#### 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) = 3^{f(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) = x^{3} +
38672829692869996018691368369283446938196939432x^{2} +
497034821646805997815668685413075152492306930145922975521, and
n = 574573399985770665652749316630737506074434357183163842707.
(*Hint:* The root is less than n^{2/9} and the optimal
m value is 3.)