I am generating a ciphertext by XORing the message bits with key stream bits of a stream cipher. But, if I know a priori that message bits contain a predefined number of 0's (say 60%) at unknown positions, then how to analyze the security of such system both mathematically and empirically.
Can we analyze using hypothesis testing (given two messages m1 and m2 with the same distribution and analyze whether ciphertext leaks any information about messages) or using entropy bounds?