Gregory V. Bard
Visiting Assistant Professor of Mathematics

Publications

Here I am sharing pre-prints of my publications, as well as my dissertation. My monograph, Algebraic Cryptanalysis which started initially as my dissertation but now has triple the original word-count (both in the form of elementary examples for pedagogical purposes as well as newer material) is available from Amazon.com. Also, my lecture notes for "Group Theory" can be found below. Basically, my publications are divided into three categories:

Firstly, research articles submitted to, or published in, journals as well as to Lecture Notes in Computer Science.

Secondly, research articles in progress, a few of which are mentioned here.

Thirdly, expository articles and technical reports. These are not publishable papers but documents might be very useful for my collaborators, my students, or those outside the subject interested in having some background.

The Published and Submitted Articles

Gregory Bard. "The Application of Polynomials over the Field of Two Elements to a problem in Intellectual Property." Submitted to a journal, awaiting judgment.

Gregory Bard. "Matrix Inversion, LUP-Factorization, and System Solving, via the Method of Four Russians, in Theta(n3 / log n) Time". Being revised after referee's initial comments.

Nicolas Courtois, Gregory Bard, and Shaun van Ault. "Statistics of Random Permutations and the Cryptanalysis of Periodic Block Ciphers." Being revised after referee's initial comments.

Kenneth Wong, Gregory Bard, and Robert Lewis. "Partitioning Multivariate Polynomial Equations via Vertex Separators for Algebraic Cryptanalysis and Mathematical Applications." Submitted to a journal, awaiting judgment.

Martin Albrecht, Gregory Bard, and Bill Hart. "Algorithm 898: Efficient Multiplication of Dense Matrices over GF (2)." ACM Transactions on Mathematical Software.

Vol. 37

Nicolas Courtois, Gregory Bard, and Andrey Bogdanov. "Periodic Ciphers with Small Blocks and Cryptanalysis of KeeLoq." Tatra Mountains Mathematical Publications. (This is the mathematical Journal of the Slovak Academy of Sciences). Vol. 41, Pp. 167..188, 2008.

Nicolas Courtois, Gregory Bard, Grant Wagner, "Algebraic and Slide Attacks on KeeLoq." Fast Software Encryption (FSE '08). Lecture Notes in Computer Science, (Springer-Verlag). Vol. 5086, Pp. 97..115, 2008. ISBN 978-3-540-71038-7.

Nicolas Courtois, and Gregory Bard. "Algebraic Cryptanalysis of the Data Encryption Standard." Proceedings of the IMA International Conference on Cryptography and Coding (IMA-CCC '07). Lecture Notes in Computer Science, (Springer-Verlag). Vol. 4887, Pp. 152..169, 2008. ISBN: 3-540-77271-5.

Gregory Bard. "Modes of Encryption Secure Against Blockwise-Adaptive Chosen-Plaintext Attack." Proceedings of the IMA International Conference on Cryptography and Coding (IMA-CCC '07). Lecture Notes in Computer Science, (Springer-Verlag). Vol. 4887, Pp. 129..151, 2008. ISBN: 3-540-77271-5.

Gregory Bard. "Spelling-Error and Reordering Tolerant Pass-phrases via the Damerau-Levenshtein String-Edit Distance Metric." Proceedings of the Australasian Information Security Workshop, (AISW '06). ACM International Conference Proceeding Series, Vol. 249, Pp. 117..124, 2007. ISBN: 1-920-68285-X.

Gregory Bard. "A Challenging but Feasible Blockwise-Adaptive Chosen-Plaintext Attack on SSL." Proceedings of the IEEE-IACR joint International Conference on Security and Cryptography, (SECRYPT '06). Pages 99...109. 2006. ISBN: 972-8865-63-5.

Gregory Bard. "FLOWHUNT: An Attempt at Specification-Based Intrusion Detection using Neural Networks." Proceedings of the 2nd Annual Computer Network Exploitation Conference, (CNE '02). A conference limited to the US Department of Defense and Intelligence Community, and the Ministries of Defense of certain allied nations, but competitive and peer-reviewed. While the proceedings were classified, this paper, however, was not.

Works in Progress

Gregory Bard. "Improvements on the Atkinson-Santoro Algorithm for Matrix Multiplication in very small Rings." In progress.

Gregory Bard, Michael Levin, and Michael Black. "Darwinian Gradient Descent." In progress.

Gregory Bard, Seena Vali, and Robert Miller. "Algorithms for the Reduction of Sparse Matrices, over Fields of non-Zero Characteristic." In progres.

Gregory Bard. "New Practical Approximate Matrix Multiplication Algorithms found via Solving a System of Cubic Equations." The mathematical parts are done, but I am awaiting the results of a potentially very long series of computations. I am realeasing an early draft here, but still need to rephrase my results in light of Igor Kaporin's work. When finished, this will be submitted to The Mathematics of Computation.

Gregory Bard. "Extending SAT-Solvers to Low-Degree Extension Fields of GF(2)." Under revision.

Gregory Bard, Nicolas Courtois, and Chris Jefferson. "Solution of Sparse Polynomial Systems over GF(2) via SAT-Solvers." Under revision.

Expository and Technical Reports

Gregory Bard, Carmi Gressel, Avi Hecht. "Security Analysis of the ZK Crypt Data Authenticator and Stream Cipher against Algebraic Cryptanalysis, Differential and Correlation Attacks." This is my security analysis of the ZK-Crypt hash function as part of the NIST competition.

Gregory Bard. "Group Theory." Lecture Notes from when I taught Abstract Algebra. These were intended to be a chapter of a book which is currently a stalled project, Mathematics, It's Not Just Calculus! Intended for those who have had a course in proof-writing or elementary notions (e.g. bijectivite, injective, surjective, ...), but otherwise as elementary as possible. April 2008. 79 pp.

Gregory Bard. "Achieving a log(n) Speed Up for Boolean Matrix Operations and Calculating the Complexity of the Dense Linear Algebra step of Algebraic Stream Cipher Attacks and of Integer Factorization Methods."January 2006. 20 pp.

Gregory Bard. "Algorithms for Fast Matrix Operations." Scholarly paper for Master of Science without Thesis in Applied Mathematics and Scientific Computation, December 2005. 13 pp.

Gregory Bard. "Vulnerability of SSL to Chosen-Plaintext Attack." March 2004. 10 pp.

Gregory Bard. "Hurdles in High-Speed Intrusion Detection." Scholarly paper for Master of Science without Thesis in Electrical & Computer Engineering, April 2002. Available on request. 20 pp.

Gregory Bard. "A Glance at Cantor's Theorem and Cardinality." This is just an expository article, discussing what it means to be countably infinite or uncountably infinite, even though I didn't really go into full detail.