On Non-Parallelizable Deterministic Client Puzzle Scheme with Batch Verification Modes

A (computational) client puzzle scheme enables a client to prove to a server that a certain amount of computing resources (CPU cycles and/or Memory look-ups) has been dedicated to solve a puzzle. Researchers have identified a number of potential applications, such as constructing timed cryptography, fighting junk emails, and protecting critical infrastructure from DoS attacks. In this paper, we first revisit this concept and formally define two properties, namely deterministic computation and parallel computation resistance. Our analysis show that both properties are crucial for the effectiveness of client puzzle schemes in most application scenarios. We prove that the RSW client puzzle scheme, which is based on the repeated squaring technique, achieves both properties. Secondly, we introduce two batch verification modes for the RSW client puzzle scheme in order to improve the verification efficiency of the server, and investigate three methods for handling errors in batch verifications. Lastly, we show that client puzzle schemes can be integrated with reputation systems to further improve the effectiveness in practice

Type 2 Structure-Preserving Signature Schemes Revisited

Abstract. Abe, Groth, Ohkubo and Tibouchi recently presented structure-preserving signature schemes using Type 2 pairings. The schemes are claimed to enjoy the fastest signature verification. By properly accounting for subgroup membership testing of group elements in signatures, we show that the schemes are not as efficient as claimed. We presen

Snappy: Fast On-chain Payments with Practical Collaterals

Permissionless blockchains offer many advantages but also have significant limitations including high latency. This prevents their use in important scenarios such as retail payments, where merchants should approve payments fast. Prior works have attempted to mitigate this problem by moving transactions off the chain. However, such Layer-2 solutions have their own problems: payment channels require a separate deposit towards each merchant and thus significant locked-in funds from customers; payment hubs require very large operator deposits that depend on the number of customers; and side-chains require trusted validators. In this paper, we propose Snappy, a novel solution that enables recipients, like merchants, to safely accept fast payments. In Snappy, all payments are on the chain, while small customer collaterals and moderate merchant collaterals act as payment guarantees. Besides receiving payments, merchants also act as statekeepers who collectively track and approve incoming payments using majority voting. In case of a double-spending attack, the victim merchant can recover lost funds either from the collateral of the malicious customer or a colluding statekeeper (merchant). Snappy overcomes the main problems of previous solutions: a single customer collateral can be used to shop with many merchants; merchant collaterals are independent of the number of customers; and validators do not have to be trusted. Our Ethereum prototype shows that safe, fast (<2 seconds) and cheap payments are possible on existing blockchains.Comment: Network and Distributed Systems Security (NDSS) Symposium 2020, 23-26 February 2020, San Diego, CA, US

Delegating a Product of Group Exponentiations with Application to Signature Schemes

Many public-key cryptosystems and, more generally, cryptographic protocols, use group exponentiations as important primitive operations. To expand the applicability of these solutions to computationally weaker devices, it has been advocated that a computationally weaker client (i.e., capable of performing a relatively small number of modular multiplications) delegates such primitive operations to a computationally stronger server. Important requirements for such delegation protocols include privacy of the client's input exponent and security of the client's output, in the sense of detecting, except for very small probability, any malicious server's attempt to convince the client of an incorrect exponentiation result. Only recently, ecient protocols for the delegation of a xed-based exponentiation, over cyclic and RSA-type groups with certain properties, have been presented and proved to satisfy both requirements. In this paper we show that a product of many xed-base exponentiations, over a cyclic groups with certain properties, can be privately and securely delegated by keeping the client's online number of modular multiplications only slightly larger than in the delegation of a single exponentiation. We use this result to show the rst delegations of entire cryptographic schemes: the well-known digital signature schemes by El-Gamal, Schnorr and Okamoto, over the q-order subgroup in Zp, for p; q primes, as well as their variants based on elliptic curves. Previous ecient delegation results seem limited to the delegation of single algorithms within cryptographic schemes

Secure location-aware communications in energy-constrained wireless networks

Wireless ad hoc network has enabled a variety of exciting civilian, industrial and military applications over the past few years. Among the many types of wireless ad hoc networks, Wireless Sensor Networks (WSNs) has gained popularity because of the technology development for manufacturing low-cost, low-power, multi-functional motes. Compared with traditional wireless network, location-aware communication is a very common communication pattern and is required by many applications in WSNs. For instance, in the geographical routing protocol, a sensor needs to know its own and its neighbors\u27 locations to forward a packet properly to the next hop. The application-aware communications are vulnerable to many malicious attacks, ranging from passive eavesdropping to active spoofing, jamming, replaying, etc. Although research efforts have been devoted to secure communications in general, the properties of energy-constrained networks pose new technical challenges: First, the communicating nodes in the network are always unattended for long periods without physical maintenance, which makes their energy a premier resource. Second, the wireless devices usually have very limited hardware resources such as memory, computation capacity and communication range. Third, the number of nodes can be potentially of very high magnitude. Therefore, it is infeasible to utilize existing secure algorithms designed for conventional wireless networks, and innovative mechanisms should be designed in a way that can conserve power consumption, use inexpensive hardware and lightweight protocols, and accommodate with the scalability of the network. In this research, we aim at constructing a secure location-aware communication system for energy-constrained wireless network, and we take wireless sensor network as a concrete research scenario. Particularly, we identify three important problems as our research targets: (1) providing correct location estimations for sensors in presence of wormhole attacks and pollution attacks, (2) detecting location anomalies according to the application-specific requirements of the verification accuracy, and (3) preventing information leakage to eavesdroppers when using network coding for multicasting location information. Our contributions of the research are as follows: First, we propose two schemes to improve the availability and accuracy of location information of nodes. Then, we study monitoring and detection techniques and propose three lightweight schemes to detect location anomalies. Finally, we propose two network coding schemes which can effectively prevent information leakage to eavesdroppers. Simulation results demonstrate the effectiveness of our schemes in enhancing security of the system. Compared to previous works, our schemes are more lightweight in terms of hardware cost, computation overhead and communication consumptions, and thus are suitable for energy-constrained wireless networks

Fast batch verification for modular exponentiation and digital signatures

Abstract Many tasks in cryptography (e.g., digital signature verification) call for verification of a basicoperation like modular exponentiation in some group: given ( g, x, y) check that gx = y. Thisis typically done by re-computing gx and checking we get y. We would like to do it differently,and faster. The approach we use is batching. Focusing first on the basic modular exponentiation oper-ation, we provide some probabilistic batch verifiers, or tests, that verify a sequence of modular exponentiations significantly faster than the naive re-computation method. This yields speedupsfor several verification tasks that involve modular exponentiations

Practical Zero-Knowledge Arguments from Structured Reference Strings

Zero-knowledge proofs have become an important tool for addressing privacy and scalability concerns in cryptographic protocols. For zero-knowledge proofs used in blockchain applications, it is desirable to have small proof sizes and fast verification. Yet by design, existing constructions with these properties such as zk-SNARKs also have a secret trapdoor embedded in a relation dependent structured reference string (SRS). Knowledge of this trapdoor suffices to break the security of these proofs. The SRSs required by zero-knowledge proofs are usually constructed with multiparty computation protocols, but the resulting parameters are specific to each individual circuit. In this thesis, we propose a model for constructing zero-knowledge arguments (i.e. zero-knowledge proofs with computational soundness) in which the generation of the SRS is directly considered in the security analysis. In our model the same SRS can be used across multiple applications. Further, the model is updatable i.e. users can update the universal SRS and the SRS is considered secure provided at least one of these users is honest. We propose two zero-knowledge arguments with updatable and universal SRSs, as well as a third which is neither updatable nor universal, but which through similar techniques achieves simulation extractability. The proposed arguments are practical, with proof sizes never more than a constant number of group elements. Verification for two of our constructions consist of a small number of pairing operations. For our other construction, which has the desirable property of a linear sized updatable and universal SRS, we describe efficient batching techniques so that verification is fast in the amortised setting