Towards Round-Optimal Secure Multiparty Computations: Multikey FHE Without a CRS

Eunkyung Kim, Hyang Sook Lee, Jeongeun Park

Research output: Contribution to journalArticlepeer-review

10 Scopus citations


Multikey fully homomorphic encryption (MFHE) allows homomorphic operations between ciphertexts encrypted under different keys. In applications for secure multiparty computation (MPC) protocols, MFHE can be more advantageous than usual fully homomorphic encryption (FHE) since users do not need to agree with a common public key before the computation when using MFHE. In EUROCRYPT 2016, Mukherjee and Wichs constructed a secure MPC protocol in only two rounds via MFHE which deals with a common random/reference string (CRS) in key generation. After then, Brakerski et al. replaced the role of CRS with the distributed setup for CRS calculation to form a four round secure MPC protocol. Thus, recent improvements in round complexity of MPC protocols have been made using MFHE. In this paper, we go further to obtain round-efficient and secure MPC protocols. The underlying MFHE schemes in previous works still involve the common value, CRS, it seems to weaken the power of using MFHE to allow users to independently generate their own keys. Therefore, we resolve the issue by constructing an MFHE scheme without CRS based on LWE assumption, and then we obtain a secure MPC protocol against semi-malicious security in three rounds. We also define a new security notion "multikey-CPA security" to prove that a multikey ciphertext cannot be decrypted unless all the secret keys are gathered and our scheme is multikey-CPA secure.

Original languageEnglish
Pages (from-to)157-174
Number of pages18
JournalInternational Journal of Foundations of Computer Science
Issue number2
StatePublished - 1 Feb 2020

Bibliographical note

Funding Information:
We would like to thank Mehdi Tibouchi and Huijia (Rachel) Lin for their helpful comments in this work. Two authors(Hyang-Sook Lee and Jeongeun Park) were supported by the National Research Foundation of Korea(NRF) grant funded by the Korea government(MSIT) (No. NRF-2018R1A2A1A05079095).

Publisher Copyright:
© 2020 World Scientific Publishing Company.


  • lattice
  • LWE assumption
  • Multikey FHE
  • multiparty computation


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