Department of Mathematics

# Simon Blackburn's Research Interests

I'm interested in three main areas, and the connections between them:

Cryptography (more properly cryptology): the science of making and breaking secret codes.

A good popular introduction: Simon Singh, The Code Book, Fourth Estate, 2000.

A good textbook for students with an undergraduate maths background: Doug R. Stinson, Cryptography: Theory and Practice, Chapman and Hall/CRC Press, 2005.

I usually work in cryptanalysis (breaking ciphers) rather than in cryptography (creating new ciphers). I'm especially interested in cryptanalysing ciphers that are based on mathematical ideas. I'm also very interested in combinatorial objects associated with cryptography (see below).

Combinatorics: the mathematics of counting and arranging objects.

A good textbook for students with an undergraduate maths background: Peter J Cameron, Combinatorics: Topics, techniques, algorithms, Cambridge University Press, 1994.

I don't know of any popular introduction to combinatorics. I think this is because of the nature of the subject: lots of beautiful intertwining techniques and problems, but few big problems that make good narrative. On the plus side, large parts of combinatorics can be understood without needing to know lots of theory beforehand.

Many of the areas I work in have connections to cryptography (for example: IPP codes, frameproof codes, random intersection graphs) or communication theory (runlength constrained arrays, perfect hash functions). I often use probabilistic techniques, and techniques from the theory of error correcting codes, in my work.

Group theory: the mathematics of symmetry.

A good popular introduction: Marcus du Sautoy, Finding Moonshine: A Mathematician's Journey Through Symmetry, Fourth Estate,2008.

A good textbook for students with an undergraduate maths background: Joseph J. Rotman, An Introduction to the Theory of Groups, Springer-Verlag, 1999.

I tend to work on questions in group theory that are combinatorial in nature. (This is not to be confused with questions in combinatorial group theory!) I'm especially interested in group enumeration (finding good asymptotic bounds on the number of isomorphism classes of finite groups in various families), in pairwise generation of finite groups and in group-based cryptography (I am currently a sceptic).