Email: rmoloney@gmail.com
I recently completed my PhD in Mathematics, carried out at University College Dublin, under the Claude Shannon Institute for Discrete Mathematics, Coding, Cryptography and Information Security.
My PhD supervisor was Gary McGuire.
My research has been in areas of pure mathematics which relate to cryptography. Most recently I have been working on divisibility properties of Kloosterman sums. I have also worked on Edwards curves, which have applications to elliptic curve cryptography.
Divisibility Properties of Kloosterman Sums and Division Polynomials for Edwards Curves. (pdf)
Binary Kloosterman Sums Modulo 256 And Coefficients Of The Characteristic Polynomial, with F. Göloğlu, P. Lisonek, and G. McGuire, Accepted, to appear in IEEE Transactions on Information Theory.
Binary Kloosterman sums using Stickelberger's theorem and the Gross-Koblitz formula, with Faruk Göloğlu and Gary McGuire. (Journal version) (arXiv version)
In Acta Arithmetica, Vol 148, Number 3, pp 269 - 279.
Two Kinds of Division Polynomials For Twisted Edwards Curves, with Gary McGuire. (arXiv version)
Accepted, to appear in Applicable Algebra in Engineering, Communication and Computing.
Ternary Kloosterman sums modulo 18 using Stickelberger's theorem, with Faruk Göloğlu and Gary McGuire. (SpringerLink) (arXiv version)
In Sequences and Their Applications: SETA 2010, 6th International Conference, Proceedings.
A hardware analysis of twisted Edwards curves for an elliptic
curve cryptosystem, with Brian Baldwin, Andrew Byrne, Gary McGuire and William P. Marnane. (SpringerLink) (Cryptology ePrint Archive version)
In Reconfigurable Computing: Architectures, Tools and Applications, 5th International Workshop, Proceedings.
Featured in book European Success Stories in Industrial Mathematics (Springer, 2011): Optimising the Speed of Encryption. Work summarised in the preprint Efficient implementation of elliptic curve point operations using binary Edwards curves, with Aidan O'Mahony and Pierre Laurent. (Cryptology ePrint Archive)
Some Congruences of Kloosterman Sums and their Minimal Polynomials, with Faruk Göloğlu and Gary McGuire. (arXiv)
Elliptic curves in Montgomery form with B=1 and their low order torsion, with Gary McGuire and Michael Markowitz. (Cryptology ePrint Archive)
Security in the Cloud, at Intel Tech Forum, and UCD CASL Security and Trust Seminar. (pdf)
Ternary Kloosterman sums modulo 18 using Stickelberger's theorem, at SETA 2010, describing joint work with Faruk Göloğlu and Gary McGuire. (pdf)
Division polynomials for twisted Edwards curves, at Fq9, describing joint work with Gary McGuire. (pdf)