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Akavia, Gentry, Halevi, and Vald (TCC’22, JoC’25) introduced the security notion of function-chosen-plaintext-attack ( \({\textsf{FuncCPA}}\) security) for public-key encryption schemes. \({\textsf{FuncCPA}}\) is defined by adding a functional re-encryption oracle to the \(\textsf {IND-CPA} \) 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 (TCC’23) introduced a stronger variant called \({\textsf{FuncCPA}^+}\) , and conjectured that \({\textsf{FuncCPA}^+}\) is strictly stronger than \({\textsf{FuncCPA}}\) , while they showed \({\textsf{FuncCPA}^+}\) implies \({\textsf{FuncCPA}}\) . Seeking insights into this conjecture, they showed that \({\textsf{ReEncCPA}^+}\) is strictly stronger than \({\textsf{ReEncCPA}}\) , where \({\textsf{ReEncCPA}}\) and \({\textsf{ReEncCPA}^+}\) are restricted versions of \({\textsf{FuncCPA}}\) and \({\textsf{FuncCPA}^+}\) respectively. In this paper, contrary to their conjecture, we show that \({\textsf{FuncCPA}^+}\) is equivalent to \({\textsf{FuncCPA}}\) . We also introduce new variants of \({\textsf{FuncCPA}}\) ; \({\textsf{Weak}{\textsf{FuncCPA}}}\) , \(\textsf {OW-}{\textsf{FuncCPA}} \) , and \(\textsf {OW-}{\textsf{Weak}{\textsf{FuncCPA}}} \) . \({\textsf{Weak}{\textsf{FuncCPA}}}\) is a restricted variant of \({\textsf{FuncCPA}}\) in that an oracle query is prohibited after the challenge query (like \(\textsf {IND-CCA1} \) ). \(\textsf {OW-}{\textsf{FuncCPA}} \) and \(\textsf {OW-}{\textsf{Weak}{\textsf{FuncCPA}}} \) are the one-way ( \(\textsf{OW}\) ) versions of \({\textsf{FuncCPA}}\) and \({\textsf{Weak}{\textsf{FuncCPA}}}\) , respectively. This paper shows that \({\textsf{Weak}{\textsf{FuncCPA}}}\) and \(\textsf {OW-}{\textsf{FuncCPA}} \) are equivalent to \({\textsf{FuncCPA}}\) , that is, all of \({\textsf{FuncCPA}}\) , \({\textsf{FuncCPA}^+}\) , \({\textsf{Weak}{\textsf{FuncCPA}}}\) , and \(\textsf {OW-}{\textsf{FuncCPA}} \) are equivalent. Considering the separation of \(\textsf {IND-CCA1} \) and \(\textsf {IND-CCA2} \) , and that of \(\textsf{OW}\text {-}\textsf{CPA}\) and \(\textsf {IND-CPA} \) , these results are surprising. To show the equivalence, we develop novel techniques to utilize functional re-encryption oracles. We then provide the separation results that \(\textsf {OW-}{\textsf{Weak}{\textsf{FuncCPA}}} \) does not imply \({\textsf{FuncCPA}}\) and \({\textsf{ReEncCPA}^+}\) does not imply \({\textsf{FuncCPA}}\) .

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Relationships Among FuncCPA and Its Related Notions

  • 会议论文

  • 发表日期：

    2026年

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  • Takumi Shinozaki,
  • Tatsuaki Okamoto,
  • Keisuke Tanaka,
  • Masayuki Tezuka,
  • Yusuke Yoshida

摘要

Akavia, Gentry, Halevi, and Vald (TCC’22, JoC’25) introduced the security notion of function-chosen-plaintext-attack ( \({\textsf{FuncCPA}}\) security) for public-key encryption schemes. \({\textsf{FuncCPA}}\) is defined by adding a functional re-encryption oracle to the \(\textsf {IND-CPA} \) 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 (TCC’23) introduced a stronger variant called \({\textsf{FuncCPA}^+}\) , and conjectured that \({\textsf{FuncCPA}^+}\) is strictly stronger than \({\textsf{FuncCPA}}\) , while they showed \({\textsf{FuncCPA}^+}\) implies \({\textsf{FuncCPA}}\) . Seeking insights into this conjecture, they showed that \({\textsf{ReEncCPA}^+}\) is strictly stronger than \({\textsf{ReEncCPA}}\) , where \({\textsf{ReEncCPA}}\) and \({\textsf{ReEncCPA}^+}\) are restricted versions of \({\textsf{FuncCPA}}\) and \({\textsf{FuncCPA}^+}\) respectively. In this paper, contrary to their conjecture, we show that \({\textsf{FuncCPA}^+}\) is equivalent to \({\textsf{FuncCPA}}\) . We also introduce new variants of \({\textsf{FuncCPA}}\) ; \({\textsf{Weak}{\textsf{FuncCPA}}}\) , \(\textsf {OW-}{\textsf{FuncCPA}} \) , and \(\textsf {OW-}{\textsf{Weak}{\textsf{FuncCPA}}} \) . \({\textsf{Weak}{\textsf{FuncCPA}}}\) is a restricted variant of \({\textsf{FuncCPA}}\) in that an oracle query is prohibited after the challenge query (like \(\textsf {IND-CCA1} \) ). \(\textsf {OW-}{\textsf{FuncCPA}} \) and \(\textsf {OW-}{\textsf{Weak}{\textsf{FuncCPA}}} \) are the one-way ( \(\textsf{OW}\) ) versions of \({\textsf{FuncCPA}}\) and \({\textsf{Weak}{\textsf{FuncCPA}}}\) , respectively. This paper shows that \({\textsf{Weak}{\textsf{FuncCPA}}}\) and \(\textsf {OW-}{\textsf{FuncCPA}} \) are equivalent to \({\textsf{FuncCPA}}\) , that is, all of \({\textsf{FuncCPA}}\) , \({\textsf{FuncCPA}^+}\) , \({\textsf{Weak}{\textsf{FuncCPA}}}\) , and \(\textsf {OW-}{\textsf{FuncCPA}} \) are equivalent. Considering the separation of \(\textsf {IND-CCA1} \) and \(\textsf {IND-CCA2} \) , and that of \(\textsf{OW}\text {-}\textsf{CPA}\) and \(\textsf {IND-CPA} \) , these results are surprising. To show the equivalence, we develop novel techniques to utilize functional re-encryption oracles. We then provide the separation results that \(\textsf {OW-}{\textsf{Weak}{\textsf{FuncCPA}}} \) does not imply \({\textsf{FuncCPA}}\) and \({\textsf{ReEncCPA}^+}\) does not imply \({\textsf{FuncCPA}}\) .