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:**

- S.R. Blackburn, 'Non-overlapping codes'. See http://arxiv.org/abs/1303.1026.

**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*, to appear. - 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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