CSCI 7000 - Cryptanalysis - Spring 2005

Problem Set #6

Due: Apr 28th, 2005 at 11am

Remember, your homework MUST be submitted in LaTeX!

Do not hand in homework electronically; print it out and bring it to class.

Problem 1. (Difficulty: 3) Let f(x) = 3f(x-1) and f(0) = 1. What are the last 10 decimal digits of f(10)? (Be sure and explain your solution method!)

Problem 2. (Difficulty: 3) Use Coppersmith's algorithm and LLL (via the NTL library) to find a small root of f(x) mod n where f(x) = x3 + 38672829692869996018691368369283446938196939432x2 + 497034821646805997815668685413075152492306930145922975521, and n = 574573399985770665652749316630737506074434357183163842707. (Hint: The root is less than n2/9 and the optimal m value is 3.)