International Association
for Cryptologic Research

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$^+$.