Abstract
Two parties, P 1 and P 2, wish to jointly compute some function f(x,y) where P 1 only knows x, whereas P 2 only knows y. Furthermore, and most importantly, the parties wish to reveal only what the output suggests. Function f is said to be computable with complete fairness if there exists a protocol computing f such that whenever one of the parties obtains the correct output, then both of them do. The only protocol known to compute functions with complete fairness is the one of Gordon et al (STOC 2008). The functions in question are finite, Boolean, and the output is shared by both parties. The classification of such functions up to fairness may be a first step towards the classification of all functionalities up to fairness. Recently, Asharov (TCC 2014) identifies two families of functions that are computable with fairness using the protocol of Gordon et al and another family for which the protocol (potentially) falls short. Surprisingly, these families account for almost all finite Boolean functions. In this paper, we expand our understanding of what can be computed fairly with the protocol of Gordon et al. In particular, we fully describe which functions the protocol computes fairly and which it (potentially) does not. Furthermore, we present a new class of functions for which fair computation is outright impossible. Finally, we confirm and expand Asharov’s observation regarding the fairness of finite Boolean functions: almost all functions f:X×Y → {0,1} for which |X| ≠ |Y| are fair, whereas almost all functions for which |X| = |Y| are not.
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References
Agrawal, S., Prabhakaran, M.: On fair exchange, fair coins and fair sampling. In: Canetti, R., Garay, J.A. (eds.) CRYPTO 2013, Part I. LNCS, vol. 8042, pp. 259–276. Springer, Heidelberg (2013)
Asharov, G.: Towards characterizing complete fairness in secure two-party computation. In: Lindell, Y. (ed.) TCC 2014. LNCS, vol. 8349, pp. 291–316. Springer, Heidelberg (2014)
Asharov, G.: Towards characterizing complete fairness in secure two-party computation (extended version). Cryptology ePrint Archive, Report 2014/098 098 (2014), http://eprint.iacr.org/2014/098
Asharov, G., Lindell, Y., Rabin, T.: A full characterization of functions that imply fair coin tossing and ramifications to fairness. In: Sahai, A. (ed.) TCC 2013. LNCS, vol. 7785, pp. 243–262. Springer, Heidelberg (2013)
Blum, M.: Coin flipping by telephone a protocol for solving impossible problems. SIGACT News 15(1), 23–27 (1983)
Canetti, R.: Security and composition of multiparty cryptographic protocols. J. Cryptology 13(1), 143–202 (2000)
Cleve, R.: Limits on the security of coin flips when half the processors are faulty. In: STOC 1986, pp. 364–369. ACM (1986)
Goldreich, O.: Foundations of Cryptography. Basic Applications, vol. 2. Cambridge University Press (2004)
Gordon, D.S., Hazay, C., Katz, J., Lindell, Y.: Complete fairness in secure two-party computation. In: STOC 2008, pp. 413–422. ACM (2008)
Gordon, S.D., Hazay, C., Katz, J., Lindell, Y.: Complete fairness in secure two-party computation (extended version). Cryptology ePrint Archive, Report 2008/303 (2008), http://eprint.iacr.org/2008/303
Moran, T., Naor, M., Segev, G.: An optimally fair coin toss. In: Reingold, O. (ed.) TCC 2009. LNCS, vol. 5444, pp. 1–18. Springer, Heidelberg (2009)
Yao, A.C.: Protocols for secure computations, pp. 160–164 (1982)
Ziegler, G.M.: Lectures on 0/1-polytopes. In: Kalai, G., Ziegler, G.M. (eds.) Polytopes Combinatorics and Computation, DMV Seminar, pp. 1–41. Birkhauser, Basel (2000)
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Makriyannis, N. (2014). On the Classification of Finite Boolean Functions up to Fairness. In: Abdalla, M., De Prisco, R. (eds) Security and Cryptography for Networks. SCN 2014. Lecture Notes in Computer Science, vol 8642. Springer, Cham. https://doi.org/10.1007/978-3-319-10879-7_9
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DOI: https://doi.org/10.1007/978-3-319-10879-7_9
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