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(log2 s) 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].
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Keywords
- Security Parameter
- Message Authentication Code
- Commitment Scheme
- Oblivious Transfer
- Computational Setting
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.
References
Bellare, M., Impagliazzo, R., Naor, M.: Does parallel repetition lower the error in computationally sound protocols? In: FOCS, pp. 374–383 (1997)
Canetti, R., Halevi, S., Steiner, M.: Hardness amplification of weakly verifiable puzzles. In: Kilian, J. (ed.) TCC 2005. LNCS, vol. 3378, pp. 17–33. Springer, Heidelberg (2005)
Dodis, Y., Impagliazzo, R., Jaiswal, R., Kabanets, V.: Security amplification for interactivecryptographic primitives. In: Reingold, O. (ed.) TCC 2009. LNCS, vol. 5444, pp. 128–145. Springer, Heidelberg (2009)
Damgård, I., Kilian, J., Salvail, L.: On the (im)possibility of basing oblivious transfer and bit commitment on weakened security assumptions. In: Stern, J. (ed.) EUROCRYPT 1999. LNCS, vol. 1592, pp. 56–73. Springer, Heidelberg (1999)
Dwork, C., Naor, M., Reingold, O.: Immunizing encryption schemes from decryption errors. In: Cachin, C., Camenisch, J.L. (eds.) EUROCRYPT 2004. LNCS, vol. 3027, pp. 342–360. Springer, Heidelberg (2004)
Goldreich, O.: Foundations of Cryptography. Basic tools. Cambridge University Press, Cambridge (2001)
Holenstein, T., Renner, R.: One-way secret-key agreement and applications to circuit polarization and immunization of public-key encryption. In: Shoup, V. (ed.) CRYPTO 2005. LNCS, vol. 3621, pp. 478–493. Springer, Heidelberg (2005)
Halevi, S., Rabin, T.: Degradation and amplification of computational hardness. In: Canetti, R. (ed.) TCC 2008. LNCS, vol. 4948, pp. 626–643. Springer, Heidelberg (2008)
Holenstein, T., Schoenebeck, G.: General hardness amplification of predicates and puzzles. CoRR, abs/1002.3534 (2010)
Impagliazzo, R., Jaiswal, R., Kabanets, V.: Chernoff-type direct product theorems. In: Menezes, A. (ed.) CRYPTO 2007. LNCS, vol. 4622, pp. 500–516. Springer, Heidelberg (2007)
Jutla, C.S.: Almost optimal bounds for direct product threshold theorem. In: Micciancio, D. (ed.) Theory of Cryptography. LNCS, vol. 5978, pp. 37–51. Springer, Heidelberg (2010)
Maurer, U., Tessaro, S.: Computational indistinguishability amplification: Tight product theorems for system composition. In: Halevi, S. (ed.) CRYPTO 2009. LNCS, vol. 5677, pp. 350–368. Springer, Heidelberg (2009)
Pietrzak, K., Wikström, D.: Parallel repetition of computationally sound protocols revisited. In: Vadhan, S.P. (ed.) TCC 2007. LNCS, vol. 4392, pp. 86–102. Springer, Heidelberg (2007)
Valiant, L.G.: Short monotone formulae for the majority function. J. Algorithms 5(3), 363–366 (1984)
Wullschleger, J.: Oblivious-transfer amplification. In: Naor, M. (ed.) EUROCRYPT 2007. LNCS, vol. 4515, pp. 555–572. Springer, Heidelberg (2007)
Yao, A.C.-C.: Theory and applications of trapdoor functions (extended abstract). In: FOCS, pp. 80–91 (1982)
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© 2010 International Association for Cryptologic Research
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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. https://doi.org/10.1007/978-3-642-17373-8_16
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