We say that an encryption scheme or a signature scheme
provides anonymity
when it is infeasible to determine
which user generated a ciphertext or a signature.
To construct the schemes with anonymity,
it is necessary that the space of ciphertexts or signatures
is common to each user.
In this paper,
we focus on the techniques
which can be used to obtain this anonymity property,
and propose a new technique
for obtaining the anonymity property
on RSA-based cryptosystem,
which we call ``sampling twice.''
It generates the uniform distribution over [0, 2^k)
by sampling the two elements from Z_N where |N| = k.
Then, by applying the sampling twice technique,
we construct the schemes for
encryption, undeniable and confirmer signature, and ring signature,
which have some advantages to the previous schemes.