J-PAKE is a Password-Authenticated Key Exchange protocol, proposed in 2008 and presented again in 2010 and 2011. It does not require any public key infrastructure but uses zero-knowledge proofs. J-PAKE has been submitted as a candidate for the IEEE P1363.2 standard for password-based public key cryptography, and included in OpenSSL and OpenSSH. Since December 2010, J-PAKE has been used in Mozilla Firefox web browser. In this paper, we show that J-PAKE is vulnerable to password compromise impersonation attack, replay attack, and unknown key-share attack. We also propose some improvements for thwarting replay and unknown key-share attacks.
Ivan Damgård, Bernardo David, Irene Giacomelli, Jesper Buus Nielsen
We present a new compact verifiable secret sharing scheme, based on this we present the first construction of a homomorphic UC commitment scheme that requires only cheap symmetric cryptography, except for a small number of seed OTs. To commit to a k -bit string, the amortized communication cost is O ( k ) bits. Assuming a sufficiently efficient pseudorandom generator, the computational complexity is O ( k ) for the verifier and O ( k 1 + ε ) for the committer (where ε < 1 is a constant). In an alternative variant of the construction, all complexities are O ( k · polylog ( k )). Our commitment scheme extends to vectors over any finite field and is additively homomorphic. By sending one extra message, the prover can allow the verifier to also check multiplicative relations on committed strings, as well as verifying that committed vectors a , b satisfy a = φ ( b ) for a linear function φ . These properties allow us to non-interactively implement any one-sided functionality where only one party has input (this includes UC secure zero-knowledge proofs of knowledge). We also present a perfectly secure implementation of any multiparty functionality, based directly on our VSS. The communication required is proportional to a circuit implementing the functionality, up to a logarithmic factor. For a large natural class of circuits the overhead is even constant. We also improve earlier results by Ranellucci et al. on the amount of correlated randomness required for string commitments with individual opening of bits. These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.
Abstract. In this work, we first formalize the notion of dynamic group signatures with distributed traceability, where the capability to trace signatures is distributed among nmanagers without requiring any interaction. This ensures that only the participation of all tracing managers permits tracing a signature, which reduces the trust placed in a single tracing manager. The threshold variant follows easily from our definitions and constructions. Our model offers strong security requirements. Our second contribution is a generic construction for the notion which has a concurrent join protocol, meets strong security requirements, and offers efficient traceability, i.e. without requiring tracing managers to produce expensive zero-knowledge proofs for tracing correctness. To dispense with the expensive zero-knowledge proofs required in the tracing, we deploy a distributed tag-based encryption with public verifiability. Finally, we provide some concrete instantiations, which, to the best of our knowledge, are the first efficient provably secure realizations in the standard model simultaneously offering all the aforementioned properties. To realize our constructions efficiently, we construct an efficient distributed (and threshold) tag-based encryption scheme that works in the efficient Type-III asymmetric bilinear groups. Our distributed tag-based encryption scheme yields short ciphertexts (only 1280 bits at 128-bit security), and is secure under an existing variant of the standard decisional linear assumption. Our tag-based encryption scheme is of independent interest and is useful for many applications beyond the scope of this paper. As a special case of our distributed tag-based encryption scheme, we get an efficient tag-based encryption scheme in Type-III asymmetric bilinear groups that is secure in the standard model.
We introduce a novel concept of dual-system simulation-sound non-interactive zero-knowledge (NIZK) proofs. Dual-system NIZK proof system can be seen as a two-tier proof system. As op-posed to the usual notion of zero-knowledge proofs, dual-system defines an intermediate partial-simulation world, where the proof simulator may have access to additional auxiliary information about the potential language member, for example a membership bit, and simulation of proofs is only guaranteed if the membership bit is correct. Further, dual-system NIZK proofs allow a quasi-adaptive setting where the CRS can be generated based on language parameters. This allows for the further possibility that the partial-world CRS simulator may have access to fur-ther trapdoors related to the language parameters. We show that for important hard languages like the Diffie-Hellman language, such dual-system proof systems can be given which allow unbounded partial simulation soundness, and which further allow transition between partial simulation world and single-theorem full simulation world even when proofs are sought on non-members. The construction is surprisingly simple, involving only two additional group elements in asymmetric bilinear pairing groups.
Payman Mohassel, Seyed Saeed Sadeghian, Nigel P. Smart
Abstract. We propose the first general framework for designing actively secure private function eval-uation (PFE), not based on universal circuits. Our framework is naturally divided into pre-processing and online stages and can be instantiated using any generic actively secure multiparty computation (MPC) protocol. Our framework helps address the main open questions about efficiency of actively secure PFE. On the theoretical side, our framework yields the first actively secure PFE with linear complexity in the circuit size. On the practical side, we obtain the first actively secure PFE for arithmetic circuits with O(g · log g) complexity where g is the circuit size. The best previous construction (of practical interest) is based on an arithmetic universal circuit and has complexity O(g5). We also introduce the first linear Zero-Knowledge proof of correctness of “extended permutation ” of ciphertexts (a generalization of ZK proof of correct shuffles) which maybe of independent interest.
In the last few years the efficiency of secure multi-party computation (MPC) increased in several orders of magnitudes. However, this alone might not be enough if we want MPC protocols to be used in practice. A crucial property that is needed in many applications is that everyone can check that a given (secure) computation was performed correctly – even in the extreme case where all the parties involved in the computation are corrupted, and even if the party who wants to verify the result was not participating. This is especially relevant in the clients-servers setting, where many clients provide input to a secure computation performed by a few servers. An obvious example of this is electronic voting, but also in many types of auctions one may want independent verification of the result. Traditionally, this is achieved by using non-interactive zero-knowledge proofs during the computation. A recent trend in MPC protocols is to have a more expensive preprocessing phase followed by a very efficient online phase, e.g., the recent so-called SPDZ protocol by Damgard et al. Applications such as voting and some auctions are perfect use-case for these protocols, as the parties usually know well in advance when the computation will take place, and using those protocols allows us to use only cheap information-theoretic primitives in the actual computation. Unfortunately no protocol of the SPDZ type supports an audit phase. In this paper, we show how to achieve efficient MPC with a public audit. We formalize the concept of publicly auditable secure computation and provide an enhanced version of the SPDZ protocol where, even if all the servers are corrupted, anyone with access to the transcript of the protocol can check that the output is indeed correct. Most importantly, we do so without significantly compromising the performance of SPDZ i.e. our online phase has complexity approximately twice that of SPDZ.
Bitcoin is the first decentralized peer-to-peer crypto-currency founded in 2009. Its main specificity is the fact that there is no issuer of this currency. On the other hand, the supply of this currency is software-programmed and limited. Among other things, its main features are relatively secure payments, low transaction costs, anonymity, inability of counterfeiting, irreversibility of transactions, but also extremely unstable exchange rate. Despite many advantages, the use of this currency is subject of numerous discussions, as this currency offers the possibility of performing various abuses and criminal activities. The future of this and other currencies in this regard depends on both security and privacy of these currencies, and legal regulation of such payments.
The notion of Zero Knowledge introduced by Goldwasser, Micali and Rackoff in STOC 1985 is fundamental in Cryptography. Motivated by conceptual and practical reasons, this notion has been explored under stronger definitions. We will consider the following two main strengthened notions. Statistical Zero Knowledge: here the zero-knowledge property will last forever, even in case in future the adversary will have unlimited power. Concurrent Non-Malleable Zero Knowledge: here the zero-knowledge property is combined with non-transferability and the adversary fails in mounting a concurrent man-inthe-middle attack aiming at transferring zero-knowledge proofs/arguments. Besides the well-known importance of both notions, it is still unknown whether one can design a zero-knowledge protocol that satisfies both notions simultaneously. In this work we shed light on this question in a very strong sense. We show a statistical concurrent non-malleable zero-knowledge argument system for N P with a black-box simulatorextractor. 1
Abstract. We construct a 3-move public coin special honest verifier zero-knowledge proof, a so-called Sigma-protocol, for a list of commitments having at least one commit-ment that opens to 0. It is not required for the prover to know openings of the other commitments. The proof system is efficient, in particular in terms of communication requiring only the transmission of a logarithmic number of commitments. We use our proof system to instantiate both ring signatures and zerocoin, a novel mech-anism for bitcoin privacy. We use our Sigma-protocol as a (linkable) ad-hoc group identi-fication scheme where the users have public keys that are commitments and demonstrate knowledge of an opening for one of the commitments to unlinkably identify themselves (once) as belonging to the group. Applying the Fiat-Shamir transform on the group identification scheme gives rise to ring signatures, applying it to the linkable group iden-tification scheme gives rise to zerocoin. Our ring signatures are very small compared to other ring signature schemes and we only assume the users ’ secret keys to be the discrete logarithms of single group elements so the setup is quite realistic. Similarly, compared with the original zerocoin protocol we rely on a weak cryptographic assumption and do not require a trusted setup. A third application of our Sigma protocol is an efficient proof of membership of a secret committed value u belonging to a public list L = {λ1,..., λN}.
In this paper we discuss Bitcoin, the leader among the existing cryptocurrencies, to analyse its trends, success factors, current challenges and probable solutions to make it even better. In the introduction section, we discuss the history and working mechanism of Bitcoin. In the background section, we develop the ideas that evolved in the process of making a stable cryptocurrency. We also analyze the survey matrices of the present day cryptocurrencies. This survey clearly shows that Bitcoin is the clear winner among its kind. Section 3 is about the success factors of Bitcoin and the proceeding sections are a discussion about current challenges which pose as hurdles in making Bitcoin a better currency in the digital world. We finally discuss the balance between anonymity and reduced trust in the cryptocurrency world, before concluding the survey.
Zero knowledge proof system which has received extensive attention since it was proposed is an important branch of cryptography and computational complexity theory. Thereinto, noninteractive zero knowledge proof system contains only one message sent by the prover to the verifier. It is widely used in the construction of various types of cryptographic protocols and cryptographic algorithms because of its good privacy, authentication, and lower interactive complexity. This paper reviews and analyzes the basic principles of noninteractive zero knowledge proof system, and summarizes the research progress achieved by noninteractive zero knowledge proof system on the following aspects: the definition and related models of noninteractive zero knowledge proof system, noninteractive zero knowledge proof system of NP problems, noninteractive statistical and perfect zero knowledge, the connection between noninteractive zero knowledge proof system, interactive zero knowledge proof system, and zap, and the specific applications of noninteractive zero knowledge proof system. This paper also points out the future research directions.
Fabrice Benhamouda, Stephan Krenn, Vadim Lyubashevsky, Krzysztof Pietrzak
Abstract. We design an efficient commitment scheme, and companion zero-knowledge proofs of knowledge, based on the learning with errors over rings (RLWE) problem. In particular, for rings in which almost all elements have inverses, we construct a perfectly binding commitment scheme whose hiding property relies on the RLWE assumption. Our scheme maps elements from the ring (or equivalently, n elements from Fq) to a small constant number of ring elements. We then construct Σ-protocols for proving, in a zero-knowledge manner, knowledge of the message contained in a commitment. We are able to further extend our basic protocol to allow us to prove additive and multiplicative relations among committed values. Our protocols have a communication complexity of O(Mn log q) and achieve a negligible knowledge error in one run. Here M is the constant from a rejection sampling technique that we employ, and can be set close to 1 by adjusting other parameters. Previously known Σ-protocols for LWE-related languages either relied on “smudging ” out the error (which necessitates working over large fields, resulting in poor efficiency) or only achieved a noticeable or even constant knowledge error (thus requiring many repetitions of the protocol).
It is a widely spread belief that crypto-currencies implementing a proof of stake transaction validation system are less vulnerable to a 51% attack than crypto-currencies implementing a proof of work transaction validation system. In this article, we show that it is not the case and that, in fact, if the attacker's motivation is large enough (and this is common knowledge), he will succeed in his attack at no cost.
Marcin Andrychowicz, Stefan Dziembowski, Daniel Malinowski, Łukasz Mazurek
Bitcoin is a peer-to-peer cryptographic currency system. Since its introduction in 2008, Bitcoin has gained noticeable popularity, mostly due to its following properties: (1) the transaction fees are very low, and (2) it is not controlled by any central authority, which in particular means that nobody can "print" the money to generate inflation. Moreover, the transaction syntax allows to create the so-called contracts, where a number of mutually-distrusting parties engage in a protocol to jointly perform some financial task, and the fairness of this process is guaranteed by the properties of Bitcoin. Although the Bitcoin contracts have several potential applications in the digital economy, so far they have not been widely used in real life. This is partly due to the fact that they are cumbersome to create and analyze, and hence risky to use. In this paper we propose to remedy this problem by using the methods originally developed for the computer-aided analysis for hardware and software systems, in particular those based on the timed automata. More concretely, we propose a framework for modeling the Bitcoin contracts using the timed automata in the UPPAAL model checker. Our method is general and can be used to model several contracts. As a proof-of-concept we use this framework to model some of the Bitcoin contracts from our recent previous work. We then automatically verify their security in UPPAAL, finding (and correcting) some subtle errors that were difficult to spot by the manual analysis. We hope that our work can draw the attention of the researchers working on formal modeling to the problem of the Bitcoin contract verification, and spark off more research on this topic.
In Bitcoin, transaction malleability describes the fact that the signatures that prove the ownership of bitcoins being transferred in a transaction do not provide any integrity guarantee for the signatures themselves. This allows an attacker to mount a malleability attack in which it intercepts, modifies, and rebroadcasts a transaction, causing the transaction issuer to believe that the original transaction was not confirmed. In February 2014 MtGox, once the largest Bitcoin exchange, closed and filed for bankruptcy claiming that attackers used malleability attacks to drain its accounts. In this work we use traces of the Bitcoin network for over a year preceding the filing to show that, while the problem is real, there was no widespread use of malleability attacks before the closure of MtGox.
Eli Ben‐Sasson, Alessandro Chiesa, Christina Garman, Matthew Green · 7 authors
Bit coin is the first digital currency to see widespread adoption. While payments are conducted between pseudonyms, Bit coin cannot offer strong privacy guarantees: payment transactions are recorded in a public decentralized ledger, from which much information can be deduced. Zero coin (Miers et al., IEEE S&P 2013) tackles some of these privacy issues by unlinking transactions from the payment's origin. Yet, it still reveals payments' destinations and amounts, and is limited in functionality. In this paper, we construct a full-fledged ledger-based digital currency with strong privacy guarantees. Our results leverage recent advances in zero-knowledge Succinct Non-interactive Arguments of Knowledge (zk-SNARKs). First, we formulate and construct decentralized anonymous payment schemes (DAP schemes). A DAP scheme enables users to directly pay each other privately: the corresponding transaction hides the payment's origin, destination, and transferred amount. We provide formal definitions and proofs of the construction's security. Second, we build Zero cash, a practical instantiation of our DAP scheme construction. In Zero cash, transactions are less than 1 kB and take under 6 ms to verify - orders of magnitude more efficient than the less-anonymous Zero coin and competitive with plain Bit coin.
A widespread security claim of the Bitcoin system, presented in the original Bitcoin white-paper, states that the security of the system is guaranteed as long as there is no attacker in possession of half or more of the total computational power used to maintain the system. This claim, however, is proved based on theoretically flawed assumptions. In the paper we analyze two kinds of attacks based on two theoretical flaws: the Block Discarding Attack and the Difficulty Raising Attack. We argue that the current theoretical limit of attacker's fraction of total computational power essential for the security of the system is in a sense not $\frac{1}{2}$ but a bit less than $\frac{1}{4}$, and outline proposals for protocol change that can raise this limit to be as close to $\frac{1}{2}$ as we want. The basic idea of the Block Discarding Attack has been noted as early as 2010, and lately was independently though-of and analyzed by both author of this paper and authors of a most recently pre-print published paper. We thus focus on the major differences of our analysis, and try to explain the unfortunate surprising coincidence. To the best of our knowledge, the second attack is presented here for the first time.
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Blockchain Technology Applications and Security
Advanced Steganography and Watermarking Techniques
Marcelo Arenas, Juan L. Reutter, Etienne Toussaint, Martín Ugarte · 6 authors
In the consensus protocols used in most cryptocurrencies, participants called miners must find valid blocks of transactions and append them to a shared tree-like data structure. Ideally, the rules of the protocol should ensure that miners maximize their gains if they follow a default strategy, which consists on appending blocks only to the longest branch of the tree, called the blockchain. Our goal is to understand under which circumstances are miners encouraged to follow the default strategy. Unfortunately, most of the existing models work with simplified payoff functions, without considering the possibility that rewards decrease over time because of the game rules (like in Bitcoin), nor integrating the fact that a miner naturally prefers to be paid earlier than later (the economic concept of discount). In order to integrate these factors, we consider a more general model where issues such as economic discount and decreasing rewards can be set as parameters of an infinite stochastic game. In this model, we study the limit situation in which a miner does not receive a full reward for a block if it stops being in the blockchain. We show that if rewards are not decreasing, then miners do not have incentives to create new branches, no matter how high their computational power is. On the other hand, when working with decreasing rewards similar to those in Bitcoin, we show that miners have an incentive to create such branches. Nevertheless, this incentive only occurs when a miner controls a proportion of the computational power which is close to half of the computational power of the entire network.
One of important issues of information security in the interaction of users is the use of methods and tools, allowing one party to make sure of the authenticity of another party. The proof of knowledge protocols which have the additional property of zero-knowledge are applied to solve this problem. The protocols based on asymmetric encryption have received wide acceptance, such as the Fiat-Shamir, Schnorr, Okamoto, Guillou-Quisquater, Brickell-McCurley, Feige-Fiat-Shamir protocols. Cryptographic strength of these protocols is defined by discrete logarithms in a finite prime field, as well as an increase in the number of accreditation cycles. As a result of the development of methods and tools of cryptanalysis and rapid development of technologies and power of computing systems, there is a need to increase the sizes of system-wide parameters of the protocol, leading to increased resource intensity and performance complexity of basic operations in the fields.Cryptographic zero-knowledge protocols on elliptic curves are proposed in the paper. The strength of cryptosystems on elliptic curves is based on the difficulty of solving the discrete logarithm problem in the group of elliptic curve points, and is more difficult than the discrete logarithm problem in the finite field. The completeness and soundness of protocols were determined, computation examples were given. The tools of the Strength Protocol Animator package were applied to verify the protocols for resistance to enemy attacks. Consequently, the use of cryptographic protocols on elliptic curves will significantly reduce the sizes of protocol parameters and increase the cryptographic strength