Foundations, Properties, and Security Applications of Puzzles

Abstract

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 article, 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.

BAD: A Blockchain Anomaly Detection Solution

“…• Agreement: the decision values of all the correct processes are the same; • Integrity 2 : if the correct processes all proposed the same value v, then any correct process has set its decision variable to v; • Termination: eventually each correct process sets its decision variable. In the remaining part of this section we give a brief review of how standard ADS systems work and provide an overview on how we can build an ADS on top of the meta-data leveraged by a blockchain running a proof-of-work like [10] consensus protocol that generates local meta-data discarded at the time of block creation. We refer the reader to [7] for a formal and more complete treatment of blockchain's protocols.…”

Resource Burning for Permissionless Systems (Invited Paper)

“…We define resource burning as the verifiable consumption of a resource. In particular, it is computationally easy to verify both the consumption of the resource, and also the ID that consumed the resource [6]. Below we describe several resource-burning techniques.…”

Client Puzzle Protocols as Countermeasure Against Automated Threats to Web Applications

“…Finding a hash that meets a preset target is an example of a puzzle [3]. Long before rising to prominence with the Bitcoin boom, PoW schemes implemented in client puzzle protocols (CPPs) have been proposed as a deterrent to SPAM [4], [5] and as a protection from Denial-of-Service (DoS) attacks against internet facing servers [6], [7].…”

“…Some of the most popular underlying puzzles are based on prime modulo operations [4], [8]- [10], partial hash inversions [5]- [7], [11], [12], and memory intensive computations [13]- [17]. (See [3] for a recent review of puzzle types; for a review of PoW schemes applied to blockchain technology, see [18]. )…”

“…To the best of our knowledge, there has been virtually no academic research on CPPs designed to protect web applications from automated threat [3]. A possible exception is represented by a recent US patent proposing a CPP based on a partial hash inversion puzzle as mitigation against DoS attacks [23].…”