IT : 50 Years Later ...

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IT 50 Years Later ...
Professor Foto Afrati Dr. Despina
Polemi
National Technical Uni. of Athens (NTUA)
ICCS-NTUA
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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

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ENTROPY as a measure of

• unpredictability
• uncertainty
• incompressibility
• asymmetry
• delayed recurrence

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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

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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 monkeys data
  sequence

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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 ( He)
• N gt 2
• H the entropy of the source that produces the
  text of the unknown author

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ENTROPY in pure and applied math

• Combinatorics
• Ergodic Theory
• Algebra
• Operations Research
• Systems Theory
• Probability
• Statistics

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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

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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

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Logic and Theory of Algorithms

• Algorithmic IT
• Incompleteness Theorem of Kurt Goedel
• Limits of Mathematics
• Axiomatic Systems in Artificial Intelligence

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• ltlt The hard core of IT is, essentially, a branch
  of mathematics gtgt
• ltlt A thorough understanding of the mathematical
  foundation ...is surely a prerequisite to other
  applications gtgt
• 
  Claude Shannon

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Shannons Challenges

• CODING THEORY
• (1948)
• A Math. Theory of Com.
• Construct good codes

• CRYPTOGRAPHY
• (1949)
• Com. Theory of secrecy systems
• Construct secure cryprosystems

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Coding and Cryptography

• Shannons Theorems
• (entropy, key equivocation)
• Mutual Influence
• (design, applications)
• Evaluative Criteria
• (math.problem, measures, parameters, speed,
  storage, implementations)
• Mathematical Tools

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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

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Historical Breakthroughs in Coding Theory
1961 Mattson Solomon 1962 MacWilliams 1962
Massey 1967 Viterbi 1969 Massey 1970 V.D.
Goppa 1973 Delsarte 1978 Lempel-Ziv

• 1948 Shannon
• 1950 Hamming
• 1954 Golay
• 1954 Reed-Muller
• 1959 Hocquenghem
• 1960 Bose Ray
• Chaudhuri
• 1960 Reed Solomon

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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
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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)

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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
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Cryptography The Security Foundation

• Multicasting
• Mobile Communications
• Smart Card Technol.
• Electronic Payment Systems
• Internet

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Cryptography on the WWW
Internet
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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
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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/techno
  logies