Schmidt and Takagi proposed a variant of the Paillier encryption scheme
which employs
modulus n = p^2 q.  Their scheme has a good property that
the one-wayness is under the factoring assumption, and has an additively
homomorphic property.  Their scheme can be applied to
trapdoor commitment and on-line/off-line signature.   
In this paper, 
we propose a new variant of the Schmidt-Takagi encryption scheme
described as E(r, m) = r^(n^s) (1 + m * n^t) mod n^(s+1), where
n, s, t are the public key, m a message, and r a random number.
Our scheme has the one-wayness under the chosen plaintext attack based
on the factoring problem, and the indistinguishability under the chosen
plaintext attack based on the desicional composite residuosity problem.  
Our scheme implies the Schmidt-Takagi encryption scheme when s=t=1.  
Compared with the Damgard-Jurik encryption scheme, 
although the modulus of our schemes employs n = p^2q (their scheme employs
n = pq ), the encryption and decryption speed of our scheme is faster 
than that of their scheme.  
Furthermore, we get that E_t is additively homomorphic in m if t
> (s+1)/2 .  In addition, by
adding a parameter t we have some properties closely related to
homomorphic, which can be applied to cryptographic applications.