Abstract
A multi-committer threshold commitment scheme is proposed based on the intractability assumption of Learning with errors problem. A group of committers consult a secret and divide it into several share pieces. Each member possesses a share piece. When de-committing, if a committer doesn’t want to admit or reveal the secret, he may refuse to open his piece, or even he may send an improper piece purposely when corrupted by a malicious adversary. If a majority of the committers agree to contribute their correct pieces, the receiver will accept the secret. The core idea is threshold secret share. This scheme satisfies the necessary properties, such as binding, hiding, non-malleability, and adaptive corruption chosen-plaintext security against malicious adversary. The commitment expansion factor is as small as O(log2 q) so as to communicate efficiently.
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References
Fischlin, M., Fischlin, R.: Efficient Non-malleable Commitment Schemes. In: Bellare, M. (ed.) CRYPTO 2000. LNCS, vol. 1880, pp. 413–431. Springer, Heidelberg (2000)
Di Crescenzo, G., Katz, J., Ostrovsky, R., Smith, A.: Efficient and Non-interactive Non-malleable Commitment. In: Pfitzmann, B. (ed.) EUROCRYPT 2001. LNCS, vol. 2045, pp. 40–59. Springer, Heidelberg (2001)
Zhang, Z.Y., Cao, Z.F., Ding, N., Ma, R.: Non-malleable Statistically Hiding Commitment from Any One-Way Function. In: Matsui, M. (ed.) ASIACRYPT 2009. LNCS, vol. 5912, pp. 303–318. Springer, Heidelberg (2009)
Shamir, A.: How to Share a Secret. Communications of the ACM 22(11), 612–613 (1979)
Canetti, R., Goldwasser, S.: An Efficient Threshold Public Key Cryptosystem Secure against Adaptive Chosen Ciphertext Attack. In: Stern, J. (ed.) EUROCRYPT 1999. LNCS, vol. 1592, pp. 90–106. Springer, Heidelberg (1999)
Libert, B., Yung, M.: Adaptively Secure Non-interactive Threshold Cryptosystems. In: Aceto, L., Henzinger, M., Sgall, J. (eds.) ICALP 2011, Part II. LNCS, vol. 6756, pp. 588–600. Springer, Heidelberg (2011)
Bendlin, R., Damgård, I.: Threshold Decryption and Zero-Knowledge Proofs for Lattice-Based Cryptosystems. In: Micciancio, D. (ed.) TCC 2010. LNCS, vol. 5978, pp. 201–218. Springer, Heidelberg (2010)
Regev, O.: On Lattices, Learning with Errors, Random Linear Codes, and Cryptography. In: Proceedings of 37th Annual ACM Symposium on Theory of Computing-STOC 2005, pp. 84–93. ACM, New York (2005)
Gentry, C., Peikert, C., Vaikuntanathan, V.: Trapdoors for Hard Lattices and New Cryptographic Constructions. In: Proceedings of the 40th Annual ACM Symposium on Theory of Computing-STOC 2008, pp. 197–206. ACM, New York (2008)
Peikert, C.: Public-Key Cryptosystems from the Worst-case Shortest Vector Problem. In: Proceedings of the 41st Annual ACM Symposium on Theory of Computing-STOC 2009, pp. 333–342. ACM, New York (2009)
Applebaum, B., Cash, D., Peikert, C., Sahai, A.: Fast Cryptographic Primitives and Circular-Secure Encryption Based on Hard Learning Problems. In: Halevi, S. (ed.) CRYPTO 2009. LNCS, vol. 5677, pp. 595–618. Springer, Heidelberg (2009)
Cash, D., Hofheinz, D., Kiltz, E., Peikert, C.: Bonsai Trees, or How to Delegate a Lattice Basis. In: Gilbert, H. (ed.) EUROCRYPT 2010. LNCS, vol. 6110, pp. 523–552. Springer, Heidelberg (2010)
Gordon, S.D., Katz, J., Vaikuntanathan, V.: A Group Signature Scheme from Lattice Assumptions. In: Abe, M. (ed.) ASIACRYPT 2010. LNCS, vol. 6477, pp. 395–412. Springer, Heidelberg (2010)
Peikert, C., Vaikuntanathan, V., Waters, B.: A Framework for Efficient and Composable Oblivious Transfer. In: Wagner, D. (ed.) CRYPTO 2008. LNCS, vol. 5157, pp. 554–571. Springer, Heidelberg (2008)
Agrawal, S., Boneh, D., Boyen, X.: Efficient Lattice (H)IBE in the Standard Model. In: Gilbert, H. (ed.) EUROCRYPT 2010. LNCS, vol. 6110, pp. 553–572. Springer, Heidelberg (2010)
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Sun, W., Yang, B., Huang, Q., Ma, S., Li, X. (2012). Multi-Committer Threshold Commitment Scheme from Lattice. In: Chau, M., Wang, G.A., Yue, W.T., Chen, H. (eds) Intelligence and Security Informatics. PAISI 2012. Lecture Notes in Computer Science, vol 7299. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-30428-6_14
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DOI: https://doi.org/10.1007/978-3-642-30428-6_14
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