|The security assumption for the cryptosystems based on the Discrete logarithm problem (DLP) is one wayness i.e., an attacker cannot recover the discrete log, say x, from the generator g and gx. Kashyap et al.,  proposed a cryptosystem based on the DLP, ?=?a?b, where ? and ? are generators, a and b are distinct integers. The above cryptosystem and the corresponding cryptanalysis are further analyzed in the present study. Sramka  claimed that for the cipher text (c1, c2, c3) of the cryptosystem discussed in , the random integer, say k, can be obtained by the simple relation, which is given by c1c2 = (??)k . Further, he reported an attack, in obtaining the plain text from a valid cipher text, by computing the single traditional DLP. In the present study, it is shown that the above k can be obtained using above relation only for special cases and those cases are discussed. Also an improved version of the encryption scheme based on the cryptosystem proposed by Kashyap et al.,  is studied. It is observed that the proposed cryptosytem is non-vulnerable to the attack, in obtaining the plain text from a valid cipher text, by computing the single traditional DLP.