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

On Oct 25, 5:01 am, wangyong <hell...@xxxxxxx> wrote:
Huh???? So, now you *agree* that the probabilities of M=0 and M=1 are
unaffected by observing C=0? Then you should have no difficulty in
also agreeing that these probabilites are unaffected by observing
C=1,
and, therefore, that they are unaffected by observing C, whatever
value we may find that C takes. So, intercepting the message gives us
no additional information about M. What's the problem?
-----------you mistake lies in not obeying perfect secrecy. The
probability changed in the whole process. I point out OPt has good
attributes.

I get the impression that you are inventing complexities where none
exist. EITHER C is unknown and random (and M has its prior, or
initial, distribution), OR C is known and fixed (and M has its
conditional distribution). In the scenario we are discussing, the
conditional distribution of M (after C is observed) is exactly the
same as the prior distribution of M (before C is observed), whatever
value of C actually is observed. And that's all there is to it.

-------------your prior is not EITHER C is unknown and random (and M
has its prior)

but shannon's is.

This sentence does not make sense. If you have an "EITHER" you must
also have an "OR".

you do not see this paper clearly.you perpetrate a
fraud by substitute.
we discuss perfect secrecy.

From some of your follow-up replies, I'm wondering if your English
(which seemed reasonably intelligible in the main text of your
original posts) is actually good enough to continue this discussion.
Unfortunately I do not understand any Chinese.

But let's try one more thing. Let me repeat the definition of "perfect
secrecy" that you gave:

<begin quote>
A necessary and sufficient condition for perfect secrecy can be found
as follows: We have by Bayes' theorem in which:

P(M)= a priori probability of message M
PM(E)= conditional probability of cryptogram E if message M is chosen
i.e. the sum of the probabilities of all keys which produce cryptogram
E from message M.
P(E)= probability of obtaining cryptogram E from any cause.
PE(M)= a posteriori probability of message M if cryptogram E is
intercepted.

For perfect secrecy PE(M) must equal P(M) for all E and all M. Hence
either P(M)=0, a solution that must be excluded since we demand the
equality independent of the values of P(M), or PM(E)= P(E)
for every M and E. Conversely if PM(E)= P(E) then PE(M)= P(M)
and we have perfect secrecy. Thus we have the result:
Theorem 1. A necessary and sufficient condition for perfect secrecy is
that PM(E)= P(E) for all M and E. That is, PM(E) must be independent
of M.
<end quote>

Assume, as before, that the a priori probabilities are P(M=0) = p,
P(M=1) = 1-p, P(K=0) = 1/2, P(K=1) = 1/2, K and M independent. K=0
maps 0->0, 1->1, and K=1 maps 0->1, 1->0.

Now please show explicitly how you calculate each of the relevant
quantities mentioned in your above definition of perfect secrecy, and
explain how you conclude that perfect secrecy is not achieved.

.

Relevant Pages

  • Security Analyses of One-time System
    ... Security Analyses of One-time System ... Abstract-Shannon put forward the concept of perfect secrecy and proved ... cryptogram is intercepted by the enemy the a posteriori probabilities ... P= a priori probability of message M ...
    (sci.crypt)
  • Security Analyses of One-time System
    ... Security Analyses of One-time System ... Abstract—Shannon put forward the concept of perfect secrecy and proved ... cryptogram is intercepted by the enemy the a posteriori probabilities ... P= a priori probability of message M ...
    (sci.math)
  • Re: Confirmation of Shannons Mistake about Perfect Secrecy of One-time-pad
    ... <begin quote> ... P= a priori probability of message M ... PM= conditional probability of cryptogram E if message M is chosen ... For perfect secrecy PEmust equal Pfor all E and all M. ...
    (sci.math)
  • Re: Confirmation of Shannons Mistake about Perfect Secrecy of One-time-pad
    ... see the condition that the ciphertext y is a fixed value is never ... But Shannon thought of the posterior probability as the ... also agreeing that these probabilites are unaffected by observing C=1, ... conditional distribution of M is exactly the ...
    (sci.math)
  • Re: p values
    ... Everytime I've done a hypothesis test (I've only done them in ... "The definition of p-value is the PROBABILITY of observing something ... Department of Mathematics and Statistics ...
    (sci.stat.math)
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