IT : 50 Years Later ... * National Technical Uni. of Athens (NTUA) ** ICCS-NTUA Professor Foto Afrati * Dr. Despina Polemi **
Dec 20, 2015
IT : 50 Years Later ...
* National Technical Uni. of Athens (NTUA)
** ICCS-NTUA
Professor Foto Afrati * Dr. Despina Polemi **
Claude Shannon (1948)
A Mathematical Theory of Communication
Bell Systems Technical Journal
http://cm.bell-labs.com/ Probabilistic Methods on Communication
Systems Mathematical Theory of Entropy Statistical Characteristics of Data and
Communication Systems
ENTROPY as a measure of:
unpredictability
uncertainty
incompressibility
asymmetry
delayed recurrence
ENTROPY a mathematical concept
the number of typical sequences of a given length
the recurrence of blocks of symbols (patterns) in a single typical sequence
Entropy Estimation, Data Compression, Classification
ENTROPY in an example Q: A monkey types a single Latin letter
every second. How long on average will it take to type CLAUDESHANNON ?
A: 13 13 log 26 l H
26 = 2 = 2
H= log 26 = entropy of monkey’s data sequence
ENTROPY in an example
Q: We observe N characters in a text of a 16th century author. We want to determine if this unknown author is Shakespeare. What is the minimum N?
A: l ( H+e)
N > 2 H = the entropy of the source that produces the text
of the unknown author
ENTROPY in pure and applied math
Combinatorics Ergodic Theory Algebra Operations Research Systems Theory Probability Statistics
IT a tool in :
Coding Theory and Cryptology Ergodic Theory and Dynamical Systems Statistical Inference and Prediction The Physical Sciences Economics, Biology Humanities and Social Sciences Logic and the Theory of Algorithms
Logic and Theory of Algorithms
Kolmogorov Complexity Algorithmic Entropy Algorithmic Complexity of a Finite String A measure of the smallest program that
outputs the finite string incompressible strings of any length lower bounds on computational complexity
Logic and Theory of Algorithms
Algorithmic IT
Incompleteness Theorem of Kurt Goedel
Limits of Mathematics
Axiomatic Systems in Artificial
Intelligence
<< The hard core of IT is, essentially, a branch of mathematics >>
<< A thorough understanding of the mathematical foundation ...is surely a prerequisite to other applications >>
Claude Shannon
Shannon’s Challenges
CODING THEORY(1948)
“A Math. Theory of Com.”
Construct “good” codes
CRYPTOGRAPHY(1949)
“Com. Theory of secrecy systems”
Construct secure cryprosystems
Coding and Cryptography Shannon’s Theorems
(entropy, key equivocation) Mutual Influence
(design, applications) Evaluative Criteria
(math.problem, measures, parameters, speed, storage, implementations)
Mathematical Tools
Common Mathematical Tools
finite fields complexity theory algebraic geometry combinatorics sequences comput.math. group theory
BAN Logic finite state machines exponential sums dynamical systems graph theory theory of algorithms
Historical Breakthroughs in Coding Theory[1948 Shannon]
[1950 Hamming]
[1954 Golay]
[1954 Reed-Muller]
[1959 Hocquenghem]
[1960 Bose Ray
Chaudhuri]
[1960 Reed Solomon]
[1961 Mattson Solomon]
[1962 MacWilliams]
[1962 Massey]
[1967 Viterbi]
[1969 Massey]
[1970 V.D. Goppa]
[1973 Delsarte]
[1978 Lempel-Ziv]
Recent Breakthroughs
[1981 V.D. Goppa]
[1982 Tsfasman
Vladut Zink]
[1982 Ungerboek]
[1992 Moreno-Moreno]
[1993 Berrou]
[1994 Hammons Kumar Calderbank Sloane
Sole]
[1996 Conway Sloane Forney Vardy]
[1997 Calderbank Sloane Forney]
[1995-1998 Sakata Jensen Hoholdt Justesen Feng Rao]
From Theory to Practice convolutional (additive white gaussian) block codes (non additive nongaussian) RS (compact disks, space communication) Trellis (space communication) Spectral Null (recording devices) PUM (magnetic optical recording) Line (optical fiber systems) First Order Reed-Muller (range finding,
synchronising, modulation, scrambling) Turbo (CODECS)
Milestones in Cryptography
[1949 Shannon]
[1949-1967... ]
[1967 Kahn]
[1970 Ellis]
[1974 Feistel]
[1974 Gilbert]
[1974 Merkle]
[1976 Diffie Hellman]
[1977 NBS]
[1977 Merkle Hellman][1977 Rivest Shamir Adleman][1982 Goldwasser Micali][1985 Koblitz Miller][1990 Bennet Brassard][1990 Biham Shamir][1991 Zimmermann][1992 Lai-Massey][1993 Mitsui][1994 Shor]
Cryptography The Security Foundation
Multicasting
Mobile Communications
Smart Card Technol.
Electronic Payment
Systems
Internet
Crypto Tools on the WWW
Firewall Technol. Session Security
(SSL, S-HTTP,PCT) Mail Security
(S/MIME, PEM, PGP)
Ecommerce protocols
(SET, C-SET, Globe-ID)
Web technologies
(Java, Active-X,Plug-Ins,
Agents) Trustworthy Key Management
Systems Trusted Third Party Services