C1 - Unrestricted Version 1.0 Group R&D 1CMS / EPSRC – Steve Babbage25 th March 2009 Some maths from the telecommunications industry Presented by Dr Steve.

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Presentation transcript:

C1 - Unrestricted Version 1.0 Group R&D 1CMS / EPSRC – Steve Babbage25 th March 2009 Some maths from the telecommunications industry Presented by Dr Steve Babbage 25 March 2009

C1 - Unrestricted Version 1.0 Group R&D CMS / EPSRC – Steve Babbage225th March 2009 Purpose of this presentation To illustrate some industrial applications that require and inspire mathematical research Optimisation Data security And underpinning both of those: Complexity

C1 - Unrestricted Version 1.0 Group R&D 3CMS / EPSRC – Steve Babbage25 th March 2009 Optimisation

C1 - Unrestricted Version 1.0 Group R&D CMS / EPSRC – Steve Babbage425th March 2009 Frequency planning

C1 - Unrestricted Version 1.0 Group R&D CMS / EPSRC – Steve Babbage525th March 2009 Frequency planning

C1 - Unrestricted Version 1.0 Group R&D CMS / EPSRC – Steve Babbage625th March 2009 Frequency planning

C1 - Unrestricted Version 1.0 Group R&D CMS / EPSRC – Steve Babbage725th March 2009 Frequency planning

C1 - Unrestricted Version 1.0 Group R&D CMS / EPSRC – Steve Babbage825th March 2009 Site selection

C1 - Unrestricted Version 1.0 Group R&D CMS / EPSRC – Steve Babbage925th March 2009 Radial network planning

C1 - Unrestricted Version 1.0 Group R&D CMS / EPSRC – Steve Babbage1025th March 2009 Mesh network planning

C1 - Unrestricted Version 1.0 Group R&D CMS / EPSRC – Steve Babbage1125th March 2009 Traffic scheduling / queueing

C1 - Unrestricted Version 1.0 Group R&D CMS / EPSRC – Steve Babbage1225th March 2009 Traffic routing

C1 - Unrestricted Version 1.0 Group R&D CMS / EPSRC – Steve Babbage1325th March 2009 Multi-layered networks

C1 - Unrestricted Version 1.0 Group R&D 14CMS / EPSRC – Steve Babbage25 th March 2009 Cryptography and data security

C1 - Unrestricted Version 1.0 Group R&D CMS / EPSRC – Steve Babbage1525th March 2009 Types of encryption algorithm Steve Babbage

C1 - Unrestricted Version 1.0 Group R&D CMS / EPSRC – Steve Babbage1625th March 2009 Block ciphers and stream ciphers Key (128 bits) Plaintext (128 bits) Ciphertext (128 bits) Key Plaintext Key (128 bits) Plaintext (any length) Ciphertext = Key (128 bits) = Plaintext

C1 - Unrestricted Version 1.0 Group R&D CMS / EPSRC – Steve Babbage1725th March 2009 Digital signature Steve Babbage 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 5A90CB38 20FB2744 E11C4957 2C0D3919 Hash function

C1 - Unrestricted Version 1.0 Group R&D CMS / EPSRC – Steve Babbage1825th March 2009 Theory – and lack of theory Block ciphers Linear cryptanalysis Differential cryptanalysis Hash functions ??? Lots of insight still needed Symmetric ciphers Algebraic cryptanalysis Gröbner bases Public key algorithms Factoring Discrete logarithm Elliptic curve Others Quantum computers What can they do? What can't they do?

C1 - Unrestricted Version 1.0 Group R&D CMS / EPSRC – Steve Babbage1925th March 2009 Complexity

C1 - Unrestricted Version 1.0 Group R&D CMS / EPSRC – Steve Babbage2025th March 2009 Closing thoughts

C1 - Unrestricted Version 1.0 Group R&D CMS / EPSRC – Steve Babbage2125th March 2009 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