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

Foundations, Properties, and Security Applications of Puzzles: A Survey

Cryptographic algorithms have been used not only to create robust ciphertexts but also to generate cryptograms that, contrary to the classic goal of cryptography, are meant to be broken. These cryptograms, generally called puzzles, require the use of a certain amount of resources to be solved, hence introducing a cost that is often regarded as a time delay---though it could involve other metrics as well, such as bandwidth. These powerful features have made puzzles the core of many security protocols, acquiring increasing importance in the IT security landscape. The concept of a puzzle has subsequently been extended to other types of schemes that do not use cryptographic functions, such as CAPTCHAs, which are used to discriminate humans from machines. Overall, puzzles have experienced a renewed interest with the advent of Bitcoin, which uses a CPU-intensive puzzle as proof of work. In this paper, we provide a comprehensive study of the most important puzzle construction schemes available in the literature, categorizing them according to several attributes, such as resource type, verification type, and applications. We have redefined the term puzzle by collecting and integrating the scattered notions used in different works, to cover all the existing applications. Moreover, we provide an overview of the possible applications, identifying key requirements and different design approaches. Finally, we highlight the features and limitations of each approach, providing a useful guide for the future development of new puzzle schemes.Comment: This article has been accepted for publication in ACM Computing Survey

Stronger difficulty notions for client puzzles and denial-of-service-resistant protocols

Client puzzles are meant to act as a defense against denial of service (DoS) attacks by requiring a client to solve some moderately hard problem before being granted access to a resource. However, recent client puzzle difficulty definitions (Stebila and Ustaoglu, 2009; Chen et al., 2009) do not ensure that solving n puzzles is n times harder than solving one puzzle. Motivated by examples of puzzles where this is the case, we present stronger definitions of difficulty for client puzzles that are meaningful in the context of adversaries with more computational power than required to solve a single puzzle. A protocol using strong client puzzles may still not be secure against DoS attacks if the puzzles are not used in a secure manner. We describe a security model for analyzing the DoS resistance of any protocol in the context of client puzzles and give a generic technique for combining any protocol with a strong client puzzle to obtain a DoS-resistant protocol

Multi-instance publicly verifiable time-lock puzzle and its applications

Time-lock puzzles are elegant protocols that enable a party to lock a message such that no one else can unlock it until a certain time elapses. Nevertheless, existing schemes are not suitable for the case where a server is given multiple instances of a puzzle scheme at once and it must unlock them at different points in time. If the schemes are naively used in this setting, then the server has to start solving all puzzles as soon as it receives them, that ultimately imposes significant computation cost and demands a high level of parallelisation. We put forth and formally define a primitive called “multi-instance time-lock puzzle” which allows composing a puzzle’s instances. We propose a candidate construction: “chained time-lock puzzle” (C-TLP). It allows the server, given instances’ composition, to solve puzzles sequentially, without having to run parallel computations on them. C-TLP makes black-box use of a standard time-lock puzzle scheme and is accompanied by a lightweight publicly verifiable algorithm. It is the first time-lock puzzle that offers a combination of the above features. We use C-TLP to build the first “outsourced proofs of retrievability” that can support real-time detection and fair payment while having lower overhead than the state of the art. As another application of C-TLP, we illustrate in certain cases, one can substitute a “verifiabledelay function” with C-TLP, to gain much better efficiency

Separating Two-Round Secure Computation From Oblivious Transfer

We consider the question of minimizing the round complexity of protocols for secure multiparty computation (MPC) with security against an arbitrary number of semi-honest parties. Very recently, Garg and Srinivasan (Eurocrypt 2018) and Benhamouda and Lin (Eurocrypt 2018) constructed such 2-round MPC protocols from minimal assumptions. This was done by showing a round preserving reduction to the task of secure 2-party computation of the oblivious transfer functionality (OT). These constructions made a novel non-black-box use of the underlying OT protocol. The question remained whether this can be done by only making black-box use of 2-round OT. This is of theoretical and potentially also practical value as black-box use of primitives tends to lead to more efficient constructions. Our main result proves that such a black-box construction is impossible, namely that non-black-box use of OT is necessary. As a corollary, a similar separation holds when starting with any 2-party functionality other than OT. As a secondary contribution, we prove several additional results that further clarify the landscape of black-box MPC with minimal interaction. In particular, we complement the separation from 2-party functionalities by presenting a complete 4-party functionality, give evidence for the difficulty of ruling out a complete 3-party functionality and for the difficulty of ruling out black-box constructions of 3-round MPC from 2-round OT, and separate a relaxed "non-compact" variant of 2-party homomorphic secret sharing from 2-round OT

Delegated Time-Lock Puzzle

Time-Lock Puzzles (TLPs) are cryptographic protocols that enable a client to lock a message in such a way that a server can only unlock it after a specific time period. However, existing TLPs have certain limitations: (i) they assume that both the client and server always possess sufficient computational resources and (ii) they solely focus on the lower time bound for finding a solution, disregarding the upper bound that guarantees a regular server can find a solution within a certain time frame. Additionally, existing TLPs designed to handle multiple puzzles either (a) entail high verification costs or (b) lack generality, requiring identical time intervals between consecutive solutions. To address these limitations, this paper introduces, for the first time, the concept of a "Delegated Time-Lock Puzzle" and presents a protocol called "Efficient Delegated Time-Lock Puzzle" (ED-TLP) that realises this concept. ED-TLP allows the client and server to delegate their resource-demanding tasks to third-party helpers. It facilitates real-time verification of solution correctness and efficiently handles multiple puzzles with varying time intervals. ED-TLP ensures the delivery of solutions within predefined time limits by incorporating both an upper bound and a fair payment algorithm. We have implemented ED-TLP and conducted a comprehensive analysis of its overheads, demonstrating the efficiency of the construction

A Novel WLAN Client Puzzle against DoS Attack Based on Pattern Matching

Despite the popularity of 802.11 based networks, they suffer several types of DoS attack, launched by an attacker whose aim is to make an access point (AP) unavailable to legitimate users. One of the most common DoS attacks on 802.11 based networks is to deplete the resources of the AP. A serious situation like this can occur when the AP receives a burst of connection requests. This paper addresses this common DoS attack and proposes a lightweight puzzle, based on pattern-matching. Using a pattern-matching technique, this model adequately resists resource-depletion attacks in terms of both puzzle generation and solution verification. Using a sensible series of contextual comparisons, the outcomes were modelled by a simulator, and the security definition and proofs are verified, among other results

Fair Client Puzzles from the Bitcoin Blockchain

Client puzzles have been proposed as a mechanism for proving legitimate intentions by providing ``proofs of work\u27\u27, which can be applied to discourage malicious usage of resources. A typical problem of puzzle constructions is the difference in expected solving time on different computing platforms. We call puzzles which can be solved independently of client computing resources \emph{fair client puzzles}. We propose a construction for client puzzles requiring widely distributed computational effort for their solution. These puzzles can be solved using the mining process of Bitcoin, or similar cryptocurrencies. Adapting existing definitions, we show that our puzzle construction satisfies formal requirements of client puzzles under reasonable assumptions. We describe a way of transforming our client puzzles for use in denial of service scenarios and demonstrate a practical construction