{[ promptMessage ]}

Bookmark it

{[ promptMessage ]}

testsol - 1(10 points What is the number of possible keys...

Info icon This preview shows pages 1–2. Sign up to view the full content.

View Full Document Right Arrow Icon
1. (10 points) What is the number of possible keys of the following cryptosystems: A. Shift cipher over 26 letter alphabet 26 B. Affine cipher over 26 letter alphabet 26 · 12 C. Substitution cipher over 26 letter alphabet 26! D. One time pad for sending an n bit long message 2 n 2. (10 points) Explain what would go wrong and why, if someone would try to use the Affine cipher with a = 6, and an arbitrary value b . (That is, the encryption e ( x ) = ax + b mod 26, with a = 6.) Notice that for e to be a valid encryption function, e must be one-to-one, that is, for every y ∈ Z 26 , there must be at most one x such that e ( x ) = y . However, the given function with a = 6 is not one-to-one. For each x ∈ Z 26 , x and x + 13 will encrypt to the same value. For the function e ( x ) = ax + b mod 26 to be one-to-one, gcd( a, 26) must be 1. However, notice that gcd(6 , 26) = 2. 3. (10 points) Alice needs to send an element x Z 100 to Bob sometime in the future, and they don’t like mods. Instead they pick a random key K Z 100 , and Alice plans to send x + K to Bob (without the mod). Prove or disprove: this achieves perfect secrecy. If you cannot prove your answer, give intuition. No, perfect secrecy is not achieved. For example, if Oscar sees the ciphertext y = 198, he will know exactly what was the value of both x and K .
Image of page 1

Info icon This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document Right Arrow Icon
Image of page 2
This is the end of the preview. Sign up to access the rest of the document.

{[ snackBarMessage ]}

What students are saying

  • Left Quote Icon

    As a current student on this bumpy collegiate pathway, I stumbled upon Course Hero, where I can find study resources for nearly all my courses, get online help from tutors 24/7, and even share my old projects, papers, and lecture notes with other students.

    Student Picture

    Kiran Temple University Fox School of Business ‘17, Course Hero Intern

  • Left Quote Icon

    I cannot even describe how much Course Hero helped me this summer. It’s truly become something I can always rely on and help me. In the end, I was not only able to survive summer classes, but I was able to thrive thanks to Course Hero.

    Student Picture

    Dana University of Pennsylvania ‘17, Course Hero Intern

  • Left Quote Icon

    The ability to access any university’s resources through Course Hero proved invaluable in my case. I was behind on Tulane coursework and actually used UCLA’s materials to help me move forward and get everything together on time.

    Student Picture

    Jill Tulane University ‘16, Course Hero Intern