Gregory V. Bard

Associate Professor of Mathematics
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Publications Page

Warning: This information has not been updated in a while. 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 (17 pages).

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.

Published and Submitted Articles
Bachelors' and Master's Theses Supervised
  • 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.

Expository and Technical Reports
My Books, Lecture Notes, and My Dissertation
  • 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.