C1 - Unrestricted Version 1.0 Group R&D 1CMS / EPSRC – Steve Babbage25 th March 2009 Some maths...
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Transcript of C1 - Unrestricted Version 1.0 Group R&D 1CMS / EPSRC – Steve Babbage25 th March 2009 Some maths...
![Page 1: 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.](https://reader034.fdocuments.us/reader034/viewer/2022051820/56649c7c5503460f94930bb1/html5/thumbnails/1.jpg)
1 CMS / EPSRC – Steve Babbage C1 - Unrestricted
Version 1.0
25th March 2009
Group R&D
Some maths from the telecommunications industry
Presented by Dr Steve Babbage
25 March 2009
![Page 2: 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.](https://reader034.fdocuments.us/reader034/viewer/2022051820/56649c7c5503460f94930bb1/html5/thumbnails/2.jpg)
CMS / EPSRC – Steve Babbage2 C1 - Unrestricted
Version 1.0
25th March 2009
Group R&D
Purpose of this presentation
To illustrate some industrial applications that require and inspire mathematical research
• Optimisation
• Data security
And underpinning both of those:
• Complexity
![Page 3: 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.](https://reader034.fdocuments.us/reader034/viewer/2022051820/56649c7c5503460f94930bb1/html5/thumbnails/3.jpg)
3 CMS / EPSRC – Steve Babbage C1 - Unrestricted
Version 1.0
25th March 2009
Group R&D
Optimisation
![Page 4: 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.](https://reader034.fdocuments.us/reader034/viewer/2022051820/56649c7c5503460f94930bb1/html5/thumbnails/4.jpg)
CMS / EPSRC – Steve Babbage4 C1 - Unrestricted
Version 1.0
25th March 2009
Group R&D
Frequency planning
![Page 5: 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.](https://reader034.fdocuments.us/reader034/viewer/2022051820/56649c7c5503460f94930bb1/html5/thumbnails/5.jpg)
CMS / EPSRC – Steve Babbage5 C1 - Unrestricted
Version 1.0
25th March 2009
Group R&D
Frequency planning
![Page 6: 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.](https://reader034.fdocuments.us/reader034/viewer/2022051820/56649c7c5503460f94930bb1/html5/thumbnails/6.jpg)
CMS / EPSRC – Steve Babbage6 C1 - Unrestricted
Version 1.0
25th March 2009
Group R&D
Frequency planning
![Page 7: 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.](https://reader034.fdocuments.us/reader034/viewer/2022051820/56649c7c5503460f94930bb1/html5/thumbnails/7.jpg)
CMS / EPSRC – Steve Babbage7 C1 - Unrestricted
Version 1.0
25th March 2009
Group R&D
Frequency planning
![Page 8: 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.](https://reader034.fdocuments.us/reader034/viewer/2022051820/56649c7c5503460f94930bb1/html5/thumbnails/8.jpg)
CMS / EPSRC – Steve Babbage8 C1 - Unrestricted
Version 1.0
25th March 2009
Group R&D
Site selection
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CMS / EPSRC – Steve Babbage9 C1 - Unrestricted
Version 1.0
25th March 2009
Group R&D
Radial network planning
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CMS / EPSRC – Steve Babbage10 C1 - Unrestricted
Version 1.0
25th March 2009
Group R&D
Mesh network planning
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CMS / EPSRC – Steve Babbage11 C1 - Unrestricted
Version 1.0
25th March 2009
Group R&D
Traffic scheduling / queueing
![Page 12: 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.](https://reader034.fdocuments.us/reader034/viewer/2022051820/56649c7c5503460f94930bb1/html5/thumbnails/12.jpg)
CMS / EPSRC – Steve Babbage12 C1 - Unrestricted
Version 1.0
25th March 2009
Group R&D
Traffic routing
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CMS / EPSRC – Steve Babbage13 C1 - Unrestricted
Version 1.0
25th March 2009
Group R&D
Multi-layered networks
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14 CMS / EPSRC – Steve Babbage C1 - Unrestricted
Version 1.0
25th March 2009
Group R&D
Cryptography and data security
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CMS / EPSRC – Steve Babbage15 C1 - Unrestricted
Version 1.0
25th March 2009
Group R&D
Types of encryption algorithm
Steve Babbage
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CMS / EPSRC – Steve Babbage16 C1 - Unrestricted
Version 1.0
25th March 2009
Group R&D
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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CMS / EPSRC – Steve Babbage17 C1 - Unrestricted
Version 1.0
25th March 2009
Group R&D
Digital signature
Steve BabbageThis 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
5A90CB3820FB2744E11C49572C0D3919
Hash function
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CMS / EPSRC – Steve Babbage18 C1 - Unrestricted
Version 1.0
25th March 2009
Group R&D
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?
![Page 19: 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.](https://reader034.fdocuments.us/reader034/viewer/2022051820/56649c7c5503460f94930bb1/html5/thumbnails/19.jpg)
CMS / EPSRC – Steve Babbage19 C1 - Unrestricted
Version 1.0
25th March 2009
Group R&D
Complexity
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CMS / EPSRC – Steve Babbage20 C1 - Unrestricted
Version 1.0
25th March 2009
Group R&D
Closing thoughts
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CMS / EPSRC – Steve Babbage21 C1 - Unrestricted
Version 1.0
25th March 2009
Group R&D
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