Publications

  1. S. Blackburn, S. Blake-Wilson, M. Burmester, S. Galbraith, Shared generation of shared RSA keys, University of Waterloo technical report CORR 98-19 (1998)

  2. S. Galbraith, S. Paulus, N. Smart, Arithmetic on superelliptic curves, Mathematics of Computation 71, No. 237 (2002) 393-405.
    Preliminary Version: Hewlett-Packard Labs technical report HPL-98-179 (1998).

  3. S. Galbraith, Elliptic curve public key cryptography, Mathematics Today, 35, No. 3, p. 76-79 (1999)

  4. S. Galbraith, Constructing isogenies between elliptic curves over finite fields, gzipped ps, London Math. Soc., Journal of Computational Mathematics, Vol. 2, p. 118-138 (1999)

  5. S. Galbraith, Rational points on X0+(p), Experimental Math., 8, No. 4, p. 311-318 (1999)

  6. S. Blackburn, S. Galbraith, Cryptanalysis of two cryptosystems based on group actions, ASIACRYPT'99, Springer LNCS 1716, p. 52-61 (1999)

  7. S. Blackburn, S. Galbraith, Certification of secure RSA keys, Electronics Letters, Vol. 36, No. 1, p. 29-30 (2000)
    Full Version: University of Waterloo technical report CORR 99-44 (1999)

  8. S. Galbraith, N. Smart, A cryptographic application of Weil descent, in Codes and Cryptography, Cirencester, Springer LNCS 1746, p. 191-200 (1999)
    Preliminary version: Hewlett-Packard Labs technical report HPL-1999-70 (1999).

  9. S. Blackburn, M. Burmester, S. Blake-Wilson, S. Galbraith, Weaknesses in shared RSA key generation, in Codes and Cryptography, Cirencester, Springer LNCS 1746, p. 300-306 (1999)

  10. S. Galbraith, J. McKee, The probability that the number of points on an elliptic curve over a finite field is prime, gzipped ps, Journal of the London Mathematical Society, 62, no. 3, p. 671-684 (2000)
    Preliminary version: University of Waterloo technical report CORR 99-51 (1999)

  11. S. Galbraith, On the efficiency of elliptic curves arising in French literature, In Journal of Craptology (2000).

  12. S. Galbraith, Limitations of constructive Weil descent, ps, in Alster, Kazimierz (ed.) et al., Public-Key Cryptography and Computational Number Theory September 11-15, 2000, Warsaw, Poland, Walter de Gruyter (2001) 59--70.

  13. S. Galbraith, Weil descent of Jacobians, Discrete Applied Mathematics Vol. 128, Issue 1, (2003) 165--180. electronic journal version
    Conference version: in D. Augot and C. Carlet (eds.), WCC2001, Elsevier, Electron. Notes Discrete Math. 6 (2001).
    Full version (gzipped ps).

  14. S. Galbraith, Supersingular curves in cryptography, in C. Boyd (ed.) ASIACRYPT 2001, Springer LNCS 2248 (2001) 495--513.
    Asiacrypt slides.
    Full version (gzipped ps).

  15. S. Galbraith, W. Mao, K. G. Paterson, RSA-based undeniable signatures for general moduli, ps, in B. Preneel (ed.), Topics in Cryptology - CT-RSA 2002, Springer LNCS 2271, p. 200-217 (2002)
    Preliminary version: HP Labs technical report HPL-2001-304,

  16. S. Galbraith, F. Hess, N. P. Smart, Extending the GHS Weil descent attack, in L. Knudsen (ed.), EUROCRYPT 2002, Springer LNCS 2332 (2002) 29--44.

  17. S. Galbraith, Elliptic curve Paillier schemes, ps, Journal of Cryptology, Vol. 15, No. 2 (2002) 129--138.
    This paper contains the work of both of the preprints `Cryptanalysis of some elliptic curve based cryptosystems of Paillier' and `An elliptic curve Paillier scheme'.

  18. S. Galbraith, J. Malone-Lee, N. P. Smart, Public key signatures in the multi-user setting, Information Processing Letters, Volume 83, Issue 5 (2002) 263--266. abstract.

  19. S. Galbraith, W. Mao, K. G. Paterson, A cautionary note regarding cryptographic protocols based on composite integers, HP labs technical report HPL-2001-284.

  20. S. Galbraith, K. Harrison and D. Soldera, Implementing the Tate pairing, in C. Fieker and D. Kohel (eds.), ANTS-V, Springer LNCS 2369 (2002) 324--337.
    ANTS slides.
    Preliminary version: (Hewlett-Packard laboratories technical report) HPL-2002-23.

  21. S. Galbraith, Rational points on X0+(N) and quadratic Q-curves, gzipped ps, J. de la Theorie des Nombres de Bordeaux, 14 (2002) 205--219.

  22. S. Galbraith and W. Mao, Invisibility and anonymity of undeniable and confirmer signatures, in M. Joye (ed.) Topics in Cryptology CT-RSA 2003, Springer LNCS 2612 (2003) 80--97.
    Full version: ps.
    Early version: Anonymity and denial of undeniable and confirmer signatures, HP Labs technical report HPL-2001-303 (2001).

  23. S. Galbraith, H. Hopkins and I. Shparlinski, Secure Bilinear Diffie-Hellman Bits, in H. Wang, J. Pieprzyk and V. Varadharajan (eds.), ACISP 2004, Springer LNCS 3108 (2004) 370--378.
    Earlier version in eprint archive 2002/155.

  24. S. D. Galbraith and V. Rotger, Easy decision Diffie-Hellman groups, LMS J. Comput. Math. 7 (2004) 201--218.
    Draft version pdf.
    Slides from a survey of this work presented in August 2004 at Chuo University, Tokyo.

  25. S. D. Galbraith, Pairings, Chapter IX of book Advances in elliptic curve cryptography edited by I. Blake, G. Seroussi and N. Smart, Cambridge University Press, 2005.

  26. S. D. Galbraith, J. McKee and P. Valença, Ordinary abelian varieties having small embedding degree, eprint 2004/365.
    in R. Cramer and T. Okamoto (eds.), Proceedings of a workshop on Mathematical Problems and Techniques in Cryptology, CRM Barcelona (2005) 29--45.

    Full version: S. D. Galbraith, J. F. McKee and P. C. Valença, Ordinary abelian varieties having small embedding degree, Finite Fields and Their Applications, 13 (2007) 800--814.

    For full tables of families of elliptic curves with cofactors up to 1024 see Paula Valença's web page.

  27. S. D. Galbraith and J. Pujolas, Distortion maps for genus two curves, in R. Cramer and T. Okamoto (eds.), Proceedings of a workshop on Mathematical Problems and Techniques in Cryptology, CRM Barcelona (2005) 46--58.

  28. S. D. Galbraith, C. Heneghan and J. McKee, Tunable balancing of RSA, in C. Boyd and J. M. Gonzalez Nieto (eds.), ACISP 2005, Springer LNCS 3574 (2005) 280--292.
    Electronic edition

    Updated version: Full version of the paper.
    Also see: D. Bleichenbacher and A. May, New attacks on RSA with small secret CRT-exponents, PKC 2006, Springer LNCS 3958.

  29. S. D. Galbraith and A. Menezes, Algebraic curves and cryptography, Finite fields and applications, Volume 11, Issue 3 (2005) 544--577.
    Earlier version: CACR Technical report 2005/2 pdf.

  30. S. D. Galbraith and J. F. McKee, Pairings on elliptic curves over finite commutative rings, in N. P. Smart (ed.), Cryptography and Coding: 10th IMA International Conference, Cirencester, UK, Springer LNCS 3796 (2005) 392--409. electronic version

  31. S. R. Blackburn, C. Cid and S. D. Galbraith, Cryptanalysis of a Cryptosystem based on Drinfeld modules, IEE Proceedings Information Security, Vol. 153, No. 1 (2006) 12--14.
    Earlier version: eprint 2003/223.

  32. A. W. Dent and S. D. Galbraith, Hidden Pairings and Trapdoor DDH Groups, in F. Hess, S. Pauli and M. Pohst (eds.), ANTS-VII, Springer LNCS 4076 (2006) 436--451.

  33. P. S. L. M. Barreto, S. D. Galbraith, C. O'hEigeartaigh and M. Scott, Efficient Pairing Computation on Supersingular Abelian Varieties, Designs, Codes and Cryptography, Vol. 42, No. 3 (2007) 239--271. Online.
    Earlier version on eprint 2004/375.

  34. S. D. Galbraith, F. Hess and F. Vercauteren, Hyperelliptic pairings, pdf, in T. Takagi et al (eds), Pairing 2007, Springer LNCS 4575 (2007) 108--131.

  35. S. D. Galbraith, C. O hEigeartaigh, C. Sheedy, Simplified pairing computation and security implications, eprint 2006/169, J. Mathematical Crypt, Vol. 1, No. 3 (2007) 267--281.

  36. W. D. Benits Jr. and S. D. Galbraith, Constructing pairing-friendly elliptic curves using Groebner basis reduction, in S. D. Galbraith (ed.), Cryptography and Coding, Springer LNCS 4887 (2007) 336--345.

  37. S. D. Galbraith, Proceedings of the 11th IMA International Conference on Cryptography and Coding, Springer LNCS 4887 (2007)

  38. S. D. Galbraith and E. R. Verheul, An analysis of the vector decomposition problem, in R. Cramer (ed), PKC 2008, Springer LNCS 4939 (2008) 308-327.
    Full version (pdf)

  39. S. D. Galbraith, M. Harrison and D. Mireles, Efficient Hyperelliptic Arithmetic using Balanced Representation for Divisors, in A. J. van der Poorten and A. Stein (eds.), ANTS 2008, Springer LNCS 5011 (2008) 342--356. electronic version

  40. W. D. Benits Jr. and S. D. Galbraith, The GPS identification scheme using Frobenius expansions, in S. Lucks, A.-R. Sadeghi and C. Wolf (eds.), Research in Cryptology, Proceedings of the Second Western European Workshop, WEWoRC 2007, Bochum, Germany, Springer LNCS 4945 (2008) 13-27.

  41. S. D. Galbraith and K. G. Paterson (eds), Pairing 2008, Springer LNCS 5209 (2008).

  42. S. D. Galbraith and M. Scott, Exponentiation in pairing-friendly groups using homomorphisms, in S. D. Galbraith and K. G. Paterson (eds), Pairing 2008, Springer LNCS 5209 (2008) 211--224.
    Early version: eprint 2008/117

  43. S. D. Galbraith, X. Lin and D. J. Mireles, Pairings on hyperelliptic curves with a real model, in S. D. Galbraith and K. G. Paterson (eds), Pairing 2008, Springer LNCS 5209 (2008) 265--281.
    Early version: eprint 2008/250

  44. S. D. Galbraith, K. G. Paterson and N. P. Smart, Pairings for cryptographers, Discrete Applied Mathematics, Volume 156, Issue 16 (2008) 3113-3121
    Online version: doi:10.1016/j.dam.2007.12.010 Early version: eprint 2006/165.

  45. S. D. Galbraith, F. Hess and F. Vercauteren, Aspects of pairing inversion, IEEE Trans. Information Theory, Volume 54, Issue 12 (2008) 5719-5728.
    eprint 2007/256.

  46. S. D. Galbraith and X. Lin, Computing Pairings Using x-Coordinates Only, Designs, Codes and Cryptography, Vol. 50, No. 3 (2009) 305-324.
    eprint 2008/019.

  47. S. D. Galbraith, X. Lin and M. Scott, Endomorphisms for faster elliptic curve cryptography on general curves, in A. Joux (ed.), EUROCRYPT 2009, Springer LNCS 5479 (2009) 518-535.
    eprint 2008/194.

  48. S. D. Galbraith, J. Pujolas, C. Ritzenthaler and B. A. Smith, Distortion maps for genus two curves, arxiv math.NT/0611471. Journal of Mathematical Cryptology, Volume 3, Issue 1 (2009) 1-18.

  49. S. D. Galbraith and R. S. Ruprai, An Improvement to the Gaudry-Schost Algorithm for Multidimensional Discrete Logarithm Problems, in M. Parker (ed.), Twelfth IMA International Conference on Cryptography and Coding, Cirencester, Springer LNCS 5921 (2009) 368-382. pdf

Preprints

  1. S. D. Galbraith, The Weil pairing on elliptic curves over C, preprint (2005).

  2. S. D. Galbraith, Disguising tori and elliptic curves, eprint 2006/248.

  3. S. D. Galbraith and B. A. Smith, Discrete Logarithms in Generalized Jacobians, arxiv math.NT/0610073.

  4. W. Castryck, S. D. Galbraith and R. Rezaeian Farashahi, Efficient arithmetic on elliptic curves using a mixed Edwards-Montgomery representation, eprint 2008/218.

  5. P.N.J. Eagle and S.D. Galbraith, Point Compression for Koblitz Elliptic Curves, eprint 2009/086.

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Last Modified: 6-3-2009