Discrete Mathematics Coding Theory

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(Discrete Mathematics) Coding Theory
Cryptology (CC)prof.dr.ir. H.C.A. van Tilborg
(Henk) dr. A.G. van Asch (Bram) prof.dr. A.E.
Brouwer (Andries) prof.dr. A.K. Lenstra (Arjen)
dr. G.R. Pellikaan (Ruud) dr.ir. L.A.M.
Schoenmakers (Berry) dr. B.M.M. de Weger (Benne)

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Areas

• Specific Areas
• Coding Theory Error-correcting Codes
• Cryptology Secrecy Authenticity
• Information Theory Data Compression
• Signal Analysis Data Modulation
• Broad Areas
• Digital Communication
• Information Security

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Coding Theory

• How to achieve reliable communication over a
  noisy channel?
• Radio transmission (e.g., satellites, Voyager)
• CD/DVDs
• Typical questions
• How to get a good code
• how to add redundancy in a clever way
• efficient encoding
• efficient decoding (removal of errors)

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Cryptology

• Cryptology divided into two areas
• cryptography
• design of (mathematical) schemes related to
  information security which resist cryptanalysis
• e.g., encryption, digital signatures,
  zero-knowledge proofs
• also, quantum crypto (based on physics)
• cryptanalysis
• study of (mathematical) techniques for attempting
  to break cryptographic schemes, i.e., to make
  these schemes deviate from their intended behavior

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Challenges

• Mathematical (cf. Wiskunde 1, Wiskunde 3)
• algebra, number theory, discrete math
• Algorithmic
• algorithms data structures
• complexity theory
• special factoring of large integers, search for
  large primes
• Architecture
• security architecture integrated approach
• embedded systems
• special copy-protection mechanisms (digital
  media, but also digital money)

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Applications

• Protect against Viruses, worms, Trojans, Spam
• Wireless GSM, Bluetooth, WiFi, RFID
• Piracy Digital Rights Management,
  DVD-encryption, Pay-TV
• Smartcards ChipKnip, OV chip
• Biometrics (fingerprint, iris scans, ...)
• Security vs. Privacy
• Electronic payment systems, voting, auctions, ...
  

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Afstuderen / Stages

• Concrete voorbeelden
• Bij Chipper Differential Power Analysis aanval,
  geheime sleutel uit smartcards halen
• Bij Interpay gebruik van smartcards in een
  creditcard betaalsysteem voor Internet
• Bij British Telecom theoretisch onderzoek op
  gebied van elektronisch stemmen
• Bij Philips Crypto Competence Center, en NBV
  onderzoek naar elliptische kromme cryptografie

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Current Projects

• Examples
• Quantum cryptography using photons for
  transmitting data securely
• Digital Rights Management limits and
  possibilities of code obfuscation
• Study of algebraic attacks on block ciphers such
  as AES (Advanced Encryption Standard)
• Implementation of Byzantine agreement for a
  secure broadcast channel