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Modular Square Root Puzzles: Design of Non-Parallelizable and Non-Interactive Client Puzzles

Author(s): Yves Igor Jerschow, Martin Mauve.
Title: Modular Square Root Puzzles: Design of Non-Parallelizable and Non-Interactive Client Puzzles
Published: Computers & Security 35 (), pp. 25-36, 2013
Keyword(s): client puzzles, Denial of Service (DoS), network protocols, authentication, computational puzzles
Abstract: Denial of Service (DoS) attacks aiming to exhaust the resources of aserver by overwhelming it with bogus requests have become a serious threat.Especially protocols that rely on public key cryptography and perform expensiveauthentication handshakes may be an easy target. A well-known countermeasureagainst resource depletion attacks are client puzzles. The victimized serverdemands from the clients to commit computing resources before it processestheir requests. To get service, a client must solve a cryptographic puzzle andsubmit the right solution. Existing client puzzle schemes have some drawbacks.They are either parallelizable, coarse-grained or can be used only interactively.In case of interactive client puzzles where the server poses the challenge anattacker might mount a counterattack on the clients by injecting faked packetswith bogus puzzle parameters bearing the server's sender address. In thispaper we introduce a novel scheme for client puzzles which relies on thecomputation of square roots modulo a prime. Modular square root puzzles arenon-parallelizable, i. e., the solution cannot be obtained faster than scheduledby distributing the puzzle to multiple machines or CPU cores, and they can beemployed both interactively and non-interactively. Our puzzles provide polynomialgranularity and compact solution and verification functions. Benchmarkresults demonstrate the feasibility of our approach to mitigate DoS attacks onhosts in 1 or even 10 Gbit networks. In addition, we show how to raise theefficiency of our puzzle scheme by introducing a bandwidth-based cost factor forthe client. Furthermore, we also investigate the construction of client puzzlesfrom modular cube roots.
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