Summary from last week
! We have introduced the fundamental ideas behind
cryptographic systems (ciphers).
! We have set up a methodology for attacking these systems.
! We looked at shift and affine ciphers and how to analyze them.
! We have examined a num
SIT281
Week 8
1. Factorization of composite numbers
2. Discrete Logarithm
PUZZLE 6
Find an irreducible polynomial that could be used to
build the field
GF(37)
Puzzle solution
An example is
x7 + x6 + x4 + 1 (mod 3)
None of 0, 1 -1 is a solution and it
SIT281 Introduction to Cryptography
Lecture 1a
About the Unit and Cryptography
The Unit Guide…
> Is on DSO and you should read through it carefully.
> The outline for what we cover each week is there.
> We rely heavily on the textbook, so you will need i
DES Round Structure—Decryption
Essentially the same as the Encryption Procedure
Swap left and right
Use the keys Ki in the reversed order.
You begin with Ln, Rn and swap them to get the input
for Round 1, i.e. Rn, Ln
and the output is supposed to
SIT281 2010 TRIMESTER 2 ASSIGNMENT 1 SOLUTIONS
Due: Thursday August 12 by 4p.m.
NO EXTENSIONS allowed without medical or other certification. LATE ASSIGNMENTS will automatically lose 10% per day up to a maximum of three days, including weekends and holida
6/22/2010
SIT281 Introduction to Cryptography
Week 1 About the Unit and Cryptography the Unit and Cryptography
The Unit Guide
> . is on DSO and you should read through it carefully. > The outline for what we cover each week is there. > We rely heavily on
7/15/2010
SIT281 Introduction to Cryptography
WEEK 2
Lecture objectives
In this lecture: thi > We look at examples of substitution ciphers. > We see how block ciphers work. > We are introduced to linear shift registers.
1
7/15/2010
Substitution ciphers
>
7/27/2010
SIT 281 Introduction to Cryptography
WEEK 3
Objectives
> We cover sections
3.1, 3.2, 3.3 and 3.4
> of Chapter 3 this week.
1
7/27/2010
Modular arithmetic arithmetic
Of course, we saw that the Caesar cipher and other modular arithmetics are cycli
8/4/2010
SIT281 Introduction to Cryptography
Week 4
Objectives
In this lecture we cover sections 3.5, 3.6, 3.7 and 3.9. The topics we study are: >Modular Exponentiation >Theorems of Fermat and Euler of Fermat and Euler >Primitive roots >Finding square roo
SIT281 Introduction to Cryptography Introduction to Cryptography
Week 5
Objectives
> In this lecture, we examine how DES, one of the most commonly used cryptosystems, works. > DES (Data Encryption Standard) is prevalent worldwide. > The major components,
A summary of the maths youve learnt from Week 1 to Week 4
Written by: Vicky Mak (Burwood) [email protected] August, 2008
1
The maths weve learnt so far
1. Do you know how to solve ax + by = gcd(a, b)?
The Extended Euclidean Algorithm
2. What can say abo
Initialization
p, q, k1, k 2
CentralAuthority
publishes
g, g1, g2 H, H 0
Spending thecoin
Coin generation
1
Computationsinthe generationofthecoin
h g x , h1 g1x ,
gw ,
4
x h2 g2 (mod p)
Computationsinthe spendingofthecoin
w
TheBankMaksBank
( A, B, z, a,
Week 2: Additional notes on Modular Arithmetic
Written by: Vicky Mak (Burwood) [email protected] Contents based on: Introduction to Cryptography with Coding Theory, by Trappe et al. July, 2008
1
Finding a1( mod n)
Solve as + nt = 1.
We have that a1 s (