Abstract
The universal composability (UC) for commitment is a very strong security notion. It guarantees that commitment schemes remain secure even if they are composed with arbitrary protocols and polynomially many copies of the schemes are run concurrently. Several UC commitment schemes in the common reference string (CRS) model have been proposed, but, they are either interactive commitment or bit-commitment (not string-commitment) schemes. We propose new non-interactive string-commitment schemes that achieve UC security in the CRS model assuming the difficulty of the decisional Diffie-Hellman problem or the decisional composite residuosity problem, but our schemes are not reusable. The main building blocks of our constructions are all-but-one trapdoor functions (ABO-TDFs) introduced by Peikert and Waters in STOC 2008 to construct secure public-key encryption schemes. Our main idea is to use the homomorphic properties of the function indices of the all-but-one trapdoor functions and to extend the functions to probabilistic ones by using re-randomization of ciphertexts. This is a new application of ABO-TDFs.
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References
Barak, B., Canetti, R., Nielsen, J.B., Pass, R.: Universally Composable Protocols with Relaxed Set-up Assumptions. In: FOCS 2004, pp. 186–195 (2004)
Camenisch, J., Shoup, V.: Practical Verifiable Encryption and Decryption of Discrete Logarithms. In: Boneh, D. (ed.) CRYPTO 2003. LNCS, vol. 2729, pp. 126–144. Springer, Heidelberg (2003)
Canetti, R.: Universally Composable Security: A New Paradigm for Cryptograpic Protocols. In: Cryptology ePrint Archive, Report 2000/067, Preliminary version appeared in FOCS 2001 (2005)
Canetti, R., Dodis, Y., Pass, R., Walfish, S.: Universally Composable Security with Global Setup. In: Vadhan, S.P. (ed.) TCC 2007. LNCS, vol. 4392, pp. 61–85. Springer, Heidelberg (2007)
Canetti, R., Fischlin, M.: Universally Composable Commitments. In: Kilian, J. (ed.) CRYPTO 2001. LNCS, vol. 2139, pp. 19–40. Springer, Heidelberg (2001)
Canetti, R., Kushilevitz, E., Lindell, Y.: On the Limitations of Universally Composable Two-Party Computation Without Set-Up Assumptions. J. Cryptology 19(2), 135–167 (2006)
Canetti, R., Lindell, Y., Ostrovsky, R., Sahai, A.: Universally Composable Two-Party and Multi-Party Secure Computation. In: STOC 2002, pp. 494–503 (2002)
Canetti, R., Pass, R., Shelat, A.: Cryptography from Sunspots: How to Use an Imperfect Reference String. In: FOCS 2007, pp. 249–259 (2007)
Canetti, R., Rabin, T.: Universal Composition with Joint State. In: Boneh, D. (ed.) CRYPTO 2003. LNCS, vol. 2729, pp. 265–281. Springer, Heidelberg (2003)
Damgård, I., Jurik, M.: A Generalisation, a Simplification and Some Applications of Paillier’s Probabilistic Public-Key System. In: Kim, K.-c. (ed.) PKC 2001. LNCS, vol. 1992, pp. 125–140. Springer, Heidelberg (2001)
Damgård, I., Groth, J.: Non-interactive and Reusable Non-Malleable Commitment Schemes. In: STOC 2003, pp. 426–437 (2003)
Damgård, I., Nielsen, J.B.: Perfect Hiding and Perfect Binding Universally Composable Commitment Schemes with Constant Expansion Factor. In: Yung, M. (ed.) CRYPTO 2002. LNCS, vol. 2442, pp. 581–596. Springer, Heidelberg (2002)
Dodis, Y., Ostrovsky, R., Reyzin, L., Smith, A.: Fuzzy Extractors: How to Generate Strong Keys from Biometrics and Other Noisy Data. SIAM J. Computing 38(1), 97–139 (2008)
Dolev, D., Dwork, C., Naor, M.: Non-malleable cryptography. SIAM J. Computing 30, 391–437 (2000)
Goldreich, O., Micali, S., Wigderson, A.: Proofs that Yield Nothing but their Validity, or All Languages in NP have Zero-Knowledge Proof Systems. Journal of the ACM 38(3), 691–729 (1991); Preliminary version appeared in FOCS 1986
Hofheinz, D., Müller-Quade, J.: Universally Composable Commitments Using Random Oracles. In: Naor, M. (ed.) TCC 2004. LNCS, vol. 2951, pp. 58–76. Springer, Heidelberg (2004)
Katz, J.: Universally Composable Multi-party Computation Using Tamper-Proof Hardware. In: Naor, M. (ed.) EUROCRYPT 2007. LNCS, vol. 4515, pp. 115–128. Springer, Heidelberg (2007)
Naor, M.: Bit Commitment Using Pseudorandomness. J. Cryptology 4(2), 151–158 (1991)
Pedersen, T.P.: Non-Interactive and Information-Theoretic Secure Verifiable Secret Sharing. In: Feigenbaum, J. (ed.) CRYPTO 1991. LNCS, vol. 576, pp. 129–140. Springer, Heidelberg (1992)
Peikert, C., Waters, B.: Lossy Trapdoor Functions and Their Applications. In: STOC 2008, pp. 187–196 (2008)
Prabhakaran, M., Sahai, A.: New Notions of Security: Achieving Universal Composability without Trusted Setup. In: STOC 2004, pp. 242–251 (2004)
Rosen, A., Segev, G.: Efficient Lossy Trapdoor Functions based on the Composite Residuosity Assumption. In: Cryptology ePrint Archive, Report 2008/134 (2008)
Zhu, H.: New Constructions for Reusable, Non-erasure and Universally Composable Commitments. In: Bao, F., Li, H., Wang, G. (eds.) ISPEC 2009. LNCS, vol. 5451, pp. 102–111. Springer, Heidelberg (2009)
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Nishimaki, R., Fujisaki, E., Tanaka, K. (2009). Efficient Non-interactive Universally Composable String-Commitment Schemes. In: Pieprzyk, J., Zhang, F. (eds) Provable Security. ProvSec 2009. Lecture Notes in Computer Science, vol 5848. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-04642-1_3
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DOI: https://doi.org/10.1007/978-3-642-04642-1_3
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