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Some maths from the telecommunications industry

Presented by Dr Steve Babbage 25 March 2009. Some maths from the telecommunications industry. Purpose of this presentation. To illustrate some industrial applications that require and inspire mathematical research Optimisation Data security And underpinning both of those: Complexity.

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Some maths from the telecommunications industry

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  1. Presented by Dr Steve Babbage 25 March 2009 Some maths from the telecommunications industry CMS / EPSRC – Steve Babbage

  2. CMS / EPSRC – Steve Babbage Purpose of this presentation To illustrate some industrial applications that require and inspire mathematical research Optimisation Data security And underpinning both of those: Complexity

  3. Optimisation CMS / EPSRC – Steve Babbage

  4. CMS / EPSRC – Steve Babbage Frequency planning

  5. CMS / EPSRC – Steve Babbage Frequency planning

  6. CMS / EPSRC – Steve Babbage Frequency planning

  7. CMS / EPSRC – Steve Babbage Frequency planning

  8. CMS / EPSRC – Steve Babbage Site selection

  9. CMS / EPSRC – Steve Babbage Radial network planning

  10. CMS / EPSRC – Steve Babbage Mesh network planning

  11. CMS / EPSRC – Steve Babbage Traffic scheduling / queueing

  12. CMS / EPSRC – Steve Babbage Traffic routing

  13. CMS / EPSRC – Steve Babbage Multi-layered networks

  14. Cryptography and data security CMS / EPSRC – Steve Babbage

  15. CMS / EPSRC – Steve Babbage Types of encryption algorithm Steve Babbage

  16. CMS / EPSRC – Steve Babbage Block ciphers and stream ciphers Plaintext (any length) Plaintext (128 bits) 101011011101001110 ... Key (128 bits) Key (128 bits) 011101110100101101 ... = Ciphertext (128 bits) Ciphertext 110110101001100011 ... Key (128 bits) Key 011101110100101101 ... = Plaintext 101011011101001110 ... Plaintext

  17. CMS / EPSRC – Steve Babbage Digital signature Hash function This is an extremely long document which could go on for pages and pages and pages and pages and pages and pages and pages and pages and pages and pages and pages and pages and pages and pages and pages and pages and pages and pages and pages and pages Steve Babbage 5A90CB3820FB2744E11C49572C0D3919

  18. CMS / EPSRC – Steve Babbage Theory – and lack of theory Block ciphers Linear cryptanalysis Differential cryptanalysis Hash functions ??? • Public key algorithms • Factoring • Discrete logarithm • Elliptic curve • Others • Symmetric ciphers • Algebraic cryptanalysis • Gröbner bases • Quantum computers • What can they do? • What can't they do? Lots of insight still needed

  19. CMS / EPSRC – Steve Babbage Complexity

  20. CMS / EPSRC – Steve Babbage Closing thoughts

  21. CMS / EPSRC – Steve Babbage Thanks to: Terry Lyons – Oxford / WIMCS Bart Preneel – Leuven Robert Leese – Oxford / Smith Institute Peter Grindrod – Reading John McWhirter – Cardiff Thank you • Further input taken from: • Zuse Institute Berlin

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