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

On Nov 6, 10:28 pm, wangyong <hell...@xxxxxxx> wrote:
On 11 7 , 9 26 , William Hughes <wpihug...@xxxxxxxxxxx> wrote:



On Nov 6, 7:49 pm, wangyong <hell...@xxxxxxx> wrote:

how can you use the condition c is fixed to compute, it is not a
value,

Agreed. The condition "c is fixed" is not a value. C has
two possible values. So you have to compute the probablity
distributions twice. You assume that the value
of C is fixed. You then calculate the probablity
distributions for one possible value of C assuming the value of
C is fixed. You then calculate the probability distributions for the
other
possible value of C assuming the value of C is fixed.
In both case you find that the probability distribution on M is
unchanged.
You get two different probability distributions for K, but neither is
uniform.

- William Hughes

how you can compute, how can you find the probability M not changed.
do not just the the result ,that is useless.

Compute the joint probability of M, K and C
(use the known probability distribtuions of M and K
the fact that M and K are independent, and the formula
for getting C from M and K)

Assume C fixed. Two cases.

For each case note the value of C and compute
the conditional probability of M using the known
joint probability of M, K and C and the definition
of conditional probability.

In both cases you get the same probability
distribution for M

- William Hughes

.

Relevant Pages

  • Re: Probability of picking a positive rational number at random
    ... Classical probability is more limited than measure-theoretic ... there are infinitely many distributions satisfying that relation. ... distributions over all well-orderings of distributions over natural ... natural numbers, in a bijection to the unit interval of reals, by ...
    (sci.math)
  • Re: Probability of picking a positive rational number at random
    ... start with the definition of a probability ... from each Lebesgue measurable set you construct a set of distributions ... asymptotically for much larger ordinals in abandon than the order type ... naturals a natural number is indicated, ...
    (sci.math)
  • Re: An uncountable countable set
    ... there are no uniform distributions over countable sample spaces, ... probability distribution. ... distributions on infinite sets. ...
    (sci.math)
  • Re: chi-square test with large numbers
    ... different question from the one that a statistical test of independence vs ... probability of the worse test for all situations where the null hypothesis ... independence vs. dependence tests. ... distributions are not distributions of _independent_ random variates. ...
    (sci.stat.math)
  • Re: An uncountable countable set
    ... there are no uniform distributions over countable sample spaces, ... probability distribution. ... distributions on infinite sets. ...
    (sci.math)