TY - JOUR

T1 - On perfectly secure 2PC in the OT-hybrid model

AU - Alon, Bar

AU - Paskin-Cherniavsky, Anat

N1 - Publisher Copyright:
© 2021

PY - 2021/11/4

Y1 - 2021/11/4

N2 - A well known result by Kilian (1988) [23] asserts that general secure two computation (2PC) with statistical security, can be based on OT. Specifically, in the client-server model, where only one party – the client – receives an output, Kilian's result shows that given the ability to call an ideal oracle that computes OT, two parties can securely compute an arbitrary function of their inputs with unconditional security. Ishai et al. (2011) [20] further showed that this can be done efficiently for every two-party functionality in NC1 in a single round. However, their results only achieve statistical security, namely, it is allowed to have some error in security. This leaves open the natural question as to which client-server functionalities can be computed with perfect security in the OT-hybrid model, and what is the round complexity of such computation. So far, only a handful of functionalities were known to have such protocols. In addition to the obvious theoretical appeal of the question towards better understanding secure computation, perfect, as opposed to statistical reductions, may be useful for designing secure multiparty protocols with high concrete efficiency, achieved by eliminating the dependence on a security parameter. In this work, we identify a large class of client-server functionalities f:X×Y↦{0,1}, where the server's domain X is larger than the client's domain Y, that have a perfect reduction to OT. Furthermore, our reduction is 1-round using an oracle to secure evaluation of many parallel invocations of 1-out-of-2 bit OT, as done by Ishai et al. (2011) [20]. Interestingly, the set of functions that we are able to compute was previously identified by Asharov (2014) [3] in the context of fairness in two-party computation, naming these functions full-dimensional. Our result also extends to randomized non-Boolean functions f:X×Y↦{0,…,k−1} satisfying |X|>(k−1)⋅|Y|.

AB - A well known result by Kilian (1988) [23] asserts that general secure two computation (2PC) with statistical security, can be based on OT. Specifically, in the client-server model, where only one party – the client – receives an output, Kilian's result shows that given the ability to call an ideal oracle that computes OT, two parties can securely compute an arbitrary function of their inputs with unconditional security. Ishai et al. (2011) [20] further showed that this can be done efficiently for every two-party functionality in NC1 in a single round. However, their results only achieve statistical security, namely, it is allowed to have some error in security. This leaves open the natural question as to which client-server functionalities can be computed with perfect security in the OT-hybrid model, and what is the round complexity of such computation. So far, only a handful of functionalities were known to have such protocols. In addition to the obvious theoretical appeal of the question towards better understanding secure computation, perfect, as opposed to statistical reductions, may be useful for designing secure multiparty protocols with high concrete efficiency, achieved by eliminating the dependence on a security parameter. In this work, we identify a large class of client-server functionalities f:X×Y↦{0,1}, where the server's domain X is larger than the client's domain Y, that have a perfect reduction to OT. Furthermore, our reduction is 1-round using an oracle to secure evaluation of many parallel invocations of 1-out-of-2 bit OT, as done by Ishai et al. (2011) [20]. Interestingly, the set of functions that we are able to compute was previously identified by Asharov (2014) [3] in the context of fairness in two-party computation, naming these functions full-dimensional. Our result also extends to randomized non-Boolean functions f:X×Y↦{0,…,k−1} satisfying |X|>(k−1)⋅|Y|.

KW - Oblivious transfer

KW - Perfect security

KW - Two-party computation

UR - http://www.scopus.com/inward/record.url?scp=85116587655&partnerID=8YFLogxK

U2 - 10.1016/j.tcs.2021.08.035

DO - 10.1016/j.tcs.2021.08.035

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AN - SCOPUS:85116587655

SN - 0304-3975

VL - 891

SP - 166

EP - 188

JO - Theoretical Computer Science

JF - Theoretical Computer Science

ER -