We first propose the notion of
universal anonymizable public-key encryption.
Suppose that we have the encrypted data
made with the same security parameter, and
that these data do not satisfy the anonymity property.
Consider the situation that
we would like to transform these encrypted data
to those with the anonymity property
without decrypting these encrypted data.
In this paper,
in order to formalize this situation,
we propose a new property
for public-key encryption called universal anonymoizablity.
We then propose
the universal anonymizable public-key encryption schemes
based on RSA-OAEP, the ElGamal encryption, and
the Cramer-Shoup encryption schemes, and
prove their security.