General Hardness Amplification of Predicates and Puzzles

(Extended Abstract)
  • Thomas Holenstein
  • Grant Schoenebeck
Conference paper

DOI: 10.1007/978-3-642-19571-6_2

Part of the Lecture Notes in Computer Science book series (LNCS, volume 6597)
Cite this paper as:
Holenstein T., Schoenebeck G. (2011) General Hardness Amplification of Predicates and Puzzles. In: Ishai Y. (eds) Theory of Cryptography. TCC 2011. Lecture Notes in Computer Science, vol 6597. Springer, Berlin, Heidelberg


We give new proofs for the hardness amplification of efficiently samplable predicates and of weakly verifiable puzzles which generalize to new settings. More concretely, in the first part of the paper, we give a new proof of Yao’s XOR-Lemma that additionally applies to related theorems in the cryptographic setting. Our proof seems simpler than previous ones, yet immediately generalizes to statements similar in spirit such as the extraction lemma used to obtain pseudo-random generators from one-way functions [Håstad, Impagliazzo, Levin, Luby, SIAM J. on Comp. 1999].

In the second part of the paper, we give a new proof of hardness amplification for weakly verifiable puzzles, which is more general than previous ones in that it gives the right bound even for an arbitrary monotone function applied to the checking circuit of the underlying puzzle.

Both our proofs are applicable in many settings of interactive cryptographic protocols because they satisfy a property that we call “non-rewinding”. In particular, we show that any weak cryptographic protocol whose security is given by the unpredictability of single bits can be strengthened with a natural information theoretic protocol. As an example, we show how these theorems solve the main open question from [Halevi and Rabin, TCC2008] concerning bit commitment.

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Copyright information

© International Association for Cryptologic Research 2011

Authors and Affiliations

  • Thomas Holenstein
    • 1
  • Grant Schoenebeck
    • 2
  1. 1.Department of Computer ScienceETH ZurichSwitzerland
  2. 2.Department of Computer SciencePrinceton UniversityPrincetonUSA

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