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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

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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

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

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

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

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

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

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

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

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

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

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

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

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

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

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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) 011101110100101101... Plaintext (any length) 101011011101001110... Ciphertext 110110101001100011... = Key (128 bits) 011101110100101101... = Plaintext 101011011101001110...

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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

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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?

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

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

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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

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