Warning: The information below has not been updated since 2013. I hope to remedy that soon, but in the meantime you can find links to the articles that I have written by opening my CV. Each article is hot-linked.

For a copy of my curriculum vitae, I offer a short form (8 pages) as well as a long form (19 pages). I also have a document that tracks my citation counts, according to Google Scholar, last updated on August 31st, 2017.

On this page, I am sharing pre-prints and reprints of my publications, patents, and information about the books I have written.

• C. Gressel, N. Courtois, G. Bard, A. Hecht, R. Granot, T. J. Salmon, I. Mintz. System and Methods for Encryption with Authentication Integrity. Filed January 28, 2010. Published August 5, 2010. Awarded October 2, 2012. US Patent No.: 8,280,056.


• C. Gressel, G. Bard, O. Dunkelman, A. Hecht, R. Granot. System and Method to Preclude Message Modification in Data Authentications Systems through Efficient Use of Feedback in Cryptographic Functions. Filed Sept 6, 2007. Published March 13, 2008. Awarded October 2, 2012. US Patent No.: 8,107,622.

• 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 hopefully be submitted to The Mathematics of Computation.


• Gregory Bard, and David Hagman. "Are We Lying to Our Children? Conflating Real and Nominal Rates of Return in Saving for Retirement." To be submitted soon to the journal Teaching Mathematics and its Applications, Oxford University Press.


• Nicolas Courtois, Gregory Bard, and Daniel Hulme. "A new General-Purpose Method to Multiply 3x3 Matrices Using Only 23 Multiplications." Under revision.


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


• Gregory Bard. "The Application of Polynomials over the Field of Two Elements to a problem in Intellectual Property." Under revision. Hopefully to be submitted soon to the International Journal of Digital Crime and Forensics.


• Gregory Bard, and Alexander Basyrov. "Error Bounds on Derivatives During Simulations." To be submitted soon to the journal Applied Numerical Mathematics.


• Martin Albrecht, Gregory Bard, and Clement Pernet. "Effective Dense Gaussian Elimination over the Finite Field with Two Elements." Submitted to the journal ACM Transactions on Mathematical Software.


• Nicolas Courtois, Gregory Bard, and Shaun van Ault. "Statistics of Random Permutations and the Cryptanalysis of Periodic Block Ciphers." The journal Cryptologia. Vol. 36 No. 3. Pp 240-262, 2012.


• Nicolas Courtois, and Gregory Bard. "Random Permutation Statistics and An Improved Slide-Determine Attack on KeeLoq." Lecture Notes in Computer Science, Vol. 6805, Pp 35-54, 2012.


• Michael Black, and Gregory Bard. "SAT Over BOINC: An Application-Independent Volutneer Grid Project." Proceedings of the 12th IEEE/ACM International Conference on Grid Computing (GRID'11), Lyon, France. IEEE Press, Pp 226-227, 2011.


• Gregory Bard. "Numerically Estimating Derivatives During Simulations." Proceedings of the 2011 International Conference on Modelling, Simulation, and Visualization Methods (MSV'11). Las Vegas, Nevada. CSREA Press, Pp 341-347, 2011.


• Gregory Bard, Nicolas Courtois, Jorge Nakahara Jr., Pouyan Sepehrdad, and Bingsheng Zhang. "Algebraic, AIDA/Cube and Side-Channel Analysis of the KATAN family of Block Ciphers." Progress in Cryptology (INDOCRYPT'10). Hyderabad, India. Lecture Notes in Computer Science, Vol. 6498, Pp 176-196, 2010.


• Kenneth Wong, and Gregory Bard. "Improved Algebraic Cryptanalysis of QUAD, Bivium and Trivium via Graph Partitioning on Equation Systems." Proceedings of the Australasian Conference on Information Security and Privacy (ACISP'10). Sydney, Australia. Lecture Notes in Computer Science, Vol. 6168, Pp. 19-36, 2010.


• Gregory Bard. "DEMOCRACY: A Heuristic for Polynomial Systems of Equations over Finite Fields." The journal ACM Communications in Computer Algebra. Vol. 44 No. 1, Pg 25, 2010.
  • Note, the above is only an abstract.
  
  
  • However, the full paper is available here.


• Martin Albrecht, Gregory Bard, and Bill Hart. "Algorithm 898: Efficient Multiplication of Dense Matrices over GF (2)." The journal ACM Transactions on Mathematical Software. Vol. 37, No. 1, 2009.


• Nicolas Courtois, Gregory Bard, and Andrey Bogdanov. "Periodic Ciphers with Small Blocks and Cryptanalysis of KeeLoq." The journal 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, and David Wagner, "Algebraic and Slide Attacks on KeeLoq." Fast Software Encryption (FSE'08). Laussanne, Switzerland. Lecture Notes in Computer Science, Vol. 5086, Pp. 97-115, 2008.


• 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). Cirencester, Wales. Lecture Notes in Computer Science, Vol. 4887, Pp. 152-169, 2008.


• 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). Cirencester, Wales. Lecture Notes in Computer Science, Vol. 4887, Pp. 129-151, 2008.


• 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.


• 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). Pp 99-109, 2006.


• Note: The following is posted only for sentimental reasons, it was my first research paper, and also the only bit of my work from my days at the National Security Agency that I can talk about:
  
  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 was not.

• Joseph Bertino, Honors Bachelor of Science in Mathematics and Economics, from Fordham University. Thesis: "Solving Systems of Polynomial Equations Using Gradient Descent and Other Conjugate Gradient Methods, Enhanced by Darwinian and Evolutionary Methods." Successfuly defended May of 2011.


• Kyle Kloster, Honors Bachelor of Science in Mathematics, from Fordham University. Thesis: " Factoring a semiprime n by estimating phi(n)." Successfully defended on May 7th, 2010.


• Michael Levin, Master of Science with Thesis in Computer Science, from American University. Thesis: "Darwinian Gradient Descent." Successfully defended on April 22, 2010.


• Seena Vali, Bachelor of Science in Mathematics, from Fordham. (While Seena was not in the honors program, and so could not submit a Bachelor's Thesis, he and I engaged in a great deal of research that resulted in several conference presentations.

• Gregory Bard. "DEMOCRACY: A Heuristic for Polynomial systems of Equations over Finite Fields." October 2010. (7 pp.)


• Gregory Bard. "Matrix Inversion, LUP-Factorization, and System Solving, via the Method of Four Russians, in Theta(n3 / log n) Time." June 2009. (15 pp.)


• Kenneth Wong, Gregory Bard, and Robert Lewis. "Partitioning Multivariate Polynomial Equations via Vertex Separators for Algebraic Cryptanalysis and Mathematical Applications." July 2009. (33 pp.)


• 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. January 2008. (20 pp.)


• Gregory Bard, Nicolas Courtois, and Chris Jefferson. "Solution of Sparse Polynomial Systems over GF(2) via SAT-Solvers." January 2007. (14 pp.)


• Gregory Bard. "Accelerating Cryptanalysis with the Method of Four Russians." July 2006. (20 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. "On the Distributive Law." This is only one page, but it is a favorite handout of mine in all elementary classes. Any math teacher in high school or college who is tired of seeing "(log a+b)" replaced with "(log a)+(log b)" should download this. I hereby place the document "On the Distributive Law" in the public domain, and waive all copyrights of this one-page document.

• For details on these, just click on "Books I Have Written" on the left of this page.
• Gregory Bard and Joseph Bertino. Applied Finite and Financial Mathematics for University Freshmen. In progress, scheduled to be finished in a few years.


• Gregory Bard. Sage for Undergraduates. To be published by the American Mathematical Society in September 2014. Here is a link to the electronic version, which the AMS has permitted me to circulate for free---only the printed version costs money.


• Gregory Bard. Algebraic Cryptanalysis. Published by Springer in 2009. The book has its own webpage.


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


• Gregory Bard. "Algorithms for Solving Linear and Polynomial Systems of Equations over Finite Fields with Applications to Cryptanalysis." (Submitted in fulfillment of the requirements of the degree Doctor of Philosophy of Applied Mathematics and Scientific Computation, under the supervision of Prof. Lawrence C. Washington.) 2007. (181 pp.)

Last updated October 23rd, 2013.