title: Leakage through Ciphertext-Plaintext Homomorphic Operations
body: <p>Consider two parties, namely, P_0 and P_1. P_0 and P_1 have plaintexts p_a and p_b respectively.<br>
  P_0 encrypts p_a to get <code>c_a = Enc(p_a)</code> with its public key, and sends it to P_1.<br>
  P_1 performs <code>multiply_plain(c_a, p_b, c)</code>, followed by <code>sub_plain_inplace(c, p_R)</code> (where p_R is a random plaintext polynomial to hide the product of a and b), and then sends c to P_0.<br>
  Can the noise in c reveal some information about p_b to P_0, despite the product being masked by p_R?  </p>
  
  <p>If yes, then how can I avoid this leakage? Is there a way to add random noise to c to drown the impact of p_b on noise in c?<br>
  Is there a function in SEAL to encrypt using noise from a larger interval? If there is, then maybe I can encrypt p_R with extra noise to drown the impact.</p>