Re: Confirmation of Shannon's Mistake about Perfect Secrecy of One-time-pad

Due to the mapping of M, K and C, the probabilities of M, K and C are
complicatedly interactional. For the above example, the probability
of
plaintext changes when the ciphertext is fixed, even though the
ciphertext is unknown.
When only considering the fixed ciphertext and the equiprobability of
key, we can gain that plaintexts are equally likely for there is a
one-
to-one correspondence between all the plaintexts and keys for fixed
ciphertext. There is conflict between the prior probability and the
uniformly distributed probability gained above.
In order to understand the inconsistency of probability in the
example
and the need for fusion of the probabilities in this case, we adopt
the combinations of different conditions for the following deduction
to analyze the existence of probability conflict.
For our simple example about OTP, when considering the condition that
ciphertext is 0, the probability of ciphertext being 0 is 1, and the
probability of ciphertext being 1 is 0. But according to the prior
probability distribution of plaintexts given and uniformly
distributed
keys, we can easily find that ciphertext is uniformly distributed,
that is to say, all ciphertext are equally likely. We can see the two
probability distributions of ciphertext in different conditions are
conflictive.
When only considering that the intercepted ciphertext is 0 and prior
probability of plaintext being 0 we call P(M=0) is 0.9, and prior
probability of plaintext being 1 we call P(M=1) is 0.1, the
probability of key being 0 we call P(K=0) is 0.9, and the probability
of key being 1 we call P(K=1) is 0.1 because there is a one-to-one
correspondence between all the plaintexts ands keys. However,
according to the requirement of OTP, all the keys are equally likely,
so conflict of the probabilities occurs as before.
Such conflicts show that under different conditions we may draw
inconsistent probabilities, so it needs to fuse and compromise. The
probabilities obtained by the different combinations of unilateral
conditions are inconsistent. That is to say, the conditions in OPT
can
not coexist. When all the conditions are considered, some of the
conditions must change, so it is not proper to use these conditions
when computing the final posterior probability. It likes four
irregular feet of a same table. There is always one foot that is
turnup when the table is on the horizontal ground. If the four feet
should touch the horizontal ground at the same time, distortion would
happen. In literature [7], formula was presented to fuse the
inconsistent probabilities.
Shannon did not realize that the conditions were impossible to
coexist. When taking them into the formula, there must be mistake for
the conditions cannot coexist and the probabilities have changed when
all the conditions are considered at the same time.
For the conditions in the example are very complex, and some are
connotative, it is essential to list them and analyze the impact of
the conditions on the probability. Literature [4] considered an
especially understanding following which OTP could be thought
perfectly secure if some added conditions were satisfied and analyzed
that was unlikely to be Shannon's view. This paper analyzes the
problem in detail and confirms the result that the especially
understanding is not Shannon's view using the information gained from
Shannon' s proof.

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