Goldwasser and Kharchenko (TCC 2006) showed a proof of plaintext knowledge for the Ajtai-Dwork 
cryptosystem and left the open problem designing a proof of plaintext knowledge for the Regev'04 cryptosystem (JACM 2004). 
In this paper, we show a proof of plaintext knowledge for the Regev?04 cryptosystem (JACM 2004) using their technique. 
Furthermore, we show that it can be applied to the Regev'05 cryptosystem (STOC 2005). 
The key idea is to analyze tradeoffs between the hardness of the underlying lattice problem and the variance of ciphertexts, 
which given by Kawachi, Tanaka, and Xagawa (SCIS 2006).