You are given a black box f : Z10 → Z10 that contains either a random permutation or a random function. Your distinguisher is allowed to invoke f twice. What is the best advantage you can achieve? Express your answer as a reduced fraction without any spaces (eg, 1/3 and not 12/36), or as 0 or 1 if appropriate.

Solution :

The function :       be a random permutation.

f is a permutation on ,  i.e. f is permutation 10.

Now we know that the total number of distinct permutation on to symbolize 10!.

Each of these 10! permutation to a permutation function    

Therefore, total number of permutation functions     are 10!.

Now we want the total number of permutation functioning :

  such that  f(0) = 0 and f(1)= 1

Now we notice that when f(0)=0 and f(1)=1, then two symbol '0' and '1 are fixed under permutation f.

So essentially when f(0) = 0 and f(1) = 1, f becomes permutation on 8 symbol.

Total number of permutation functioning    , f(0)=0 and f(1)=1 are 8!

Now we want the probability that a random permutation     satisfies f(0) = 0 and f(1) = 1.

The number of permutation function    , i.e.

The probability that a random permutation     satisfies f(0) = 0 and f(1) = 1 is

Therefore, the probability that a random permutation     satisfies f(0)= 0 and f(1)=1 is  

points are handed out whenever you post answers.

brainliest answers are handed out by the person asking the question, so whether your answer is picked depends entirely on whether the asker bothers to pick

if you're asking about your rank, it depends on having a certain number of points and a certain number of brainliest answers. for example, at the time of this writing, i have 44338 points out of 15000 needed for the next (nearly triple the requirement! ) but i only have 24 out of 50 required brainliest answers. this number decays, meaning after a certain amount of time (i think about a month), the total number of brainliest answers you've earned doesn't count toward this total. (i've been stuck at the same rank for a long

the lesson to learn here is that you shouldn't worry about points or rank. chances are, no matter how good an answer you may provide, your efforts will go mostly unnoticed unless you focus on the newest/most active questions that get posted.

answer: 34rtyj,jkhtyetwrhyjeuiejnbhdfknbkguxfrbhkfdbjvkmbd,kvbsd.kxjvbhjnfbgjxdfn

step-by-step explanation: