# CSE 127: Lecture 5

The topics covered in this lecture are Euler Phi function buffer overflows under construction

## Euler Phi Function

Euler's theorem showed that for all x in {1, ..., n-1}:
xphi(n) = 1 mod n

where phi(n) is defined as follows:
Write n = prodi piei, where pi =/= pj if i =/= j.
(I.e., express n as its prime factorization, with multiple occurences of primes in the factorization coalesced and expressed as exponents.) Then
phi(n) = prodi piei-1(pi-1)
So in RSA where n=p*q, where p and q are primes, phi(n) = (p-1)(q-1).

## Buffer Overflows

Anatomy of a Unix process's stack. Stack frames, environment variables, argument lists. (Windows is not very different.)

Task: use gdb commands (info reg, x/x addr) to figure out where a process's stack is and look at the environment. You should write a ``hello world'' program, run gdb on it, set a break point, e.g., "break main", run the program until it hits the break point, then use the info and x commands to explore.

These are links additional security-related information. Exploring them is optional unless otherwise stated.

Here is a New York Times article on Warning on Iraqi Hackers and U.S. Safety. Note the 2% success rate figure.

Hacking physical master keys.

You are required to read this web site on electronic voting machines.

New worm attack slows down the Internet. Read the story at the BBC, the story at CNN, and the original CERT advisory about the vulnerability, and the current advisory about the worm.

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bsy+cse127.w03@cs.ucsd.edu, last updated Sat Jan 25 15:06:55 PST 2003. Copyright 2003 Bennet Yee.
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