Hamidi, Amirreza, and Ghodosi, Hossein (2022) Verifiable DOPE from Somewhat Homomorphic Encryption, and the Extension to DOT. In: Lecture Notes in Computer Science (13580) pp. 105-120. From: SciSec 2022: 4th International Conference on Science of Cyber Security, 10-12 August 2022, Matsue, Japan.

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Abstract

Distributed oblivious polynomial evaluation (DOPE) is a special case of two-party computation where a sender party holds a polynomial f(x) of degree t and a receiver party has an input x2. They communicate with a set of distributed cloud servers to implement a secure computation such that the receiver party obtains f(x2), while the privacy of their inputs is preserved. We present a verifiable and private DOPE protocol using additive homomorphic encryption in the presence of k distributed servers where k does not depend on the degree t. The sender is involved in the offline phase which can be implemented at any time well in advance of the actual online computation phase. Our protocol holds the unconditional security against a malicious sender in the offline phase and a static active adversary corrupting a coalition of at most k- 1 dishonest servers in the online computation phase with negligible probability of error. In addition, it preserves strong privacy conditions for a DOPE system. The communication complexity is determined by the term kt which improves the DOPE approaches of [18] and [5]. Also, the proposed protocol can be extended to a protocol of secure (12) distributed oblivious transfer with the linear communication complexity O(k) where the same setting of security is achieved.

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