Abstract
Secure multiparty computation (MPC) allows multiple parties to evaluate functions without disclosing the private inputs. Secure comparisons (testing equality and greater-than) are important primitives required by many MPC applications. We propose two equality tests for ℓ-bit values with O(1) online communication that require O(ℓ) respectively O(κ) total work, where κ is a correctness parameter.
Combining these with ideas of Toft [16], we obtain (i) a greater-than protocol with sublinear online complexity in the arithmetic black-box model (O(c) rounds and O(c·ℓ1/c) work online, with c = logℓ resulting in logarithmic online work). In difference to Toft, we do not assume two mutually incorruptible parties, but O(ℓ) offline work is required, and (ii) two greater-than protocols with the same online complexity as the above, but with overall complexity reduced to O(logℓ(κ + loglogℓ)) and O(c·ℓ1/c (κ + logℓ)); these require two mutually incorruptible parties, but are highly competitive with respect to online complexity when compared to existing protocols.
Access provided by Autonomous University of Puebla. Download to read the full chapter text
Chapter PDF
Similar content being viewed by others
References
Aiello, W., Ishai, Y., Reingold, O.: Priced Oblivious Transfer: How to Sell Digital Goods. In: Pfitzmann, B. (ed.) EUROCRYPT 2001. LNCS, vol. 2045, pp. 119–135. Springer, Heidelberg (2001)
Bar-Ilan, J., Beaver, D.: Non-Cryptographic Fault-Tolerant Computing in a Constant Number of Rounds of Interaction. In: Rudnicki, P. (ed.) PODC 1989, pp. 201–209. ACM Press (1989)
Ben-Or, M., Goldwasser, S., Wigderson, A.: Completeness Theorems for Non-Cryptographic Fault-Tolerant Distributed Computation. In: STOC 1988, pp. 1–10. ACM Press (1988)
Bogetoft, P., Christensen, D.L., Damgård, I., Geisler, M., Jakobsen, T., Krøigaard, M., Nielsen, J.D., Nielsen, J.B., Nielsen, K., Pagter, J., Schwartzbach, M., Toft, T.: Secure Multiparty Computation Goes Live. In: Dingledine, R., Golle, P. (eds.) FC 2009. LNCS, vol. 5628, pp. 325–343. Springer, Heidelberg (2009)
Chaabouni, R., Lipmaa, H., Zhang, B.: A Non-interactive Range Proof with Constant Communication. In: Keromytis, A.D. (ed.) FC 2012. LNCS, vol. 7397, pp. 179–199. Springer, Heidelberg (2012)
Damgård, I.B., Fitzi, M., Kiltz, E., Nielsen, J.B., Toft, T.: Unconditionally Secure Constant-Rounds Multi-party Computation for Equality, Comparison, Bits and Exponentiation. In: Halevi, S., Rabin, T. (eds.) TCC 2006. LNCS, vol. 3876, pp. 285–304. Springer, Heidelberg (2006)
Damgård, I.B., Nielsen, J.B.: Universally Composable Efficient Multiparty Computation from Threshold Homomorphic Encryption. In: Boneh, D. (ed.) CRYPTO 2003. LNCS, vol. 2729, pp. 247–264. Springer, Heidelberg (2003)
Groth, J.: Short Pairing-Based Non-interactive Zero-Knowledge Arguments. In: Abe, M. (ed.) ASIACRYPT 2010. LNCS, vol. 6477, pp. 321–340. Springer, Heidelberg (2010)
Laur, S., Lipmaa, H.: A New Protocol for Conditional Disclosure of Secrets and Its Applications. In: Katz, J., Yung, M. (eds.) ACNS 2007. LNCS, vol. 4521, pp. 207–225. Springer, Heidelberg (2007)
Lipmaa, H.: On Diophantine Complexity and Statistical Zero-Knowledge Arguments. In: Laih, C.-S. (ed.) ASIACRYPT 2003. LNCS, vol. 2894, pp. 398–415. Springer, Heidelberg (2003)
Lipmaa, H.: Progression-Free Sets and Sublinear Pairing-Based Non-Interactive Zero-Knowledge Arguments. In: Cramer, R. (ed.) TCC 2012. LNCS, vol. 7194, pp. 169–189. Springer, Heidelberg (2012)
Naor, M., Pinkas, B.: Oblivious Transfer and Polynomial Evaluation. In: STOC 1999, pp. 245–254. ACM Press (1999)
Nishide, T., Ohta, K.: Multiparty Computation for Interval, Equality, and Comparison Without Bit-Decomposition Protocol. In: Okamoto, T., Wang, X. (eds.) PKC 2007. LNCS, vol. 4450, pp. 343–360. Springer, Heidelberg (2007)
Paillier, P.: Public-Key Cryptosystems Based on Composite Degree Residuosity Classes. In: Stern, J. (ed.) EUROCRYPT 1999. LNCS, vol. 1592, pp. 223–238. Springer, Heidelberg (1999)
Thorbek, R.: Linear Integer Secret Sharing. Ph.D. thesis, Aarhus University (2009)
Toft, T.: Sub-linear, Secure Comparison with Two Non-colluding Parties. In: Catalano, D., Fazio, N., Gennaro, R., Nicolosi, A. (eds.) PKC 2011. LNCS, vol. 6571, pp. 174–191. Springer, Heidelberg (2011)
Toft, T.: Primitives and Applications for Multiparty Computation. Ph.D. thesis, Aarhus University (2007)
Yu, C.H.: Sign Modules in Secure Arithmetic Circuits. Tech. Rep. 2011/539, IACR (October 1, 2011), http://eprint.iacr.org/2011/539 (checked in February 2013)
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2013 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Lipmaa, H., Toft, T. (2013). Secure Equality and Greater-Than Tests with Sublinear Online Complexity. In: Fomin, F.V., Freivalds, R., Kwiatkowska, M., Peleg, D. (eds) Automata, Languages, and Programming. ICALP 2013. Lecture Notes in Computer Science, vol 7966. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-39212-2_56
Download citation
DOI: https://doi.org/10.1007/978-3-642-39212-2_56
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-39211-5
Online ISBN: 978-3-642-39212-2
eBook Packages: Computer ScienceComputer Science (R0)