{[ promptMessage ]}

Bookmark it

{[ promptMessage ]}

quiz4_solution

# quiz4_solution - Quiz 4 solution Math 187 Prof Garsia Alex...

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

Quiz 4 solution Math 187, Prof. Garsia Alex Brik UC San Diego May 7, 2010 1. a) Suppose that the plaintext is composed of the columns P 1 , P 2 , ... P n in that order. A permutation a = ( a 1 ; a 2 ; :::; a n ) means that the ciphertext is composed of collumns P a 1 , P a 2 , ... P a n in that order. Given the matrix of statistics M such as that in this problem M ( i; j ) = B indicates that in the plaintext, columns j of ciphertext follows column i of the ciphertext. That is a j = a i + 1 . For the matrix M in this problem we note that M (1 ; 3) = M (2 ; 1) = M (4 ; 2) = M (5 ; 6) = M (6 ; 4) = B with all the other entries equal to s . (Here B means "big" number and s means small number). Hence a 3 = a 1 + 1 , a 1 = a 2 + 1 , a 2 = a 4 + 1 , a 6 = a 5 + 1 , and a 4 = a 6 + 1 . Note that a 3 is the largest number and a 5 is the smallest number. Hence a 5 = 1 and a 3 = 6 . Thus we have a 5 a 6 a 4 a 2 a 1 a 3 1 2 3 4 5 6 Thus it must be that ( a 1 ; a 2 ; a 3 ; a 4 ; a 5 ; a 6 ) = (5 ; 4 ; 6 ; 3 ; 1 ; 2) : Thus the permutation is (5 ; 4 ; 6 ; 3 ; 1 ; 2) b) WEBSTER IS USED TO LOOKUP WORDS IN THE ONLINE COPY OF THE MER- RIAM WEBSTER NINTH COLLEGIATE DICTI 2.

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

View Full Document
This is the end of the preview. Sign up to access the rest of the document.

{[ snackBarMessage ]}

### What students are saying

• 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.

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

• 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.

Dana University of Pennsylvania ‘17, Course Hero Intern

• 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.

Jill Tulane University ‘16, Course Hero Intern