Probability of success in guessing the key in cryptography after $k$ guesses. [on hold]

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I was given a vector



beginalign p = [0.2, 0.15, 0.12, 0.11, 0.11, 0.1, 0.1, 0.05, 0.03, 0.03] endalign



So I constructed a random variables probability table as shown below.



beginarrayc
hline
k& 1 & 2 & 3 & 4 & 5 & 6 & 7 & 8 & 9 & 10 \ hline
P(X=k) & 0.2 & 0.15 & 0.12 & 0.11 & 0.11 & 0.1 & 0.1 & 0.05 & 0.03 & 0.03 \ hline
hline
hline
endarray



Question 1: Use this function to compute the probability of success after 3 guesses.



beginalign p_textsuccess(k,p) = sum_i=1^k p_i endalign



For this question I was able to solve it easily by substituting $k$ as $3$. However, concerning the random variable, I have no idea what $P(X = 1), P(X = 2), dotsc , P(X = 10)$ means in this situation. I only knew that the probability of success after $k$ guesses is equals to the sum of $P(X = 1)$ up to $P(X = k)$ according to the above function. I also knew that the more guesses I attempt, the higher chance I select the correct key. Subsequently, I have been struggling with question 2.



Question 2: The above distribution $p$ is a worst case distribution for the cryptographer and a best case distribution for the cryptanalyst. Why?



Is the reason is because each value of random variable is dependent on each other?



I would greatly appreciate if you guys kindly give me some thoughts.




probability probability-theory probability-distributions random-variables cryptography




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put on hold as unclear what you're asking by Math1000, ancientmathematician, José Carlos Santos, mfl, Q the Platypus Sep 3 at 21:37


Please clarify your specific problem or add additional details to highlight exactly what you need. As it's currently written, it’s hard to tell exactly what you're asking. See the How to Ask page for help clarifying this question. If this question can be reworded to fit the rules in the help center, please edit the question.










  • 1




    $X$ is the value of the key? What is the crypto system?
    – Henno Brandsma
    Aug 26 at 21:19










  • Are guesses made at random (from the remaining candidates, if one or more guesses are wrong)?
    – Math1000
    Sep 3 at 7:54














up vote
1
down vote

favorite












I was given a vector



beginalign p = [0.2, 0.15, 0.12, 0.11, 0.11, 0.1, 0.1, 0.05, 0.03, 0.03] endalign



So I constructed a random variables probability table as shown below.



beginarrayc
hline
k& 1 & 2 & 3 & 4 & 5 & 6 & 7 & 8 & 9 & 10 \ hline
P(X=k) & 0.2 & 0.15 & 0.12 & 0.11 & 0.11 & 0.1 & 0.1 & 0.05 & 0.03 & 0.03 \ hline
hline
hline
endarray



Question 1: Use this function to compute the probability of success after 3 guesses.



beginalign p_textsuccess(k,p) = sum_i=1^k p_i endalign



For this question I was able to solve it easily by substituting $k$ as $3$. However, concerning the random variable, I have no idea what $P(X = 1), P(X = 2), dotsc , P(X = 10)$ means in this situation. I only knew that the probability of success after $k$ guesses is equals to the sum of $P(X = 1)$ up to $P(X = k)$ according to the above function. I also knew that the more guesses I attempt, the higher chance I select the correct key. Subsequently, I have been struggling with question 2.



Question 2: The above distribution $p$ is a worst case distribution for the cryptographer and a best case distribution for the cryptanalyst. Why?



Is the reason is because each value of random variable is dependent on each other?



I would greatly appreciate if you guys kindly give me some thoughts.




probability probability-theory probability-distributions random-variables cryptography




share|cite|improve this question














put on hold as unclear what you're asking by Math1000, ancientmathematician, José Carlos Santos, mfl, Q the Platypus Sep 3 at 21:37


Please clarify your specific problem or add additional details to highlight exactly what you need. As it's currently written, it’s hard to tell exactly what you're asking. See the How to Ask page for help clarifying this question. If this question can be reworded to fit the rules in the help center, please edit the question.










  • 1




    $X$ is the value of the key? What is the crypto system?
    – Henno Brandsma
    Aug 26 at 21:19










  • Are guesses made at random (from the remaining candidates, if one or more guesses are wrong)?
    – Math1000
    Sep 3 at 7:54












up vote
1
down vote

favorite









up vote
1
down vote

favorite











I was given a vector



beginalign p = [0.2, 0.15, 0.12, 0.11, 0.11, 0.1, 0.1, 0.05, 0.03, 0.03] endalign



So I constructed a random variables probability table as shown below.



beginarrayc
hline
k& 1 & 2 & 3 & 4 & 5 & 6 & 7 & 8 & 9 & 10 \ hline
P(X=k) & 0.2 & 0.15 & 0.12 & 0.11 & 0.11 & 0.1 & 0.1 & 0.05 & 0.03 & 0.03 \ hline
hline
hline
endarray



Question 1: Use this function to compute the probability of success after 3 guesses.



beginalign p_textsuccess(k,p) = sum_i=1^k p_i endalign



For this question I was able to solve it easily by substituting $k$ as $3$. However, concerning the random variable, I have no idea what $P(X = 1), P(X = 2), dotsc , P(X = 10)$ means in this situation. I only knew that the probability of success after $k$ guesses is equals to the sum of $P(X = 1)$ up to $P(X = k)$ according to the above function. I also knew that the more guesses I attempt, the higher chance I select the correct key. Subsequently, I have been struggling with question 2.



Question 2: The above distribution $p$ is a worst case distribution for the cryptographer and a best case distribution for the cryptanalyst. Why?



Is the reason is because each value of random variable is dependent on each other?



I would greatly appreciate if you guys kindly give me some thoughts.




probability probability-theory probability-distributions random-variables cryptography




share|cite|improve this question














I was given a vector



beginalign p = [0.2, 0.15, 0.12, 0.11, 0.11, 0.1, 0.1, 0.05, 0.03, 0.03] endalign



So I constructed a random variables probability table as shown below.



beginarrayc
hline
k& 1 & 2 & 3 & 4 & 5 & 6 & 7 & 8 & 9 & 10 \ hline
P(X=k) & 0.2 & 0.15 & 0.12 & 0.11 & 0.11 & 0.1 & 0.1 & 0.05 & 0.03 & 0.03 \ hline
hline
hline
endarray



Question 1: Use this function to compute the probability of success after 3 guesses.



beginalign p_textsuccess(k,p) = sum_i=1^k p_i endalign



For this question I was able to solve it easily by substituting $k$ as $3$. However, concerning the random variable, I have no idea what $P(X = 1), P(X = 2), dotsc , P(X = 10)$ means in this situation. I only knew that the probability of success after $k$ guesses is equals to the sum of $P(X = 1)$ up to $P(X = k)$ according to the above function. I also knew that the more guesses I attempt, the higher chance I select the correct key. Subsequently, I have been struggling with question 2.



Question 2: The above distribution $p$ is a worst case distribution for the cryptographer and a best case distribution for the cryptanalyst. Why?



Is the reason is because each value of random variable is dependent on each other?



I would greatly appreciate if you guys kindly give me some thoughts.





probability probability-theory probability-distributions random-variables cryptography





share|cite|improve this question













share|cite|improve this question




share|cite|improve this question








edited Sep 3 at 18:53









Jendrik Stelzner

7,58221037




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asked Aug 26 at 10:02









Maninthemiddleattack

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put on hold as unclear what you're asking by Math1000, ancientmathematician, José Carlos Santos, mfl, Q the Platypus Sep 3 at 21:37


Please clarify your specific problem or add additional details to highlight exactly what you need. As it's currently written, it’s hard to tell exactly what you're asking. See the How to Ask page for help clarifying this question. If this question can be reworded to fit the rules in the help center, please edit the question.






put on hold as unclear what you're asking by Math1000, ancientmathematician, José Carlos Santos, mfl, Q the Platypus Sep 3 at 21:37


Please clarify your specific problem or add additional details to highlight exactly what you need. As it's currently written, it’s hard to tell exactly what you're asking. See the How to Ask page for help clarifying this question. If this question can be reworded to fit the rules in the help center, please edit the question.









  • 1




    $X$ is the value of the key? What is the crypto system?
    – Henno Brandsma
    Aug 26 at 21:19










  • Are guesses made at random (from the remaining candidates, if one or more guesses are wrong)?
    – Math1000
    Sep 3 at 7:54












  • 1




    $X$ is the value of the key? What is the crypto system?
    – Henno Brandsma
    Aug 26 at 21:19










  • Are guesses made at random (from the remaining candidates, if one or more guesses are wrong)?
    – Math1000
    Sep 3 at 7:54







1




1




$X$ is the value of the key? What is the crypto system?
– Henno Brandsma
Aug 26 at 21:19




$X$ is the value of the key? What is the crypto system?
– Henno Brandsma
Aug 26 at 21:19












Are guesses made at random (from the remaining candidates, if one or more guesses are wrong)?
– Math1000
Sep 3 at 7:54




Are guesses made at random (from the remaining candidates, if one or more guesses are wrong)?
– Math1000
Sep 3 at 7:54















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