On the Relationship between FuncCPA and FuncCPA+

Takumi Shinozaki; Keisuke Tanaka; Masayuki Tezuka; Yusuke Yoshida

Paper 2024/1166

On the Relationship between FuncCPA and FuncCPA+

Takumi Shinozaki, Tokyo Institute of Technology

Keisuke Tanaka, Tokyo Institute of Technology

Masayuki Tezuka, Tokyo Institute of Technology

Yusuke Yoshida, Tokyo Institute of Technology

Abstract

Akavia, Gentry, Halevi, and Vald introduced the security notion of function-chosen-plaintext-attack (FuncCPA security) for public-key encryption schemes. FuncCPA is defined by adding a functional re-encryption oracle to the IND-CPA game. This notion is crucial for secure computation applications where the server is allowed to delegate a part of the computation to the client. Dodis, Halevi, and Wichs introduced a stronger variant called FuncCPA. They showed FuncCPA implies FuncCPA and conjectured that FuncCPA is strictly stronger than FuncCPA. They left an open problem to clarify the relationship between these variants. Contrary to their conjecture, we show that FuncCPA is equivalent to FuncCPA. We show it by two proofs with a trade-off between the number of queries and the number of function inputs. Furthermore, we show these parameters determine the security levels of FuncCPA and FuncCPA.

Metadata

Available format(s): PDF
Category: Public-key cryptography
Publication info: Preprint.
Keywords: FuncCPA public-key encryption
Contact author(s): shinozaki t ae @ m titech ac jp
keisuke @ is titech ac jp
tezuka m ac @ m titech ac jp
yoshida yusuke @ c titech ac jp
History: 2024-07-19: approved; 2024-07-19: received; See all versions
Short URL: https://ia.cr/2024/1166
License: CC BY

BibTeX

@misc{cryptoeprint:2024/1166,
      author = {Takumi Shinozaki and Keisuke Tanaka and Masayuki Tezuka and Yusuke Yoshida},
      title = {On the Relationship between {FuncCPA} and {FuncCPA}+},
      howpublished = {Cryptology {ePrint} Archive, Paper 2024/1166},
      year = {2024},
      url = {https://eprint.iacr.org/2024/1166}
}