CIS 5371 Cryptography
6*. An Introduction to Number Theory
1
Congruence and Residue classes
Arithmetic modulo n, Zn
Solving linear equations
The Chinese Remainder Theorem
Eulers phi function
The theorems of Fermat and Euler
Quadratic residues
Legendre & J
CIS 5371 Cryptography
6. Practical Constructions of
Symmetric-Key Primitives
Based on: Jonathan Katz and Yehuda Lindell Introduction to Modern Cryptography
1
Stream ciphers
A
stream cipher is a pair of deterministic
algorithms (Init, GetBits), where
Init
CIS 5371 Cryptography
8. Asymmetric
encryption-
1
Public Key Cryptography
Alice
Bob
Alice and Bob want to exchange a private key in public.
Public Key Cryptography
The Diffie-Hellman protocol
Let
p is a large prime and .
The
order of is a factor of .
has
CIS 5371 Cryptography
4a. Message Authentication Codes
Based on: Jonathan Katz and Yehuda Lindell Introduction to Modern Cryptography
1
Message Authentication
Codes
Encryption
vs message authentication
Different functionalities
Encryption does not provi
CIS 5371 Cryptography
3c. Pseudorandom Functions
Based on: Jonathan Katz and Yehuda Lindell Introduction to Modern Cryptography
1
Definition
.
2
Definition 3.23
Let be an efficient length preserving keyed
function. is a pseudorandom function if
PPT disti
CIS 5371 Cryptography
3. Private-Key Encryption and
Pseudorandomness
Based on: Jonathan Katz and Yehuda Lindel Introduction to Modern Cryptography
1
A Computational Approach
to Cryptography
The principal of Kerchoffs essentially
says that it is not neces
CIS 5371 Cryptography
3b. Pseudorandomness
Based on: Jonathan Katz and Yehuda Lindell Introduction to Modern Cryptography
1
Pseudorandomness
An introduction
A distribution D is pseudorandom if no PPT
distinguisher can detect if it a string sampled
accord
CIS 5371 Cryptography
6b. Practical Constructions of
Symmetric-Key Primitives.
1
DES
DES is a special type of iterated cipher based on
the Feistel network.
Block length 64 bits
Key length 56 bits
Ciphertext length 64 bits
2
DES
The round function is:
g ([
CIS 5371 Cryptography
4b. Collision Resistant Hash
Functions
Based on: Jonathan Katz and Yehuda Lindell Introduction to Modern Cryptography
1
Collision Resistance
A collision in a function H is a pair of distinct
inputs x, x
Collision resistance is trivia
CIS 5371 Cryptography
1. Introduction
1
Prerequisites for this
course
Basic Mathematics, in particular
Number Theory
Basic Probability Theory
Problem solving skills
Programming skills (for projects)
2
Goals for the Introduction
Discuss the effectiveness &
CIS 5371 Cryptography
5a. Pseudorandom Objects in Practice
Block Ciphers
Based on: Jonathan Katz and Yehuda Lindell Introduction to Modern Cryptography
1
Block ciphers as encryption schemes
or pseudorandom permutations
Block ciphers should be viewed as ps
CIS 5371 Cryptography
3b. Pseudorandomness
Based on: Jonathan Katz and Yehuda Lindell Introduction to Modern Cryptography
1
Pseudorandomness
An introduction
A distribution D is pseudorandom if no PPT
distinguisher can detect if it a string sampled
accord
CIS 5371 Cryptography
3c. Pseudorandom Functions
Based on: Jonathan Katz and Yehuda Lindell Introduction to Modern Cryptography
1
Definition
A is a two input function
0,1 0,1 0,1
where the first input is called the key, denoted ,
.and the second is just
CIS 5371 Cryptography
3. Private-Key Encryption and
Pseudorandomness
Based on: Jonathan Katz and Yehuda Lindel Introduction to Modern Cryptography
1
A Computational Approach
to Cryptography
The principal of Kerchoffs essentially
says that it is not neces
CIS 5371 Cryptography
1. Introduction
1
Prerequisites for this
course
Basic Mathematics, in particular
Number Theory
Basic Probability Theory
Problem solving skills
Programming skills (for projects)
2
Goals for the Introduction
Discuss the effectiveness &
CIS 5371 Cryptography
4. Collision Resistant Hash Functions
Based on: Jonathan Katz and Yehuda Lindell Introduction to Modern Cryptography
1
Collision Resistance
A collision in a function H is a pair of distinct
inputs x, x for which = .
Collision resista
CIS 5371 Cryptography
7. Asymmetric encryption-
1
Public Key Cryptography
Alice
Bob
Alice and Bob want to exchange a private key in public.
Public Key Cryptography
The Diffie-Hellman protocol
Let p is a large prime and .
The order of is a factor of 1.
ha
CIS 5371 Cryptography
5b. Pseudorandom Objects in Practice
Block Ciphers
1
DES
DES is a special type of iterated cipher based on
the Feistel network.
Block length 64 bits
Key length 56 bits
Ciphertext length 64 bits
2
DES
The round function is:
g ([Li-1,R
Introduction to Number Theory
1
Preview
Number Theory Essentials
Congruence classes, Modular arithmetic
Prime numbers challenges
Fermats Little theorem
The Totient function
Euler's Theorem
Quadratic residuocity
Foundation of RSA
2
Number Theory Essentials
CIS 5371 Cryptography
4. Message Authentication Codes
Based on: Jonathan Katz and Yehuda Lindell Introduction to Modern Cryptography
1
Message Authentication
Codes
Encryption vs message authentication
Different functionalities
Encryption does not provid
CIS 5371 Cryptography
8. Data Integrity Techniques
1
Asymmetric techniques, I
Digital signatures
With PK encryption, Alice can use her private key
to decrypt a message and the resultant
ciphertext can be encrypted to recover the
message.
This ciphertext c
CIS 5371 Cryptography
6*. An Introduction to Number
Theory
1
Congruence and Residue
classes
Arithmetic modulo n, Zn
Solving linear equations
The Chinese Remainder Theorem
Eulers phi function
The theorems of Fermat and Euler
Quadratic residues
Legendre & J
CIS 5371 Cryptography
QUIZ 14 (5 minutes only) with answers
This quiz concerns the birthday attack and the Merkle-Damg transform.
ard
1. Use some of the following words/expressions to describe the birthday attack:
H : cfw_0, 1 cfw_0, 1 , cfw_0, 1 , y = H
CIS 5371 Cryptography
Home Assignment 1
Due: At the beginning of the class on on Feb 12, 2013
Exercises taken from the course textbook. Jonathan Katz and Yehuda Lindell, Introduction to
Modern Cryptography.
1.3 Consider an improved version of the Vigen`r
CIS 5371 Cryptography
8. Encryption -Asymmetric Techniques
Textbook
Textbook encryption algorithms
In this chapter, security (confidentiality) is considered
this chapter security (confidentiality) is considered
in the following sense:
All-or-nothing secr
CIS
CIS 5371 Cryptography
6. An Introduction to Number Theory
1
Congruence and Residue classes
Arithmetic modulo n, Zn
Solving linear equations
The Chinese Remainder Theorem
Eulers phi function
The theorems of Fermat and Euler
Quadratic residues
Legendre