Dr. rer. nat. in Computer Science,
Technische Universität Darmstadt, 07/99 Subexponential Class Group Computation in Quadratic Orders,
Technische Universität Darmstadt, Darmstadt, Germany, 1999.
Published by Shaker Verlag GmbH.
(abstract)
M.Sc. in Computer Science, University of Manitoba, 10/95 Computational Techniques in Quadratic Fields,
University of Manitoba, Winnipeg, Manitoba, 1995.
(PDF)
Books
M.J. Jacobson, Jr. and H.C. Williams, Solving the Pell equation, CMS Books in Mathematics, Springer-Verlag, 2009.
(Flyer)
(Errata list)
Journal Publications
A. Mosunov and M. J. Jacobson, Jr.,
Unconditional class group tabulation of imaginary quadratic
fields to |Δ| < 2^{40},
Math. Comp.,
to appear.
P. Rozenhart, M. J. Jacobson, Jr., and R. Scheidler,
Computing quadratic function fields with high 3-rank via cubic field
tabulation,
Rocky Mountain Journal of Mathematics,
to appear.
M. J. Jacobson, Jr., Y. Lee, R. Scheidler, and H. C. Williams,
Construction of all cubic function fields of a given square-free
discriminant,
International Journal of Number Theory11 (2015), no. 6, 1839-1885.
M. J. Jacobson, Jr., M. Rezai Rad, and R. Scheidler,
Comparison of scalar multiplication on real hyperelliptic
curves,
Advances in Mathematics of Communications8 (2014), no. 4, 389-406.
M. J. Jacobson, Jr. and R. Scheidler,
Infrastructure: Structure inside the class group of a real
quadratic field,
Notices of the AMS61 (2014), no. 1, 36-46.
M. D. Velichka, M. J. Jacobson, Jr., and A. Stein,
Computing discrete logarithms on high-genus hyperelliptic curves
over even characteristic finite fields,
Math. Comp.83 (2014),no. 286, 935-963.
L. Imbert and M. J. Jacobson, Jr.,
Empirical optimization of divisor arithmetic on hyperelliptic curves over F^{2m},
Advances in Mathematics of Communications7 (2013), no. 4, 485-502.
N. Carlsson, C. Williamson, A. Hirt, and M. J. Jacobson, Jr.,
Performance modelling of anonymity protocols,
Performance Evaluation69 (2012), 643-661.
P. Rozenhart, M. J. Jacobson, Jr., and R. Scheidler,
Tabulation of cubic function fields with polynomial binary cubic forms,
Math. Comp.81 (2012), no. 280, 2335-2359.
S. Erickson, M. J. Jacobson, Jr., and A. Stein,
Explicit formulas for real hyperelliptic curves of genus 2 in affine representation,
Advances in Mathematics of Communications5 (2011), no. 4, 623-666.
R. Avanzi, M. J. Jacobson, Jr., and R. Scheidler,
Efficient divisor reduction on hyperelliptic curves,
Advances in Mathematics of Communications4 (2010), no. 2, 261-279.
L. Imbert, M. J. Jacobson, Jr., and A. Schmidt,
Fast ideal cubing in imaginary quadratic number and function fields,
Advances in Mathematics of Communications4 (2010), no. 2, 237-260.
V. S. Dimitrov, K. Järvinen, M. J. Jacobson, Jr., W. F. Chan, and Z. Huang,
Provably sublinear point multiplication on Koblitz curves and
its hardware implementation,
IEEE Transactions on Computers57 (2008), no. 11, 1469-1481.
M. Bauer, M. J. Jacobson, Jr., Y. Lee, and R. Scheidler,
Construction of hyperelliptic function fields of high three-rank,
Math. Comp.77 (2008), no. 261, 503-530.
R. de Haan, M. J. Jacobson, Jr., and H. C. Williams,
A fast, rigorous technique for computing the regulator of a real quadratic field,
Math. Comp.76 (2007), no. 260, 2139-2160.
M. J. Jacobson, Jr., R. Scheidler, and A. Stein,
Cryptographic protocols on real and imaginary hyperelliptic curves,
Advances in Mathematics of Communications1 (2007), no. 2, 197-221.
J. Aycock, R. deGraaf, and M. J. Jacobson, Jr.,
Anti-disassembly using cryptographic hash functions,
Journal in Computer Virology2 (2006), 79-85.
M. J. Jacobson, Jr., R. Scheidler, and H. C. Williams,
An improved real quadratic field based key exchange procedure,
Journal of Cryptology19 (2006), 211-239.
D. Hühnlein, M. J. Jacobson, Jr., and D. Weber,
Towards practical non-interactive public-key cryptosystems using non-maximal imaginary quadratic orders,
Designs, Codes, and Cryptography30 (2003), no. 3, 281-299.
M. J. Jacobson, Jr., A. Pinter, and P. G. Walsh,
A computational approach for solving y^{2} = 1^{k} + 2^{k} + ... + x^{k},
Math. Comp.72 (2003), no. 244, 2099-2110.
M. J. Jacobson, Jr. and H. C. Williams,
New quadratic polynomials with high densities of prime values,
Math. Comp.72 (2003), no. 241, 499-519.
M. J. Jacobson, Jr. and H. C. Williams,
Modular arithmetic on elements of small norm in quadratic fields,
Designs, Codes, and Cryptography27, (2002), no. 1-2, 93-110.
M. J. Jacobson, Jr., A. J. Menezes, and A. Stein,
Solving elliptic curve discrete logarithm problems using Weil descent,
Journal of the Ramanujan Mathematical Society16 (2001), no. 3, 231-260.
M. J. Jacobson, Jr. and H. C. Williams,
The size of the fundamental solutions of consecutive Pell equations,
Experimental Mathematics9 (2000), no. 4, 631-640.
M. J. Jacobson, Jr.,
Computing discrete logarithms in quadratic orders,
Journal of Cryptology13 (2000), 473-492.
M. J. Jacobson, Jr., N. Koblitz, J. H. Silverman, A. Stein, and E. Teske,
Analysis of the xedni calculus attack,
Designs, Codes, and Cryptography20 (2000), 41-64.
M. J. Jacobson, Jr.,
Applying sieving to the computation of quadratic class groups,
Math. Comp.68 (1999), no. 226, 859-867.
J. Buchmann, M. J. Jacobson, Jr., and E. Teske,
On some computational problems in finite abelian groups,
Math. Comp.,
66 (1997), no. 220, 1663-1687.
M. J. Jacobson, Jr., R. F. Lukes, and H. C. Williams,
An investigation of bounds for the regulator of quadratic fields,
Experimental Mathematics,
4 (1995), no. 3, 211-225.
Conference Publications
A. K. Silvester, M. J. Jacobson, Jr., and H. C. Williams,
Shorter compact representations in real quadratic fields,
Buchmann Festschrift (M. Fischlin and S. Katzenbeisser, eds.),
Lecture Notes in Computer Science, vol. 8260, Springer-Verlag, 2013, pp. 50-72.
W. Lorimer and M. J. Jacobson, Jr.,
Double blind comparisons: Matching database records without
database aggregation,
2012 IEEE Conference on Technologies for Homeland Security (HST),
IEEE Conference Publications, 2012, pp. 672-677.
V. Dixon, M. J. Jacobson, Jr., and R. Scheidler,
Improved exponentiation and key agreement in the infrastructure of a real quadratic field,
LATINCRYPT 2012, Lecture Notes in Computer Science, vol. 7533, 2012, pp. 214-233.
H. Labrande and M. J. Jacobson, Jr.,
Sublinear scalar multiplication on hyperelliptic Koblitz curves,
SAC 2011, Lecture Notes in Computer Science, vol. 7118, 2011, pp. 399-411.
J.-F. Biasse, M. J. Jacobson, Jr., and A. K. Silvester,
Security estimates for quadratic field based cryptosystems,
ACISP 2010, Lecture Notes in Computer Science, vol. 6168, 2010, pp. 233-247.
J.-F. Biasse and M. J. Jacobson, Jr.,
Practical improvements to class group and regulator computation of real quadratic fields,
Algorithmic Number Theory - ANTS-IX (Nancy, France), Lecture Notes in
Computer Science, vol. 6197, 2010, pp. 50-65.
A. Hirt, M. J. Jacobson, Jr., and C. Williamson,
Taxis: Scalable strong anonymous communication,
Proceedings of IEEE/ACM International Symposium on Modeling,
Analysis, and Simulation of Computer and Telecommunication Systems
(MASCOTS 2008) (Baltimore, MD, USA), September 2008, pp.~269--278.
M. J. Jacobson, Jr., R. Scheidler, and D. Weimer,
An adaptation of the NICE cryptosystem to real quadratic orders,
AFRICACRYPT 2008, Lecture Notes in Computer Science, vol. 5023, 2008,
pp. 191-208.
R. Vogt, J. Aycock, and M. J. Jacobson, Jr.,
Quorum sensing and self-stopping worms,
WORM '07: Proceedings of the 2007 ACM workshop on Recurring Malcode
(New York, NY, USA), ACM, 2007, pp. 16-22.
M. J. Jacobson, Jr., R. Scheidler, and A. Stein,
Fast arithmetic on hyperelliptic curves via continued fraction expansions,
Advances in Coding Theory and Cryptography (T. Shaska, W.C. Huffman,
D. Joyner, and V. Ustimenko, eds.), Series on Coding Theory and
Cryptology, vol. 3, World Scientific Publishing, 2007, Invited Paper,
pp. 201-244.
S. Erickson, M. J. Jacobson, Jr., N. Shang, S. Shen, and A. Stein,
Explicit formulas for real hyperelliptic curves of genus 2 in affine representation,
WAIFI 2007 (C. Carlet and B. Sunar, eds.), Lecture Notes in
Computer Science, vol. 4547, Springer Verlag, 2007, pp. 202-218.
R. Vogt, J. Aycock, and M. J. Jacobson, Jr.,
Army of botnets,
Proceedings of the 2007 Network and Distributed System Security
Symposium (NDSS 2007) (San Diego, CA), Internet Society, 2007, pp. 111-123.
V. S. Dimitrov, K. Järvinen, M. J. Jacobson, Jr., W. F. Chan, and Z. Huang,
FPGA implementation of point multiplication on Koblitz curves using Kleinian integers,
CHES 2006 (Yokohama, Japan), Lecture Notes in Computer
Science, vol. 4249, Springer-Verlag, 2006, pp. 445-459.
M. J. Jacobson, Jr., S. Ramachandran, and H. C. Williams,
Numerical results on class groups of imaginary quadratic fields,
Algorithmic Number Theory - ANTS-VII (Berlin, Germany), Lecture Notes in
Computer Science, vol. 4076, Springer-Verlag, 2006, pp. 87-101.
J. Aycock, R. deGraaf, and M. J. Jacobson, Jr.,
Anti-disassembly using cryptographic hash functions,
15th Annual EICAR 2006 (Hamburg, Germany), 2006, pp. 38-47.
R. deGraaf, J. Aycock, and M. J. Jacobson, Jr.,
Port knocking with strong authentication,
Proceedings of the 21st Annual Computer Security Applications Conference
(ACSAC 2005) (Tucson, Arizona), IEEE Computer Society, 2005, pp. 409-418.
A. Hirt, M. J. Jacobson, Jr., and C. Williamson,
A practical buses protocol for anonymous internet communication,
Proceedings of the Third Annual Conference on Privacy, Security, and Trust
(PST 2005) (St.\ Andrews, New Brunswick), 2005, pp. 233-236.
M. J. Jacobson, Jr.,
The security of cryptosystems based on class semigroups of imaginary quadratic non-maximal orders,
ACISP 2004 (Sydney, Australia), Lecture Notes in Computer Science,
vol. 3108, Springer-Verlag, 2004, pp. 149-156.
M. J. Jacobson, Jr., H. C. Williams, and K. Wooding,
Imaginary cyclic quartic fields with large minus class numbers,
Algorithmic Number Theory - ANTS-VI (Burlington, Vermont), Lecture Notes
in Computer Science, vol. 3076, Springer-Verlag, 2004, pp. 280-292.
M. J. Jacobson, Jr., A. J. Menezes, and A. Stein,
Hyperelliptic curves and cryptography,
High Primes and Misdemeanors: Lectures in Honour of the 60th Birthday
of Hugh Cowie Williams, Fields Institute Communications, vol. 41,
American Mathematical Society, 2004, pp. 255-282.
M. J. Jacobson, Jr. and A. J. van der Poorten,
Computational aspects of NUCOMP,
Algorithmic Number Theory - ANTS-V (Sydney, Australia), Lecture
Notes in Computer Science, vol. 2369, Springer-Verlag, Berlin, 2002,
pp. 120-133.
M. Giesbrecht, M. J. Jacobson, Jr., and A. Storjohann,
Algorithms for large integer matrix problems,
Applied Algebra, Algebraic Algorithms and Error-Correcting Codes - AAECC-14
(Melbourne, Australia), Lecture Notes in Computer Science, vol. 2227,
Springer, 2001, pp. 297-307.
M. J. Jacobson, Jr., R.~Scheidler, and H. C. Williams,
The efficiency and security of a real quadratic field based key exchange protocol,
Public-Key Cryptography and Computational Number Theory (Warsaw, Poland),
de Gruyter, 2001, pp. 89-112.
D. Hühnlein, M. J. Jacobson, Jr., and D. Weber,
Towards practical non-interactive public-key cryptosystems using non-maximal imaginary quadratic orders (extended abstract),
Selected Areas in Cryptography - SAC2000, Lecture Notes in Computer Science,
vol. 2012, 2001, pp. 275-287.
J. Buchmann, M. J. Jacobson, Jr., S. Neis, P. Theobald, and D. Weber,
Sieving methods for class group computation,
Proceedings of Algorithmic Algebra and Number Theory (Heidelberg),
Springer, 1999, pp. 3-10.
M. J. Jacobson, Jr.,
Experimental results on class groups of real quadratic fields (extended abstract),
Algorithmic Number Theory - ANTS-III (Portland, Oregon), Lecture Notes in
Computer Science, vol. 1423, Springer-Verlag, Berlin, 1998, pp. 463-474.
D. Hühnlein, M. J. Jacobson, Jr., S. Paulus, and T. Takagi,
A cryptosystem based on non-maximal imaginary quadratic orders with fast decryption,
Advances in Cryptology - EUROCRYPT '98, Lecture Notes in Computer Science,
vol. 1403, 1998, pp. 294-307.