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Some maths from the
telecommunications industry
Presented by Dr Steve Babbage
25 March 2009
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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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CMS / EPSRC – Steve Babbage
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Group R&D
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Optimisation
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CMS / EPSRC – Steve Babbage
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Frequency planning
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CMS / EPSRC – Steve Babbage
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25th March 2009
Frequency planning
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CMS / EPSRC – Steve Babbage
C1 - Unrestricted
Group R&D
Version 1.0
25th March 2009
Frequency planning
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CMS / EPSRC – Steve Babbage
C1 - Unrestricted
Group R&D
Version 1.0
25th March 2009
Frequency planning
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Site selection
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Radial network planning
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Mesh network planning
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Traffic scheduling / queueing
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Traffic routing
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Multi-layered networks
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Cryptography and data security
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Types of encryption algorithm
Steve Babbage
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Block ciphers and stream ciphers
Plaintext 101011011101001110
(any length)
Plaintext (128 bits)
Key
Key
(128 bits)
(128 bits)
Ciphertext (128 bits)
011101110100101101 ...
=
Ciphertext
Key
Key
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Plaintext
CMS / EPSRC – Steve Babbage
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110110101001100011 ...
011101110100101101 ...
(128 bits)
Plaintext
...
25th March 2009
=
101011011101001110 ...
Hash function
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
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CMS / EPSRC – Steve Babbage
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Theory – and lack of theory
Block ciphers
Public key algorithms
• Linear cryptanalysis
• Factoring
• Differential cryptanalysis
• Discrete logarithm
Hash functions
• Elliptic curve
• ???
• Others
Symmetric ciphers
Quantum computers
• Algebraic cryptanalysis
• What can they do?
• Gröbner bases
• What can't they do?
Lots of insight still needed
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CMS / EPSRC – Steve Babbage
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Complexity
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Closing thoughts
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CMS / EPSRC – Steve Babbage
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Thank you
Thanks to:
Further input taken from:
• Terry Lyons – Oxford / WIMCS
• Zuse Institute Berlin
• Bart Preneel – Leuven
• Robert Leese – Oxford / Smith Institute
• Peter Grindrod – Reading
• John McWhirter – Cardiff
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CMS / EPSRC – Steve Babbage
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25th March 2009