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Title:
Ciphertext-Simulatable HE from BFV with Randomized Evaluation
Authors: Intak Hwang, Seonhong Min, Yongsoo Song
Abstract:Homomorphic Encryption (HE) is a privacy-enhancing technology that enables computation over encrypted data without the need for decryption. A primary application of HE is in the construction of communication-efficient Two-Party Computation (2PC) protocols between a client and a server, serving as the key owner and the evaluator, respectively. In this context, it is reasonable to assume that the evaluation circuit involves some confidential information of the server; otherwise, the client could compute it on their own. However, the 2PC protocol built on an HE scheme is not necessarily secure, as the standard IND-CPA security of HE does not guarantee the privacy of the evaluation circuit. Several enhanced security notions for HE, such as circuit privacy and sanitization, have been proposed to address this issue, but they require significant overhead in terms of parameter size or complexity.
In this work, we introduce a novel security notion for HE, called ciphertext simulatability, which precisely captures the security requirements of HE in the construction of 2PC. Then, we provide a concrete construction of ciphertext-simulatable HE from the BFV scheme by modifying its evaluation algorithm. We provide theoretical analysis and demonstrate experimental results to ensure that our solution has insignificant overhead in terms of parameter size and error growth. As a matter of independent interest, we demonstrate how our approach of designing ciphertext-simulatable BFV can be further extended to satisfy stronger security notions such as sanitization.
ePrint: https://eprint.iacr.org/2025/203
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