Abstract
An N argument function f(x 1,...,x N ) is called t-private if a protocol for computing f exists so that no coalition of at most t parties can infer any additional information from the execution, other than the value of the function. The motivation of this work is to understand what levels of privacy are attainable. So far, only two levels of privacy are known for N argument functions which are defined over finite domains: functions that are N-private and functions that are ⌊(N − 1)/2⌋-private but not ⌈N/2⌉-private.
In this work we show that the privacy hierarchy for N-argument functions which are defined over finite domains, has exactly ⌈(N + 1)/2⌉ levels. We prove this by constructing, for any ⌈N/2⌉ ≤ t ≤ N − 2, an N-argument function which is t-private but not (t + 1)-private.
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References
Beaver, D., Perfect Privacy for Two Party Protocols, Technical Report TR-11-89, Harvard University, 1989.
Benaloh (Cohen), J. D., Secret Sharing Homomorphisms: Keeping Shares of a Secret Secret, Advances in Cryptography—Crypto 86 (Proceedings), A. M. Odlyzko (ed.), Lecture Notes in Computer Science, Vol. 263, Springer-Verlag, Berlin, 1987, pp. 251–260.
Ben-Or, M., S. Goldwasser, and A. Wigderson, Completeness Theorems for Non-Cryptographic Fault-Tolerant Distributed Computation Proc. 20th STOC, 1988, pp. 1–10.
Blakley, G. R., Safeguarding Cryptographic Keys, Proc. NCC AFIPS, 1979, pp. 313–317.
Chaum, D., C. Crepeau, and I. Damgard, Multiparity Unconditionally Secure Protocols, Proc. 20th STOC, 1988, pp. 11–19.
Chor, B., M. Geréb-Graus, and E. Kushilevitz, Private Computations Over the Integers, Proc. 31th IEEE Conf. on the Foundations of Computer Science, October 1990, pp. 335–344.
Chor, B., and E. Kushilevitz, A Zero-One Law for Boolean Privacy, SIAM J. Discrete Math., Vol. 4, No. 1, 1991, pp. 36–47. Early version in Proc. 21th STOC, 1989, pp. 62–72.
Chor, B., and N. Shani, Privacy of Dense Symmetric Functions, Proc. 2nd Positano Workshop on Sequences, 1991.
Kushilevitz, E., Privacy and Communication Complexity, SIAM J. Discrete Math., Vol. 5, No. 2, 1992, pp. 273–284. Early version in Proc. 30th IEEE Conf. on the Foundations of Computer Science, 1989, pp. 416–421.
Shamir, A., How To Share a Secret, Comm. ACM, Vol. 22, 1979, pp. 612–613.
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Communicated by Oded Goldreich
This research was supported by US-Israel Binational Science Foundation Grant 88-00282.
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Chor, B., Geréb-Graus, M. & Kushilevitz, E. On the structure of the privacy hierarchy. J. Cryptology 7, 53–60 (1994). https://doi.org/10.1007/BF00195209
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DOI: https://doi.org/10.1007/BF00195209