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

Cryptography on the WWW

InternetInternet

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

Challenges of the Nineties Multi-user communication

Efficient Compression & Encryption Schemes

for High Speed Networks

Advanced Modulation coding for Mobile Web

browsing

Secure, optimise, converge Web

applications/technologies