CS7001/4001: Introduction to Cryptography
Rohit Chadha
Chadha
Cryptography
Organizational matters
O ce: 111 EBW
Email address: chadhar@missouri.edu
O ce hrs: Wednesday : 2 PM- 4 PM
Textbooks:
Introduction to Modern Cryptography
Authors: Jonathan Katz and
Topics Course: Introduction to
cryptography
Prerequisites: CS 3050 and MATH 2320. More specically, the course
will assume a familiarity with discrete math used in computer science, big-O
notation and elementary probability theory.
Course Overview: Cryptog
Homework 2
The homework carries 20 points. It is due November 6, 2014. Please submit
the homework electronically on Blackboard.
1. Suppose that (G, enc, dec) is a public-key encryption scheme such that
enc is a deterministic, i.e, non-probabilistic, algor
Homework 1
Due September 25, 2014. The answers can be handed in person or submitted
electronically on Blackboard. All problems carry 4 points.
1. The probabilities (or frequencies) of the 26 letters of the English alphabet
in English text are as follows.
Digital signatures
Rohit Chadha
Chadha
Cryptography
Digital signatures
Non-repudiation: A participant should not be able to back out of
their commitment
Scenario
Two parties are involved in a commercial exchange (over the
Internet)
They agree on terms of
Secret Sharing
Rohit Chadha
Chadha
Cryptography
Secret sharing (scenario)
Consider a bank vault
3 people have a key to the vault
Two keys are needed to open the vault
Cannot be opened with 1 key
Chadha
Cryptography
t out of t secret sharing
A secret value
Classical cryptosystems
Rohit Chadha
Chadha
Cryptography
Condentiality
Two parties, Alice and Bob, wish to send secret messages to
each other
Alice and Bob share some initial secret k. This initial secret is
called a key
How do they share this initial sec
RSA
Rohit Chadha
Chadha
Cryptography
Textbook RSA
GEN: Find two random n-digit primes number p, q and let
N = pq.
In this case (N) = (p 1)(q 1).
Find random numbers e, d 2 Z (N) s.t e.d = 1 mod (N).
The public key is (N, e) and secret key is (N, d).
enc:
Block Ciphers
Rohit Chadha
Chadha
Cryptography
Recap: stream ciphers
Advantages
Stream ciphers provide protection against COA attacks
Protect against COA attacks
Disadvantages
Keys cannot be re-used
Synchronized mode can be used to encrypt multiple times.
Stream Ciphers
Rohit Chadha
Chadha
Cryptography
Recap
One-time pad is perfectly secure
Not practical since the key-length has to be as large as the
plaintext
Practical versions of one-time pad are called stream ciphers
which we study next
From now on, our
Some Number Theory
Rohit Chadha
Chadha
Cryptography
Modulus
For every integer a and a positive integer N, there exist unique
numbers q and r s.t.
a = qN + r
0r <N
We write r = a mod N
1
100 mod 6 = 4
2
18 mod 6 = 0
3
3 mod 6 = 3
Notation: ZN = cfw_0, 1, .
Introduction to Key Exchange
Rohit Chadha
Chadha
Cryptography
How do Alice and Bob share secret keys
Block ciphers, Macs, authenticated encryption all need Alice
and Bob to share secrets
How do Alice and Bob share secrets?
How do you store them?
How do yo
Integrity: Message authentication codes (MACs)
Rohit Chadha
Chadha
Cryptography
What is Integrity?
Integrity
No authorized party can alter the data
So far, we have only considered condentiality
Integrity is independent of condentiality
For now, we will no
Homework 1
Due 1:59:59 pm, September 20, 2016.
All problems carry 4 points. The answers can be handed in person or submitted electronically on CANVAS.
1. The probabilities (or frequencies) of the 26 letters of the English alphabet
in English text are as f