On the amortized complexity of zero knowledge protocols for multiplicative relations

Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)

Volumn 7412 LNCS, Issue , 2012, Pages 62-79

  Cramer, Ronald ^a   Damgård, Ivan ^a   Pastro, Valerio ^a  

^a AARHUS UNIVERSITY   (Denmark)

Author keywords

[No Author keywords available]

Indexed keywords

ALGEBRAIC CIRCUITS; BASIC PROTOCOLS; CIRCUIT SATISFIABILITY; COMMITMENT SCHEME; ERROR PROBABILITIES; FINITE FIELDS; INTEGER MULTIPLICATIONS; INTEGER VALUES; INTERACTIVE PROOFS; STRONG RSA ASSUMPTION; ZERO KNOWLEDGE; ZERO-KNOWLEDGE PROTOCOLS;

INFORMATION THEORY;

SECURITY OF DATA;

EID: 84865008509     PISSN: 03029743     EISSN: 16113349     Source Type: Book Series    
DOI: 10.1007/978-3-642-32284-6_4     Document Type: Conference Paper

References (18)

1. Bendlin, R., Damgård, I., Orlandi, C., Zakarias, S.: Semi-Homomorphic Encryption and Multiparty Computation. In: Paterson, K.G. (ed.) EUROCRYPT 2011. LNCS, vol. 6632, pp. 169-188. Springer, Heidelberg (2011)
2. Boudot, F.: Efficient Proofs that a Committed Number Lies in an Interval. In: Preneel, B. (ed.) EUROCRYPT 2000. LNCS, vol. 1807, pp. 431-444. Springer, Heidelberg (2000)
3. Ben-Sasson, E., Fehr, S., Ostrovsky, R.: Near-linear unconditionally- secure multiparty computation with a dishonest minority. Cryptology ePrint Archive, Report 2011/629 (2011), http://eprint.iacr.org/
4. Chen, H., Cramer, R.: Algebraic Geometric Secret Sharing Schemes and Secure Multi-Party Computations over Small Fields. In: Dwork, C. (ed.) CRYPTO 2006. LNCS, vol. 4117, pp. 521-536. Springer, Heidelberg (2006)
5. Chen, H., Cramer, R., Goldwasser, S., de Haan, R., Vaikuntanathan, V.: Secure Computation from Random Error Correcting Codes. In: Naor, M. (ed.) EUROCRYPT 2007. LNCS, vol. 4515, pp. 291-310. Springer, Heidelberg (2007)
6. Cramer, R., Damgård, I.: Zero-Knowledge Proofs for Finite Field Arithmetic or: Can Zero-Knowledge Be for Free? In: Krawczyk, H. (ed.) CRYPTO 1998. LNCS, vol. 1462, pp. 424-441. Springer, Heidelberg (1998)
7. Cramer, R., Damgård, I.: On the Amortized Complexity of Zero-Knowledge Protocols. In: Halevi, S. (ed.) CRYPTO 2009. LNCS, vol. 5677, pp. 177-191. Springer, Heidelberg (2009)
8. Cramer, R., Damgård, I., Dziembowski, S., Hirt, M., Rabin, T.: Efficient Multiparty Computations Secure Against an Adaptive Adversary. In: Stern, J. (ed.) EUROCRYPT 1999. LNCS, vol. 1592, pp. 311-326. Springer, Heidelberg (1999)
9. Cramer, R., Damgård, I., Maurer, U.M.: General Secure Multi-party Computation from any Linear Secret-Sharing Scheme. In: Preneel, B. (ed.) EUROCRYPT2000. LNCS, vol. 1807, pp. 316-334. Springer,Heidelberg (2000)
10. Cramer, R., Damgård, I., Nielsen, J.B.: Multiparty Computation from Threshold Homomorphic Encryption. In: Pfitzmann, B. (ed.) EUROCRYPT 2001. LNCS, vol. 2045, pp. 280-299. Springer, Heidelberg (2001)
11. Damgård, I., Fujisaki, E.: A Statistically-Hiding Integer Commitment Scheme Based on Groups with Hidden Order. In: Zheng, Y. (ed.) ASIACRYPT 2002. LNCS, vol. 2501, pp. 125-142. Springer, Heidelberg (2002)
12. Damgård, I., Ishai, Y., Krøigaard, M.: Perfectly Secure Multiparty Computation and the Computational Overhead of Cryptography. In: Gilbert, H. (ed.) EUROCRYPT 2010. LNCS, vol. 6110, pp. 445-465. Springer, Heidelberg (2010)
13. Damgård, I., Pastro, V., Smart, N.P., Zakarias, S.: Multiparty Computation from Somewhat Homomorphic Encryption. In: Safavi-Naini, R. (ed.) CRYPTO 2012. LNCS, vol. 7417, pp. 643-662. Springer, Heidelberg (2012)
14. Fujisaki, E., Okamoto, T.: Statistical Zero Knowledge Protocols to Prove Modular Polynomial Relations. In: Kaliski Jr., B.S. (ed.) CRYPTO 1997. LNCS, vol. 1294, pp. 16-30. Springer, Heidelberg (1997)
15. Franklin, M.K., Yung, M.: Communication complexity of secure computation (extended abstract). In: STOC, pp. 699-710. ACM (1992)
16. Goldwasser, S., Micali, S.: Probabilistic encryption. J. Comput. Syst. Sci. 28(2), 270-299 (1984)
17. Ishai, Y., Kushilevitz, E., Ostrovsky, R., Sahai, A.: Zero-knowledge proofs from secure multiparty computation. SIAM J. Comput. 39(3), 1121-1152 (2009)
18. Karchmer, M., Wigderson, A.: On Span Programs. In: Structure in Complexity Theory Conference, pp. 102-111 (1993)