hw8 - Computer Science 340 Reasoning about Computation...

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

View Full Document Right Arrow Icon
Computer Science 340 Reasoning about Computation Homework 8 Due at the beginning of class on Wednesday, November 21, 2007 Problem 1 The ciphertext below QFL HCVPS PX V ANSWLCEZK NCJVS; PQ XQVCQX QFL BPSZQL RNZ JLQ ZT PS QFL BNCSPSJ VSW WNLX SNQ XQNT ZSQPK RNZ JLQ QN DKVXX was created by using a substitution cipher on the alphabet of 26 letters. Recover the plaintext and show all your steps. (Hint: J decodes to G.) Problem 2 1. Find the smallest integer n > 1 such that 2 n = 1 (mod 33). What is the value of 2 273648273465737284375838005837397466 (mod33)? Justify your answer. 2. Compute 3 n (mod 11) for n = 1 , 2 , . . . , 10. What is the value of 3 2736482734657372843758380058373974 (mod11)? Justify your answer. 3. Compute 5 2000378 (mod 127) as simply as you can. 4. Compute 2 5432675 (mod 13). Problem 3 Prove without factoring that 65 is not prime, using Fermat’s theorem: a p - 1 = 1 (mod p ) for all integers 0 < a < p .
Image of page 1

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

View Full Document Right Arrow Icon
Problem 4 The entropy H ( X ) of a random variable X defined as p i log(1 /p i ), where Pr[ X = k ]= p k . For example, the entropy of the outcome H, T of a fair coin is (1 / 2) log(2)+(1 / 2) log(2) = 1.
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