Department of Mathematics
Royal Holloway University Of London

Simon Blackburn's Papers and Preprints

Here is a list of my published papers and recent preprints. For a copy of any paper that doesn't appear as a link below, just email me. Note that the links to published papers are generally to the corresponding preprint, so they might differ (usually slightly) from the journal version.

 


 Recent preprints:


Published (and/or accepted) papers:

  • S.R. Blackburn and S. Scott, 'The discrete logarithm problem for exponents of bounded height', LMS J. Computation and Mathematics, Vol 17 Special Issue A (2014), pp. 148-156. See http://dx.doi.org/10.1112/S1461157014000230.
  • S.R. Blackburn, S.V. Konyagin and I.E. Shparlinski, 'Counting additive decompositions of quadratic residues in finite fields', Functiones et Approximatio, to appear. See http://arxiv.org/abs/1403.2589.
  • S.R. Blackburn, 'Enumerating finite racks, quandles and kei', Electronic J. Combinatorics, Vol. 20 Issue 3 (2013), P43, http://www.combinatorics.org/ojs/index.php/eljc/article/view/v20i3p43. Or see http://arxiv.org/abs/1203.6504.
  • S.R. Blackburn and T.A. McCourt, 'Triangulations of the sphere, bitrades and abelian groups', Combinatorica, to appear. See http://arxiv.org/abs/1112.5423.
  • S.R. Blackburn, S. Gerke and M. Wildon (Eds), Surveys in Combinatorics 2013, LMS Lecture Note Series 409, Cambridge University Press, Cambridge, UK, 2013. See www.cambridge.org/9781107651951.
  • S.R. Blackburn and T. Etzion, 'The asymptotic behavior of Grassmannian codes', IEEE Trans. Inform. Theory, Vol. 58 (2012), pp. 6605-6609. See http://arxiv.org/abs/1111.2713.
  • S.R. Blackburn, J.R. Britnell and M. Wildon, 'The probability that a pair of elements of a finite group are conjugate', J. London Math. Soc., Vol. 86 (2012), pp. 755-778. See http://arxiv.org/abs/1108.1784.
  • S.R. Blackburn, C.Cid and C. Mullan, 'Cryptanalysis of three matrix-based key establishment protocols', J. Mathematical Cryptology, Vol. 5 (2011), pp. 159-168. See http://arxiv.org/abs/1102.2358.
  • S.R. Blackburn, 'The existence of k-radius sequences', J. Comb. Theory - Series A, Vol. 119 (2012), pp. 212-217. See http://arxiv.org/abs/1101.1172.
  • S.R. Blackburn, A. Ostafe and I.S. Shparlinski, 'On the distribution of the subset sum pseudorandom number generator on elliptic curves', Uniform Distribution Theory, Vol. 6 (2011), pp. 127-142. See http://arxiv.org/abs/1102.1053.
  • S.R. Blackburn, D.R. Stinson and J. Upadhyay, 'On the complexity of the herding attack and some related attacks on hash functions', Designs, Codes and Cryptography, Vol 64 (2012), pp. 171-193. See http://eprint.iacr.org/2010/030.
  • S.R. Blackburn and J.F. McKee, 'Constructing k-radius sequences', Mathematics of Computation, Vol 81 (2012), pp. 2439-2459. See  http://arxiv.org/abs/1006.5812.
  • S.R. Blackburn, A. Panoui, M.B. Paterson and D.R. Stinson, 'Honeycomb arrays', Elec. J. Combinatorics, Vol. 17 (1) (2010), R172. See http://www.combinatorics.org/Volume_17/PDF/v17i1r172.pdf.
  • S.R. Blackburn, 'The discrete logarithm problem modulo one: cryptanalysing the Ariffin-Abu cryptosystem', J. Mathematical Cryptology, Vol 4 (2010), 193-198. See http://eprint.iacr.org/2010/114.
  • S.R. Blackburn, M.B. Paterson and D.R. Stinson, 'Putting dots in triangles', J. Combin. Math. Combin. Comput., Vol. 78 (2011), pp. 23-32. See http://arxiv.org/abs/0910.4325.
  • S.R. Blackburn, T. Etzion, K.M. Martin and M.B. Paterson, 'Distinct difference configurations: Multihop paths and key predistribution in sensor networks', IEEE Trans. Inform. Theory, Vol. 56 (2010), pp. 3961-3972. See http://arxiv.org/abs/0811.3896.
  • S.R. Blackburn, T. Etzion and S.-L. Ng, 'Traceability codes', J. Comb. Theory - Series A, Vol. 117 (2010), pp. 1049-1057. See http://eprint.iacr.org/2009/046.
  • S.R. Blackburn, C. Cid and C. Mullan, 'Cryptanalysis of the MST_3 public key cryptosystem', J. Mathematical Cryptology, Vol. 3 (2009), pp. 321-338. See http://eprint.iacr.org/2009/248.
  • S.R. Blackburn, C. Cid and C. Mullan, 'Group theory in cryptography', Groups St Andrews 2009 in Bath, Volume 1, C.M. Campbell, M.R. Quick, E.F. Robertson, C.M. Roney-Dougal, G.C. Smith and G. Traustason (Eds) (Cambridge University Press, Cambridge, 2011) 133-149. See http://arxiv.org/abs/0906.5545.
  • S.R. Blackburn, T. Etzion, K.M. Martin and M.B. Paterson, 'Two-Dimensional Patterns with Distinct Differences -- Constructions, Bounds, and Maximal Anticodes', IEEE Trans. Inform. Theory, Vol. 56 (2010), pp. 1216-1229. See http://arxiv.org/abs/0811.3832.
  • S.R. Blackburn, 'Cryptanalysing the critical group: Efficiently solving Biggs's discrete logarithm problem', J. Mathematical Cryptology, Vol. 3 (2009) pp. 199-203. See http://eprint.iacr.org/2008/170.
  • S.R. Blackburn and S. Gerke, 'Connectivity of the Uniform Random Intersection Graph', Discrete Mathematics, Vol. 309 (2009) pp. 5130-5140. See http://arxiv.org/abs/0805.2814.
  • S.R. Blackburn, T. Etzion, K.M. Martin and M.B. Paterson, 'Efficient key predistribution for grid-based wireless sensor networks', in ICITS 2008, Lecture Notes in Computer Science Vol. 5155, R. Safavi-Naini (Ed.), (Springer, Berlin, 2008), pp. 54-69.
  • S.R. Blackburn, K.M. Martin, M.B. Paterson and D.R. Stinson, 'Key refreshing in wireless sensor networks', in ICITS 2008, Lecture Notes in Computer Science Vol. 5155, R. Safavi-Naini (Ed.), (Springer, Berlin, 2008), pp. 156-170.
  • S.R. Blackburn, 'A mathematical walk in Surrey', British Society for the History of Mathematics Bulletin, Vol. 23 (2008), 178-180.
  • S.R. Blackburn, T. Etzion and S.-L. Ng, 'Prolific codes with the identifiable parent property', SIAM J. Discrete Mathematics, Vol. 22 (2008) pp. 1393-1410. See http://eprint.iacr.org/2007/276 for the extended preprint.
  • S.R. Blackburn, T. Etzion, D.R. Stinson and G.M. Zaverucha, 'A bound on the size of separating hash families', J. Comb. Theory - Series A, Vol. 115 (2008), pp. 1246-1256. See http://eprint.iacr.org/2007/304.
  • S.R.Blackburn, P.M. Neumann and G. Venkataraman, Enumeration of Finite Groups, Cambridge University Press, Cambridge, UK, 2007.
  • S.R. Blackburn and I.E. Shparlinski, 'On the average energy of circulant graphs', Linear Algebra and its Applications, Vol. 428 (2008), pp. 1956-1963.
  • S.-J. Choi, S.R. Blackburn and P.R. Wild, 'Cryptanalysis of a homomorphic public-key cryptosystem over a finite group', J. Math. Cryptography, Vol. 1 (2007), pp. 351-358. See http://eprint.iacr.org/2006/357.
  • S.R. Blackburn, 'Two Dimensional Runlength Constrained Arrays with Equal Horizontal and Vertical Constraints', IEEE Trans. Information Theory, Vol. 52 (2006), pp. 3305-3309.
  • S.R. Blackburn and I.E. Shparlinski, 'Character sums and nonlinear recurrence sequences', Discrete Mathematics, Vol. 306 (2006), pp. 1132-1138. An erratum to this paper has appeared: Discrete Mathematics Vol. 307 (2007), pp. 1218-1219.
  • S.R. Blackburn, 'Sets of permutations that generate the symmetric group pairwise', J. Comb. Theory - Series A, Vol. 113 (2006), pp. 1572-1581.
  • S. R. Blackburn, C. Cid and S.G. Galbraith, 'Cryptanalysis of a cryptosystem based on Drinfeld modules', IEE Proc. Information Security, Vol. 153 (2006), pp. 12-14. See http://eprint.iacr.org/2003/223.
  • S. R. Blackburn, D. Gomez-Perez, J. Gutierrez and I. E. Shparlinski, 'Reconstructing noisy polynomial evaluation in residue rings', J. Algorithms, Vol. 61 (2006), pp. 47-59.
  • S. R. Blackburn, D. Gomez-Perez, J. Gutierrez and I. E. Shparlinski, 'Predicting nonlinear pseudorandom number generators', Math. Comp., Vol. 74 (2005), pp. 1471-1494.
  • S. R. Blackburn and K.G. Paterson, 'Cryptanalysis of a message authentication code due to Cary and Venkatesan', in Fast Software Encryption 2004, Lecture Notes in Computer Science Vol. 3017, B. Roy and W. Meier (Eds), (Springer, Berlin, 2004), pp. 446-453. See http://eprint.iacr.org/2003/199.
  • S. R. Blackburn, D. Gomez-Perez, J. Gutierrez and I. E. Shparlinski, 'Predicting the inversive generator' in Cryptography and Coding. Proc. 9th IMA Intern. Conf on Cryptography and Coding, Lecture Notes in Computer Science 2898, K.G. Paterson (Ed.), (Springer, Berlin, 2003), pp. 264-275.
  • S.R. Blackburn and A.J. Spencer, 'Products of subsets in an abelian group', J. Comb. Theory - Series A, Vol. 103 (2003), pp. 53-68.
  • S.R. Blackburn, 'Combinatorial schemes for protecting digital content', in Surveys in Combinatorics 2003, C.D. Wensley (Ed.) (Cambridge University Press, Cambridge, 2003), pp. 43-78.
  • S.R. Blackburn, 'An Upper Bound on the Size of a Code with the k-Identifiable Parent Property', J. Comb. Theory - Series A, Vol. 102 (2003), pp. 179-185. See http://eprint.iacr.org/2002/101.
  • S.R. Blackburn, 'Frameproof Codes', SIAM Journal of Discrete Mathematics, Vol. 16 (2003), pp. 499-510.
  • S.R. Blackburn and T. Garefalakis, 'Cryptanalysis of a cryptosystem due to Yoo, Hong, Lee, Lim, Yi and Sung', Electronics Letters, Vol. 37, No. 18 (2001), pp. 1118-1119.
  • S.R. Blackburn and E. Teske, 'Baby-step giant-step algorithms for non-uniform distributions', in Proceedings of ANTS IV, Lecture Notes in Computer Science 1838, W. Bosma (Ed.) (Springer, Berlin, 2000), pp. 153-168.
  • S.R. Blackburn and S.D. Galbraith, 'Certification of secure RSA keys', Electronics Letters, Vol. 36, No. 1 (2000), pp. 29-30. Also see: 'Certification of secure RSA Keys', Tech. Report CORR 99-44, University of Waterloo.
  • S.R. Blackburn, 'Perfect hash families: probabilistic methods and explicit constructions', J. Comb. Theory - Series A, Vol. 92 (2000), pp. 54-60.
  • S.R. Blackburn and S.D. Galbraith, 'Cryptanalysis of two cryptosystems based on group actions', in Advances in Cryptology -- ASIACRYPT '99, Lecture Notes in Computer Science 1716, K.Y. Lam, E. Okamoto, C. Xing (Eds.) (Springer,Berlin, 1999) pp. 52-61.
  • S.R. Blackburn, 'Cryptanalysis of a public key cryptosystem due to Wu and Dawson', IEE Proc. Computers and Digital Techniques, Vol. 146, No. 4 (1999), pp. 185-186.
  • S.R. Blackburn, 'Groups of prime power order with derived subgroup of prime order', J. Algebra, Vol. 219 (1999), pp. 625-657.
  • S.R. Blackburn, 'The linear complexity of the self-shrinking generator', IEEE Trans. Inform. Theory, Vol. 45, No. 6 (1999), pp. 2073-2077.
  • S.R. Blackburn, 'Cryptanalysis of a Keystream Generator due to Chan and Cheng', Electronics Letters, Vol. 34, No. 18 (1998), pp. 1737-1738.
  • S.R. Blackburn, S. Blake-Wilson, M. Burmester and S.D. Galbraith, 'Weaknesses in shared RSA key generation protocols' in Cryptography and Coding, 7th IMA International Conference, Cirencester, Lecture Notes in Computer Science 1746, M. Walker (Ed.) (Springer, Berlin, 1999), pp. 300-306. Also see: 'Shared generation of shared RSA Keys', Tech. Report CORR 98-19, University of Waterloo.
  • S.R. Blackburn, K. Brincat, F. Mirza and S. Murphy, 'Cryptanalysis of ''Labyrinth'' stream cipher', Electronics Letters, Vol. 34, No. 12 (1998), pp. 1220-1221.
  • S.R. Blackburn and P.R. Wild, 'Optimal linear perfect hash families', J. Comb. Theory - Series A, Vol. 83 (1998), pp. 233-250.
  • S.R. Blackburn, 'Orthogonal Sequences of Polynomials over Arbitrary Fields', J. Number Theory, Vol. 68, No. 1 (1998), pp. 99-111.
  • S.R. Blackburn, 'Combinatorics and Threshold Cryptography', in Combinatorial Designs and their Applications (Chapman and Hall/CRC Research Notes in Mathematics 403) F.C. Holroyd, K.A.S. Quinn, C. Rowley and B.S. Web (Eds.), CRC Press, London, 1999, pp. 49-70.
  • S.R. Blackburn, 'Fast Rational Interpolation, Reed--Solomon Decoding and the Linear Complexity Profiles of Sequences', IEEE Trans. Inform. Theory, Vol. 43, No. 2 (1997), pp. 537-548.
  • S.R. Blackburn, 'A Generalised Rational Interpolation Problem and the Solution of the Welch--Berlekamp Key Equation', Designs, Codes and Cryptography, Vol. 11, No. 3 (1997), pp. 223-234.
  • S.R. Blackburn, 'The Sajdak Conjecture', Math. Spectrum, Vol. 30, No. 1 (1997), pp. 15-16.
  • S.R. Blackburn, M. Burmester, Y. Desmedt and P.R. Wild, 'Efficient Multiplicative Sharing Schemes', in Advances in Cryptology -- EUROCRYPT '96, Lecture Notes in Computer Science 1070, U. Maurer (Ed.) (Springer,Berlin, 1996) pp. 107-118.
  • S.R. Blackburn and W.G. Chambers, 'Some Remarks on an Algorithm of Fitzpatrick', IEEE Trans. Inform. Theory, Vol. 42, No. 4 (1996), pp. 1269-1271.
  • S.R. Blackburn, T. Etzion and K.G. Paterson, 'Permutation Polynomials, de Bruijn Sequences and Linear Complexity', J. Comb. Theory - Series A, Vol. 76, No. 1 (1996), pp. 55-82.
  • S.R. Blackburn, S. Murphy and K.G. Paterson, 'A Comment on ''A New Public-Key Cipher System based upon the Diophantine equations'' ', IEEE Trans. Comp., Vol. 46, No. 4 (1997), pp. 512.
  • S.R. Blackburn, S. Murphy and K.G. Paterson, 'Comments on ''Theory and Applications of Cellular Automata in Cryptography'' ', IEEE Trans. Comp., Vol. 46, No. 5 (1997), pp. 637-638.
  • S.R. Blackburn and F.C. Piper, 'Applications of Combinatorics to Security', in Proceedings of 'The Applications of Combinatorial Mathematics', Oxford, 14-16 December 1994, C. Mitchell (Ed.) (Oxford University Press, Oxford, 1997), pp. 31-47.
  • S.R. Blackburn,'A Note on Sequences with the Shift and Add Property', Designs, Codes and Cryptography, Vol. 9 (1996), pp. 251-256.
  • U. Baum and S.R. Blackburn, 'Clock-controlled Pseudorandom Generators on Finite Groups', in Fast Software Encryption, 2nd International Workshop, Leuven, Belgium, Lecture Notes in Computer Science 1008, B. Preneel (Ed.) (Springer, Berlin, 1995), pp. 6-21.
  • S.R. Blackburn, 'A Generalisation of the Discrete Fourier Transform', in Applications of Finite Fields, Proceedings of a conference held at Royal Holloway, University of London, Surrey, U.K., D. Gollmann (Ed.) (Oxford University Press, Oxford, 1996), pp. 111-116.
  • S.R. Blackburn, 'A Generalisation of the Discrete Fourier Transform: Determining the Minimal Polynomial of a Periodic Sequence' IEEE Trans. Inform. Theory, Vol. 40 (1994), No. 5, pp. 1702-1704.
  • S.R. Blackburn, 'Increasing the Rate of Output of m-Sequences', Information Processing Letters, Vol. 51 (1994), pp. 73-77.
  • S.R. Blackburn, G. Carter, D. Gollmann, S. Murphy, K. Paterson, F. Piper and P. Wild, 'Aspects of Linear Complexity', in Communications and Cryptography, (Blahut, Costello, Maurer, Mittelholzer eds) (Kluwer, Boston, 1994), pp. 35-42.
  • S.R. Blackburn, S. Murphy and J. Stern, 'Weaknesses of a Public-Key Cryptosystem based on Factorizations of Finite Groups' in Advances in Cryptology -- EUROCRYPT '93, Lecture Notes in Computer Science 765, T. Helleseth (Ed.) (Springer, Berlin, 1994), pp. 50-54.
  • S.R. Blackburn, S. Murphy and J. Stern, 'The Cryptanalysis of a Public Key Implementation of Finite Group Mappings' J. Cryptology, Vol. 8 No. 3 (1995), pp. 157-166.
  • S.R. Blackburn, 'Node Bisectors of Cayley Graphs', Mathematical Systems Theory, Vol 29 (1996), pp. 589-598.
  • S.R. Blackburn, 'Enumeration within Isoclinism Classes of Groups of Prime Power Order' J. London Math. Soc.(2) Vol. 50 (1994), pp. 293-304.



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Department of Mathematics, Royal Holloway, University of London, Egham, Surrey TW20 0EX
Tel/Fax: +44 (0)1784 443093/430766