Abstract
In an influential work aimed at understanding the communication requirements of secure computation, Feige, Kilian and Naor introduced a minimal model of secure computation (STOC 1994). In that work, among other results, Feige et al. presented a simple protocol for the 2 input AND function. It has remained an intriguing question whether the communication and randomness used in this protocol are optimal. While previous work of Data et al. (CRYPTO 2014) showed that the communication from the two parties with inputs (Alice and Bob) to the third party who gets the output is optimal, the question of optimality for the third message in the protocol – a common reference string shared between Alice and Bob – remained open. In this note we show that in fact, this message (and hence all the randomness used in the protocol) is also optimal in the protocol of Feige et al. This improves on a previous result of Rajan et al. (ISIT 2016), which showed this optimality restricted to protocols where Alice and Bob are deterministic. Further, our result holds even if only a weak secrecy condition is required of the protocol.
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Notes
- 1.
This model is also known as the Private Simultaneous Messages (PSM) model, after [11]. The PSM model was originally introduced for a variant of the FKN model with an asymptotically growing number of input parties. Since our focus, similar to [8], is on the setting of 2 input parties, we shall refer to the model as the FKN model.
- 2.
- 3.
They can be derived from AND by negating the inputs and/or the output.
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Pillai, S.R.B., Prabhakaran, M., Prabhakaran, V.M., Sridhar, S. (2019). Optimality of a Protocol by Feige-Kilian-Naor for Three-Party Secure Computation. In: Hao, F., Ruj, S., Sen Gupta, S. (eds) Progress in Cryptology – INDOCRYPT 2019. INDOCRYPT 2019. Lecture Notes in Computer Science(), vol 11898. Springer, Cham. https://doi.org/10.1007/978-3-030-35423-7_11
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