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International Conference on Availability, Reliability and Security (ARES)

Towards Secure Evaluation of Online Functionalities

Andreas Klinger, Ulrike Meyer

Published Aug 16, 2021• 0 citations
Publisher

Abstract

To date, ideal functionalities securely realized with secure multi-party computation (SMPC) mainly considers functions of the private input of a fixed number of a priori known parties. In this paper, we generalize these definitions such that protocols implementing online algorithms in a distributed fashion can be proven to be privacy-preserving. Online algorithms compute online functionalities that allow parties to join and leave over time, to provide multiple inputs and to obtain multiple outputs. In particular, the set of parties participating changes over time, i. e., at different points in time different sets of parties evaluate a function over their private inputs. To this end, we propose the notion of an online trusted third party that allows to prove the security of SMPC protocols implementing online functionalities or online algorithms, respectively. We show that any online functionality can be implemented perfectly secure in the presence of a semi-honest adversary, if strictly less than 1/2 of the parties participating are corrupted. We show that the same result holds in the presence of a malicious adversary if it corrupts strictly less than 1/3 of the parties and always allows the corrupted parties to arrive.

DOI
10.1145/3465481.3469203

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To date, ideal functionalities securely realized with secure multi-party computation (SMPC) mainly considers functions of the private input of a fixed number of a priori known parties. In this paper, we generalize these definitions such that protocols implementing online algorithms in a distributed fashion can be proven to be privacy-preserving. Online algorithms compute online functionalities that allow parties to join and leave over time, to provide multiple inputs and to obtain multiple outputs. In particular, the set of parties participating changes over time, i. e., at different points in time different sets of parties evaluate a function over their private inputs. To this end, we propose the notion of an online trusted third party that allows to prove the security of SMPC protocols implementing online functionalities or online algorithms, respectively. We show that any online functionality can be implemented perfectly secure in the presence of a semi-honest adversary, if strictly less than 1/2 of the parties participating are corrupted. We show that the same result holds in the presence of a malicious adversary if it corrupts strictly less than 1/3 of the parties and always allows the corrupted parties to arrive.
In classical secure multi-party computation (SMPC) it is assumed that a fixed and a priori known set of parties wants to securely evaluate a function of their private inputs. This assumption implies that online problems, in which the set of parties that arrive and leave over time are not a priori known, are not covered by the classical setting. Therefore, the notion of online SMPC has been introduced, and a general feasibility result has been proven that shows that any online algorithm can be implemented as a distributed protocol that is secure in this setting [22, 23]. However, so far, no online SMPC protocol that implements a concrete online algorithm has been proposed and evaluated such that the practicality of the constructive proof is an open question.
In secure multi-party computation (SMPC), it is considered that multiple parties that are known to each other evaluate a function over their private inputs in a secure fashion. The participating parties do not learn anything about each other's private inputs beyond what can be deduced from their own input and output. The assumption that the parties know each other, however, does not seem suitable for all potential applications of SMPC. In some applications participants may not only want to hide their private inputs and outputs, but may also want to hide the fact that they are participating in a given function evaluation in the first place. We therefore propose an anonymous system for SMPC that allows parties to anonymously evaluate a function of their private inputs in a fully distributed and secure fashion. The proposed system allows authorized parties to execute an SMPC protocol robust with penalty against a dishonest majority in the presence of a malicious adversary. During the protocol execution, the system guarantees that all participating parties stay anonymous w. r. t. each other as well as any third parties. In addition, it guarantees that in each function evaluation all participating parties are unique, i. e., no party can participate as more than one entity.
Secure multi-party computation (SMC) allows multiple parties to jointly and securely compute a function while preserving the privacy of the involved parties. In this regard, homomorphic cryptosystems allow users to perform addition or multiplication operations on encrypted values without having to decrypt the input values. In this paper, we propose both a cryptographic and a non-cryptographic privacy-preserving protocols that allow one party to collaboratively compute a private polynomial function with at least two other parties using semantically secure cryptosystems. In this respect, the function to be evaluated is kept private to the party in question. In addition, we assume that there is no fully trusted party and that all parties are semi-honest. Moreover, we assume that there is no collusion between the different parties. We present the two protocols in question and report on the underlying performance through the presentation of our implementation results. The proposed protocols are relevant in many applications such as evidence sharing in multi-party forensic investigations, situation awareness through the secure sharing in distributed monitoring of plan execution, etc.
The goal of secure two-party computation is to enable two parties to cooperatively evaluate a function that takes private data from both parties as input without exposing any of the private data. At the end of the computation, the participants learn nothing more than the output of the function. The two-party secure computation systems have three properties: (1) the application involves inputs from two independent parties; (2) each party wants to keep its own data secret; and (3) the participants agree to reveal the output of the computation. That is, the result itself does not imply too much information about either party's private input. Informally, the security requirements are that nothing is learned from the protocol other than the output (privacy), and that the output is distributed according to the prescribed functionality (correctness). The threat models in the two-party computation assume the presence of three different types of adversaries: 1) Semi honest, 2) Malicious and 3) Covert.
It is well known that general secure function evaluation (SFE) with information-theoretical (IT) security is infeasible in presence of a corrupted majority in the standard model. On the other hand, there are SFE protocols (Goldreich et al. [STOC’87]) that are computationally secure (without fairness) in presence of an actively corrupted majority of the participants. Now, the issue with computational assumptions is not so much that they might be unjustified at the time of protocol execution. Rather, we are usually worried about a potential violation of the privacy of sensitive data by an attacker whose power increases over time (e.g. due to new technical developments). Therefore, we ask which functions can be computed with long-term security, where we admit computational assumptions for the duration of a computation, but require IT security (privacy) once the computation is concluded. Toward this end we combinatorially characterize the classes of functions that can be computed IT securely in the authenticated channels model in presence of passive, semi-honest, active, and quantum adversaries (our results for quantum adversaries and in part for active adversaries are limited to the 2-party setting). In particular we obtain results on the fair computability of functions in the IT setting along the lines of the work of Gordon et al. [STOC’08] for the computational setting. Our treatment is constructive in the sense that if a function is computable in a given setting, then we exhibit a protocol.
We describe a highly optimized protocol for generalpurpose secure two-party computation (2PC) in the presence of malicious adversaries. Our starting point is a protocol of Kolesnikov et al. (TCC 2015). We adapt that protocol to the online/offline setting, where two parties repeatedly evaluate the same function (on possibly different inputs each time) and perform as much of the computation as possible in an offline preprocessing phase before their inputs are known. Along the way we develop several significant simplifications and optimizations to the protocol. We have implemented a prototype of our protocol and report on its performance. When two parties on Amazon servers in the same region use our implementation to securely evaluate the AES circuit 1024 times, the amortized cost per evaluation is 5.1ms offline + 1.3ms online. The total offline+online cost of our protocol is in fact less than the online cost of any reported protocol with malicious security. For comparison, our protocol’s closest competitor (Lindell & Riva, CCS 2015) uses 74ms offline + 7ms online in an identical setup. Our protocol can be further tuned to trade performance for leakage. As an example, the performance in the above scenario improves to 2.4ms offline + 1.0ms online if we allow an adversary to learn a single bit about the honest party’s input with probability 2−20 (but not violate any other security property, e.g. correctness).