICS 201

On the Depth-Robustness and Cumulative Pebbling Cost of Argon2i

Argon2i is a data-independent memory hard function that won the password hashing competition. The password hashing algorithm has already been incorporated into several open source crypto libraries such as libsodium. In this paper we analyze the cumulative memory cost of computing Argon2i. On the positive side we provide a lower bound for Argon2i. On the negative side we exhibit an improved attack against Argon2i which demonstrates that our lower bound is nearly tight. In particular, we show that (1) An Argon2i DAG is $\left(e,O\left(n^3/e^3\right)\right))$-reducible. (2) The cumulative pebbling cost for Argon2i is at most $O\left(n^{1.768}\right)$. This improves upon the previous best upper bound of $O\left(n^{1.8}\right)$ [Alwen and Blocki, EURO S&P 2017]. (3) Argon2i DAG is $\left(e,\tilde{\Omega}\left(n^3/e^3\right)\right))$-depth robust. By contrast, analysis of [Alwen et al., EUROCRYPT 2017] only established that Argon2i was $\left(e,\tilde{\Omega}\left(n^2/e^2\right)\right))$-depth robust. (4) The cumulative pebbling complexity of Argon2i is at least $\tilde{\Omega}\left( n^{1.75}\right)$. This improves on the previous best bound of $\Omega\left( n^{1.66}\right)$ [Alwen et al., EUROCRYPT 2017] and demonstrates that Argon2i has higher cumulative memory cost than competing proposals such as Catena or Balloon Hashing. We also show that Argon2i has high {\em fractional} depth-robustness which strongly suggests that data-dependent modes of Argon2 are resistant to space-time tradeoff attacks

A New Distribution-Sensitive Secure Sketch and Popularity-Proportional Hashing

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

Securing Multiparty Protocols against the Exposure of Data to Honest Parties

We consider a new adversarial goal in multiparty protocols, where the adversary may corrupt some parties. The goal is to manipulate the view of some honest party in a way, that this honest party learns the private data of some other honest party. The adversary itself might not learn this data at all. This goal, and such attacks are significant because they create a liability to the first honest party to clean its systems from second honest party\u27s data; a task that may be highly non-trivial. Protecting against this goal essentially means achieving security against several non-cooperating adversaries, where all but one adversary are passive and corrupt only a single party. We formalize the adversarial goal by proposing an alternative notion of universal composability. We show how existing, conventionally secure multiparty protocols can be transformed to make them secure against the novel adversarial goal

Data-Independent Memory Hard Functions: New Attacks and Stronger Constructions

Memory-hard functions (MHFs) are a key cryptographic primitive underlying the design of moderately expensive password hashing algorithms and egalitarian proofs of work. Over the past few years several increasingly stringent goals for an MHF have been proposed including the requirement that the MHF have high sequential space-time (ST) complexity, parallel space-time complexity, amortized area-time (aAT) complexity and sustained space complexity. Data-Independent Memory Hard Functions (iMHFs) are of special interest in the context of password hashing as they naturally resist side-channel attacks. iMHFs can be specified using a directed acyclic graph (DAG) $G$ with $N=2^n$ nodes and low indegree and the complexity of the iMHF can be analyzed using a pebbling game. Recently, Alwen et al. [CCS 17] constructed a DAG called DRSample that has aAT complexity at least $\Omega\left( N^2/\log N\right)$. Asymptotically DRSample outperformed all prior iMHF constructions including Argon2i, winner of the password hashing competition (aAT cost $\mathcal{O}\left(N^{1.767}\right)$), though the constants in these bounds are poorly understood. We show that the greedy pebbling strategy of Boneh et al. [ASIACRYPT 16] is particularly effective against DRSample e.g., the aAT cost is $\mathcal{O}\left( N^2/\log N\right)$. In fact, our empirical analysis {\em reverses} the prior conclusion of Alwen et al. that DRSample provides stronger resistance to known pebbling attacks for practical values of $N \leq 2^{24}$. We construct a new iMHF candidate (DRSample+BRG) by using the bit-reversal graph to extend DRSample. We then prove that the construction is asymptotically optimal under every MHF criteria, and we empirically demonstrate that our iMHF provides the best resistance to {\em known} pebbling attacks. For example, we show that any parallel pebbling attack either has aAT cost $\omega(N^2)$ or requires at least $\Omega(N)$ steps with $\Omega(N/\log N)$ pebbles on the DAG. This makes our construction the first practical iMHF with a strong sustained space-complexity guarantee and immediately implies that any parallel pebbling has aAT complexity $\Omega(N^2/\log N)$. We also prove that any sequential pebbling (including the greedy pebbling attack) has aAT cost $\Omega\left( N^2\right)$ and, if a plausible conjecture holds, any parallel pebbling has aAT cost $\Omega(N^2 \log \log N/\log N)$ --- the best possible bound for an iMHF

Static-Memory-Hard Functions, and Modeling the Cost of Space vs. Time

A series of recent research starting with (Alwen and Serbinenko, STOC 2015) has deepened our understanding of the notion of memory-hardness in cryptography — a useful property of hash functions for deterring large-scale password-cracking attacks — and has shown memory-hardness to have intricate connections with the theory of graph pebbling. Definitions of memory-hardness are not yet unified in the somewhat nascent field of memory-hardness, however, and the guarantees proven to date are with respect to a range of proposed definitions. In this paper, we observe two significant and practical considerations that are not analyzed by existing models of memory-hardness, and propose new models to capture them, accompanied by constructions based on new hard-to-pebble graphs. Our contribution is two-fold, as follows. First, existing measures of memory-hardness only account for dynamic memory usage (i.e., memory read/written at runtime), and do not consider static memory usage (e.g., memory on disk). Among other things, this means that memory requirements considered by prior models are inherently upper-bounded by a hash function’s runtime; in contrast, counting static memory would potentially allow quantification of much larger memory requirements, decoupled from runtime. We propose a new definition of static-memory-hard function (SHF) which takes static memory into account: we model static memory usage by oracle access to a large preprocessed string, which may be considered part of the hash function description. Static memory requirements are complementary to dynamic memory requirements: neither can replace the other, and to deter large-scale password-cracking attacks, a hash function will benefit from being both dynamic memory-hard and static-memory-hard. We give two SHF constructions based on pebbling. To prove static-memory-hardness, we define a new pebble game (“black-magic pebble game”), and new graph constructions with optimal complexity under our proposed measure. Moreover, we provide a prototype implementation of our first SHF construction (which is based on pebbling of a simple “cylinder” graph), providing an initial demonstration of practical feasibility for a limited range of parameter settings. Secondly, existing memory-hardness models implicitly assume that the cost of space and time are more or less on par: they consider only linear ratios between the costs of time and space. We propose a new model to capture nonlinear time-space trade-offs: e.g., how is the adversary impacted when space is quadratically more expensive than time? We prove that nonlinear tradeoffs can in fact cause adversaries to employ different strategies from linear tradeoffs. Finally, as an additional contribution of independent interest, we present an asymptotically tight graph construction that achieves the best possible space complexity up to log log n-factors for an existing memory-hardness measure called cumulative complexity in the sequential pebbling model

Continuous Group Key Agreement with Active Security

A continuous group key agreement (CGKA) protocol allows a long-lived group of parties to agree on a continuous stream of fresh secret key material. The protocol must support constantly changing group membership, make no assumptions about when, if, or for how long members come online, nor rely on any trusted group managers. Due to sessions\u27 long life-time, CGKA protocols must simultaneously ensure both post-compromise security and forward secrecy (PCFS). That is, current key material should be secure despite both past and future compromises. The work of Alwen et al. (CRYPTO\u2720), introduced the CGKA primitive and identified it as a crucial component for constructing end-to-end secure group messaging protocols (SGM) (though we believe there are certainly more applications given the fundamental nature of key agreement). The authors analyzed the TreeKEM CGKA, which lies at the heart of the SGM protocol under development by the IETF working group on Messaging Layer Security (MLS). In this work, we continue the study of CGKA as a stand-alone cryptographic primitive. We present $3$ new security notions with increasingly powerful adversaries. Even the weakest of the 3 (passive security) already permits attacks to which all prior constructions (including all variants of TreeKEM) are vulnerable. Going further, the 2 stronger (active security) notions additionally allow the adversary to use parties\u27 exposed states (and full network control) to mount attacks. These are closely related to so-called insider attacks, which involve malicious group members actively deviating from the protocol. Insider attacks present a significant challenge in the study of CGKA (and SGM). Indeed, we believe ours to be the first security notions (and constructions) to formulate meaningful guarantees (e.g. PCFS) against such powerful adversaries. They are also the first composable security notions for CGKA of any type at all. In terms of constructions, for each of the 3 security notions we provide a new CGKA scheme enjoying sub-linear (potentially even logarithmic) communication complexity in the number of group members. We prove each scheme optimally secure, in the sense that the only security violations possible are those necessarily implied by correctness

Public Evidence from Secret Ballots

Elections seem simple---aren't they just counting? But they have a unique, challenging combination of security and privacy requirements. The stakes are high; the context is adversarial; the electorate needs to be convinced that the results are correct; and the secrecy of the ballot must be ensured. And they have practical constraints: time is of the essence, and voting systems need to be affordable and maintainable, and usable by voters, election officials, and pollworkers. It is thus not surprising that voting is a rich research area spanning theory, applied cryptography, practical systems analysis, usable security, and statistics. Election integrity involves two key concepts: convincing evidence that outcomes are correct and privacy, which amounts to convincing assurance that there is no evidence about how any given person voted. These are obviously in tension. We examine how current systems walk this tightrope.Comment: To appear in E-Vote-Id '1

Time-Memory Tradeoff Attacks on the MTP Proof-of-Work Scheme

Proof-of-work (PoW) schemes are cryptographic primitives with numerous applications, and in particular, they play a crucial role in maintaining consensus in cryptocurrency networks. Ideally, a cryptocurrency PoW scheme should have several desired properties, including efficient verification on one hand, and high memory consumption of the prover\u27s algorithm on the other hand, making the scheme less attractive for implementation on dedicated hardware. At the USENIX Security Symposium 2016, Biryukov and Khovratovich presented a new promising PoW scheme called MTP (Merkle Tree Proof) that achieves essentially all desired PoW properties. As a result, MTP has received substantial attention from the cryptocurrency community. The scheme uses a Merkle hash tree construction over a large array of blocks computed by a memory consuming (memory-hard) function. Despite the fact that only a small fraction of the memory is verified by the efficient verification algorithm, the designers claim that a cheating prover that uses a small amount of memory will suffer from a significant computational penalty. In this paper, we devise a sub-linear computation-memory tradeoff attack on MTP. We apply our attack to the concrete instance proposed by the designers which uses the memory-hard function Argon2d and computes a proof by allocating 2 gigabytes of memory. The attack computes arbitrary malicious proofs using less than a megabyte of memory (about 1/3000 of the honest prover\u27s memory) at a relatively mild penalty of 170 in computation. This is more than 55,000 times faster than what is claimed by the designers. The attack requires a one-time precomputation step of complexity $2^{64}$, but its online cost is only increased by a factor which is less than 2 when spending $2^{48}$ precomputation time. The main idea of the attack is to exploit the fact that Argon2d accesses its memory in a way which is determined by its previous computations. This allows to inject a small fraction of carefully selected memory blocks that manipulate Argon2d\u27s memory access patterns, significantly weakening its memory-hardness

Public-Key Encryption Schemes with Auxiliary Inputs

7th Theory of Cryptography Conference, TCC 2010, Zurich, Switzerland, February 9-11, 2010. ProceedingsWe construct public-key cryptosystems that remain secure even when the adversary is given any computationally uninvertible function of the secret key as auxiliary input (even one that may reveal the secret key information-theoretically). Our schemes are based on the decisional Diffie-Hellman (DDH) and the Learning with Errors (LWE) problems. As an independent technical contribution, we extend the Goldreich-Levin theorem to provide a hard-core (pseudorandom) value over large fields.National Science Foundation (U.S.) (Grant CCF-0514167)National Science Foundation (U.S.) (Grant CCF-0635297)National Science Foundation (U.S.) (Grant NSF-0729011)Israel Science Foundation (700/08)Chais Family Fellows Progra