In this paper, we introduce a new cryptographic model, 
the encryption scheme with decomposition of ciphertexts 
which is related to the notion of the secret sharing scheme 
and additively homomorphism.  The model is described as follows:
Let R be a receiver, S_1, ... , S_u be senders, and V_1, ..., V_y 
be servers.  
By using servers V_1, ..., V_y as mediators between servers and the receiver, 
senders S_1, ... , S_u want to send information on r(m_1, m_2, ... , m_u) 
without providing each messages m_i, where r is a operation (for example, r(m_1, m_2, 
... ,m_u) = m_1+m_2+ ... + m_u).  
In addition, by using receiver's public key pk, each sender S_i wants to 
divide a message m_i to y shares, and then to distribute a part of y shares to each servers.  
Furthermore we develop with a variant of the Paillier encryption function which has several properties related to homomorphism.  
In fact, we construct our scheme by using homomorphic properties of the encryption function and decomposition of (cyclotomic) polynomials.