cse101_9_26_11

# cse101_9_26_11 - Numeric algorithms 1 Cryptography A...

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

Numeric algorithms 1. Cryptography A. Public-key cryptography has enabled e-commerce. It relies upon the algorithmic status of two classical problems. a. Factoring: given a number return its prime factorization (cannot be solved in polynomial time) There is no efficient (polynomial0 algorithm for this. b. Primality: given a number, say whether it is prime or composite. Can be solved efficiently. 2. The decimal system B. The unary system eg. 11111111 = 8. 10 100 – In unary the space required would exceed the # of particles in the universe. In decimal, need only 101 digits. C. Quantifying size – writing the number N in many require N characters. In decimal, you need log n n digits. N -> log N, exponentially smaller representation. Roman system: only a constant beter than unary, still O(N) space). D. In decimal, using d digits, you can write numbers in the range 0 to 10 d – 1. Therefore in order to write N in decimal, # of digit needed is the smallest integer d such that N <= 10 d – 1. D >= log 10 (N+1). Size = ceiling (log 10 (N+1)) ~ log 10 N E.

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