Efficient String-Commitment from Weak Bit-Commitment

  • Kai-Min Chung
  • Feng-Hao Liu
  • Chi-Jen Lu
  • Bo-Yin Yang
Conference paper

DOI: 10.1007/978-3-642-17373-8_16

Part of the Lecture Notes in Computer Science book series (LNCS, volume 6477)
Cite this paper as:
Chung KM., Liu FH., Lu CJ., Yang BY. (2010) Efficient String-Commitment from Weak Bit-Commitment. In: Abe M. (eds) Advances in Cryptology - ASIACRYPT 2010. ASIACRYPT 2010. Lecture Notes in Computer Science, vol 6477. Springer, Berlin, Heidelberg

Abstract

We study security amplification for commitment schemes and improve the efficiency of black-box security amplification in the computational setting, where the security holds against PPT active adversaries. We show that ω(logs) black-box calls to a weak bit-commitment scheme with constant security is sufficient to construct a commitment scheme with standard negligible security, where s denotes the security parameter and ω(logs) denotes any super-logarithmic function of s. Furthermore, the resulting scheme is a string commitment scheme that can commit to O(logs)-bit strings. This improves on previous work of Damgård et al. [DKS99] and Halevi and Rabin [HR08], whose transformations require ω(log2s) black-box calls to commit a single bit.

As a byproduct of our analysis, we also improve the efficiency of security amplification for message authentication codes, digital signatures, and pseudorandom functions studied in [DIJK09]. This is from an improvement of the “Chernoff-type Theorems” of dynamic weakly-verifiable puzzles of [DIJK09].

Copyright information

© International Association for Cryptologic Research 2010

Authors and Affiliations

  • Kai-Min Chung
    • 1
  • Feng-Hao Liu
    • 2
  • Chi-Jen Lu
    • 3
  • Bo-Yin Yang
    • 3
  1. 1.School of Engineering & Applied SciencesHarvard UniversityCambridgeUSA
  2. 2.Department of Computer ScienceBrown UniversityUSA
  3. 3.Institute of Information ScienceAcademia SinicaTaipeiTaiwan

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