Math 349 Cryptography, Fall 2011
Homework 7 solutions
RSA cryptosystem
(1) (5 pts) What is the ciphertext that is produced when RSA encryption with public key (e, n) = (3, 2669) is used
to encrypt the message BESTWISHES? Use the protocol A = 00, B = 01, .

1
Section 3.4 The Integers and Division
Denition If a and b are integers with a = 0, we say that a divides b if there is an integer k
such that b = ak. When a divides b, we say that a is a factor or divisor of b and that b is a multiple
of a. The notation

CSE331:
Introduction to Networks
and Security
Lecture 19
Fall 2002
Announcements
Reminder: Project 2 is due Monday, Oct. 28th
CSE331 Fall 2002
2
Recap
Block Ciphers: DES
Today:
Public Key Cryptography
RSA
CSE331 Fall 2002
3
Public Key Cryptography
S

Introduction to Computer Security (Part I)
Public-key
P bli k encryption and e-Cert
ti
d C t
Objectives:
To
To
To
To
understand the importance of computer security
understand what symmetric key encryption is
understand what public key encryption is
pu

Analysis of algorithms (Outcome (1): Alg as a core elt)
We may have > 1 algorithms (programs) solving the
y
g
(p g
)
g
same problem, so have to decide which one is better?
What do you
mean b b
by better?
Two aspects
Time: which one will run faster?
Space

Introduction to Computer Security (Part II)
RSA encryption
Objectives:
To be able t carry out th followings
T b bl to
t the f ll i
Modulo operations
Modulo exponent at on us ng repeat ng squares
exponentiation using repeating
Apply Euclidean algorithm

Google Search
Objectives:
To understand the basic ideas of how Google works.
The three basic components of Google: Googlebots;
Indexer; and Query Processor
To understand a data structure (inverted files) for
indexing webpages
To understand how Google

Artificial Intelligence
How to write a program to play games
p g m
p yg m
Objectives:
To understand the basic idea behind how we can write a
program to play games
To understand what is game tree?
g m
To be able to define a game tree for simple games su

Data Compression
How to use fewer bits to represent the data
Objectives:
To be able to construct Huffman code for data compression.
To understand the limitations of Huffman code.
To be able to construct Adaptive Huffman code for data
compression.
1
Huf

Adaptive (dynamic) Huffman code
Recall: We do not want to read the message twice; we do not
want to send the Huffman tree (or coding table) over
over.
High level idea:
When sending i-th character, using the frequencies of first (i-1)
characters to constru