hw04 - What can you say about whether the other one is...

Info iconThis preview shows page 1. Sign up to view the full content.

View Full Document Right Arrow Icon
Math 55: Discrete Mathematics, Fall 2008 Reading and Homework Assignment 4 Reading: Lecture 13: Supplementary notes on Factoring Algorithms Homework (due Monday, 9/29): Odd-numbered self-checking exercises: 3.7: 31, 33, 45, 47, 59 Problems to hand in: 3.7: 32, 46, 60 (A) In Exercise 46, also find the decryption exponent d and check that the first block of your encrypted message decrypts to the right thing using this expo- nent. (B) Apply Miller’s test to the base 2 (as discussed in 3.7 Exercise 30 and the lecture) to determine that one of the two numbers 1601, 1729 is composite.
Background image of page 1
This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: What can you say about whether the other one is prime? (C) Use Pollards algorithm, with f ( x ) = x 2 + 2, and starting value y = z = 6, to factor 17741. (D) (i) Prove that 2 n + 1 is a pseudo-prime to the base 2 if and only if n is a power of 2, and deduce that if 2 n + 1 is prime, then n must be a power of 2. (ii) Verify that 2 1 + 1, 2 2 + 1, 2 4 + 1, 2 8 + 1, and 2 16 + 1 are prime, but that 641 is a factor of 2 32 + 1. Reminder: The rst midterm exam is Friday, Oct. 3. The exam will cover the material on homework assignments 1 through 4....
View Full Document

Ask a homework question - tutors are online