Abstract. Client puzzles are moderately-hard cryptographic problems -neither easy nor impossible to solve -that can be used as a countermeasure against denial of service attacks on network protocols. Puzzles based on modular exponentiation are attractive as they provide important properties such as non-parallelisability, deterministic solving time, and linear granularity. We propose an efficient client puzzle based on modular exponentiation. Our puzzle requires only a few modular multiplications for puzzle generation and verification. For a server under denial of service attack, this is a significant improvement as the best known non-parallelisable puzzle proposed by Karame andČapkun (ESORICS 2010) requires at least 2k-bit modular exponentiation, where k is a security parameter. We show that our puzzle satisfies the unforgeability and difficulty properties defined by Chen et al. (Asiacrypt 2009). We present experimental results which show that, for 1024-bit moduli, our proposed puzzle can be up to 30× faster to verify than the Karame-Čapkun puzzle and 99× faster than the Rivest et al.'s time-lock puzzle.
Recently, Rangasamy et al. REF proposed a modular exponentiation-based client puzzle which can be seen as an efficient alternative to Rivest et al. 's time-lock puzzle.
Efficient Modular Exponentiation-based Puzzles for Denial-of-Service Protection
IACR Cryptology ePrint Archive
IACR Cryptology ePrint Archive
Computer Science Mathematics