443 topics Fall 2006
Aug. 31--------------------------------------------------------------
(1)
discussion of the class
ciphers, homework, projects, exams, syllabus
grading by the point system, webpage
fundamentals of cryptology
cryptography and cryptanalysis
cryptographic framework
plaintext, ciphertext, key, transformations, spaces
symmetrical encryption
example---
simple substitution, viewed as permutation
non-standard alphabets
cryptanalysis framework and terms
ciphertext only, known plaintext, chosen plaintext
chosen ciphertext
the notion of a secure system
unconditionally secure, computationally secure
types of attack, such as brute force attack
simple substitution
basic description
classically 'character' substitution
but -- bit string substitution
efficient representation of key
examples------
Caesar cipher - discussion
plaintext, ciphertext, key space
affine ciphers
basic form, notion of a model
congruence, computational framework
Z/n integers mod n
Spillman -- 1-13
Singh -- 1 -12
Sept 5---------------------------------------------------------------------
(2)
computational framework continued, notion, interpretation
of negative numbers, multiplicative and additive identities,
inverses, rings, zero divisors, solving computational
congruences
some improvements and types of monoalphabetic substitution---
a) Playfair cipher
b) Hill Cipher
linear algebra over Z/n , example
the idea of a block cipher
as a transposition cipher
at the binary level Z/2
c) homophonic ciphers
practical method of construction
example, brief mention of Beale ciphers
d) fractionated Morse code
Polyalphabetic substitution
definition
example - Alberti wheel
Spillman 14-33
Singh pp. 13-20
Sept. 7--------------------------------------------------------------------
(3)
handouts --
HDO-1 groups, rings, fields, etc.
HDO-2 FIPS 140-1 prn tests
HDO-3 LFSR - example
HDO-4 Unsolved ciphers
Vigenere ciphers
a little history, basic technique, -an alteration-
tools for their analysis
method of Kasiski and Babbage
IC - index of coincidence and smoothness
example - mention of cryptanalysis..coming later
Transposition ciphers
example - columnar transpositions, variations
double columnar transpositions
hexagonal placements with transformations
the idea of a group, definition
order of a group, order of an element
LaGrange's theorem, subgroups, examples
a more complicated example - Rubik's cube
2 x 2, 3 x 3, n x n basic moves
see handouts at top of today's topics
Spillman 34-51, 85-102
Singh 21`- 44
web links Wikipedia ..stream ciphers
Sept. 12-------------------------------------------------------------------
(4)
stream ciphers
an alternative to block ciphers - LFSR ciphers
linear feedback shift register (LFSR)
the basic setup, seed, taps, keystream, example
the possibility of non-linear feedback streams
Cryptanalysis of above methods --
simple substitution - frequency analysis, an example
Hill's cipher - known plaintext example
polyalphabetic substitution
more detail on the attack tools
Vigenere ciphers, Oscar -automatic attack
LFSR- am example
Spillman 51-71
Singh 45-98
genetic algorithms tutorial
genetic algorithms postscript tutorial
genetic algorithms
Wolfram's cellular atomata
Sept. 14 -----------------------------------------------
(5)
HDO5 - Index of coincidence
HD06 - Fractionated Morse Code
HD07 - Computing in Galois Fields
Rotor machines - an automated approach to encryption
their basic setup and function, simulation
read carefully the material in Singh
a two rotor simplification
discussion of key space
Famous unsolved ciphers ---
Kryptos...cipher at CIA Langley
Beale cipher ...gold in Virginia ?
Zodiac - cipher of a serial killer
Elgar's cipher..the great composer!
Poe's cipher...and its solution
Voynich manuscript...what is this?
Spillman
Singh
elonka's site
Sept.19--------------------------------------------------------------
(6)
Famous unsolved ciphers continued (finish up)...
class challenge ciphers
more on computational frameworks
finite fields
fields, rings, integral domains, groupss
Z/n^*, the reduced residues
Galois fields
examples
Chinese Remainder Theorem (CRT)
example, sketch of proof
GCD (greatest common divisor) algorithm
algorithm for multiplicative inverse
handouts
Spillman
Singh
Sept. 21=========================================================== (7)
HDO8 - columnar transposition ciphers
finite fields 1
finite fields wikipedia
finite fields planetmath
review of previous lecture's topics
Entropy (as a measure of informational uncertainty)
review of conditional probability
motivation and definition
examples, Huffman coding
properties
entropy of key space , equivocation
character entropy, unicity distance
Sept. 26------------------------------------------------------------
(8)
brief review of entropy
example
intractable problems, P, NP computational complexity
discussion
handouts
Spillman
Singh
Sept.28===========================================================
EXAM 1
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Oct. 3 -----------------------------------------------------------
informational entropy Wikipedia
entropy answers.com
Entropy and Information Theory book on the web
more on entropy
properties
entropy of key space , equivocation
character entropy, unicity distance
example
unicity distance
intractable problems, P, NP computational complexity
discussion
examples
satisfiability
Hamiltonian circuit, TSP
solving non-linear equations over Z/2
relationship to crypto systems
Oct. 5----------------------------------------------------
NP Complete Wikipedia
Compendium of NP optimization problems
The Hamiltonian Page Hamiltonian Cycle and Path problems
NP Complete NIST
NP hard
discussion of the terms
perfect secrecy
unconditional security
computational security
provable security
review of intractable algorithms
product ciphers
Feistel methods
Lucifer
small example
DES
history
detailed look
DES continued
history (handout)
detailed look
different modes of operation CBC, etc.
MACs
Oct. 10-----------------------------------------------------
breaking DES using a molecular computer
breaking DES in record time of 22 hours (1999)
comments on DES and open design
AES (hand out)
overall structure
different phases
Singh --through Chapter 5
Spillman - through Chapter 7
Oct. 12-----------------------------------------------------
Other block systems
Knapsack cipher
cryptanalysis of Knapsack cipher using genetic algorithm
Public key Cryptography
basic ideas
paper of Diffie, Hellman
public and private keys
Oct. 17-------------------------------------------------------
***Ciphers 1-3 due ***
RSA
fundamentals
definition of e,d
verification of the method
implementation of the method
primes and their propterties
The Prime Number Theorem
the great Internet Mersenne Prime Search (GIMPS)
Singh -- by this time you should have read most of Singh' book
You should at least be to page 243 'Alice and Bob go public'
Spillman -- Chapter 8
Oct. 19------------------------------------------------------
fast exponentiation
probabilistic primes
tests for prob. primes
Singh -- through Chapter 6
Spillman -- Chapter 8
Oct. 24------------------------------------------------------
Oct. 26----------------------------------------------------
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***EXAM 2***
Projects from Unit 1 due (second due date)
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Oct. 31-----------------------------------------------------
probabilistic primes
method of construction
Legendre symbol
Jacobi symbol
quadratic residues
examples
Solovay Strassen test
Miller Rabin test
Nov. 2------------------------------------------------------
conditional probability of failure
conditional probability given m successive successes
Miller Rabin algorithm
example
Factoring
complexity
recent advances
Pollard's p -1
rho
examples
Nov. 7--------------------------------------------------------
article twenty years of attacks on RSA
planetmath quadratic sieve
Wikipedia quadratic sieve
Parallel quadratic sieve using MPI
distributed quadratic sieve
quadratic sieve with grid computing
attacks on RSA
weaknesses
weak primes
small value for d
some digits of p are known
factoring
examples
Pollard's p - 1
Pollard's rho
polynomial bases
dependencies of relationships
examples
ElGamal's method of encryption
the Discrete Log problem (DLP)
Diffie-Hellman key exchange
Nov. 9--------------------------------------------------------
Timing attacks on RSA
ElGamal's method continued
Diffie-Hellman continued
man-in-the- middle
finding the square roots of quadratic residues
easy case
difficult case
probabilistic algorithm
Nov.14------------------------------------------------------
hashing
security properties
examples
digital signatures, hashes
signing and verifying functions
examples of signatures
RSA, Elgamal
possible handouts:
threshold schemes
the discrete log problem
attack strategies and classic protocol flaws
computing square roots of quadratic residues
(Las Vegas algorithms)
Nov. 16------------------------------------------------------
Hashing continued
hmac hashing
Related issues
blind signing
auctions and bids
Secret Sharing
the method of Shamir
Nov.21 -------------------------------------------------------
EXAM #3
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Nov. 23
Thanksgiving Break
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Nov. 28 secret sharing
example
example of another approach
protocols
mental poker
cheating ?
oblivious bit transfer
zero-knowledge proofs ..
using quadratic residues
log in process
zero-knowledge proofs
the graph isomorphism problem
a dialogue for graph non-isomorphism
graph isomorphism
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Nov. 30
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Dec. 5
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Dec. 7
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Dec. 12
last day of classes