Dr. Homi Bhabha Road
Pashan, Pune 411008
My interest in Mathematics is algorithmic in nature. It is my belief, the objects that we create in mathematics should offer more than mere existence. I work to innovate and to make things better. I am interested in finding out what is a Mathematician's job? Take for example, if I ask the same question to a Physicist, he will say, "to understand nature". Is there a such simple answer for a Mathematician?
I started working towards a Ph.D. with Douglas Bridges in New Zealand on Constructive Mathematics. It was a movement, started by Brower and then followed by Erett Bishop. After about two years in New Zealand, I moved to Florida Atlantic University in the U.S. to work with Fred Richman. I then wrote my dissertation with Spyros Magliveras in computational group theory and public key cryptography.
Bachelor of Science (Math Hons), Calcutta University, 1994
Master of Science (Pure Mathematics), Calcutta University, 1996
Ph.D student (University of Waikato and Canterbury, New Zealand), 1998-2000
Ph.D. Florida Atlantic University, 2000-2005
My interst is in computational mathematics. I work in the intersection of computational group theory and public key cryptography. In short, I try to build new public key cryptosystems using groups. The groups we use are mostly non-abelian. I was particulary interested in the MOR cryptosystem for a long time. I couldn't build a commercialy sucessfull cryptosystem, but we discovered a Gaussian elimination algorithm for orthogonal, symplectic and unitary groups.
I have keen interest in the elliptic curve cryptosystem. In particualr, I am interested in attacking the best cryptographic primitive, the elliptic curve discrete logarithm problem. We discovered two recent attacks on ECDLP, one is using auxiliary representation with Prabhat Kushwaha and the other is with Vivek Mallick and Ansari Abdullah. The second attack is really exciting and we are hopeful that something will come out of it. We are persuing this attack.
I am also interested in post-quantum cryptography. In particular, understanding and developing post-quantum cryptosystems based on error correcting codes.
Here is a list of some of my significant publications. The files of all recent publications are uploaded in arXiv .
Advances in applied Clifford algebras, 2020 (with Sushil Bhunia, Pralhad Shinde and Anupam Singh).
Recent preprint, available on arXiv (with Ansari Abdullah and Vivek M. Mallick).
Book Chapter, Modern Cryptography - Theory, Technology, Adaptation and Integration, IntechOpen, 2019 (with Sushil Bhunia,
Pralhad Shinde and Anupam Singh)
In Proceedings of the 14th International Joint Conference on e-Business and Telecommunications (ICETE 2017) - Volume 4: SECRYPT, pages 401-406 (with Prabhat Kushwaha) Reprint
In: O’Neill M. (eds) Cryptography and Coding. IMACC 2017. Lecture Notes in Computer Science, vol. 10655 (with Pralhad Shinde) Reprint
Journal of algebra combinatorics discrete structures andapplications 4(3) 247-260, 2017 (with Anupam Singh) Reprint
Contemporary Mathematics Vol. 633, 81-95, 2015 Reprint
International Mathematical Forum Vol. 8, no. 39, 1939-1953, 2013 Reprint
Groups-Complexity-Cryptology 2(2010), 83-89 Reprint
Israel Journal of mathematics, 165, 2008, 161-187 Reprint
Journal of Symbolic Logic 66, 2001, no. 4, 1695-1700 (with Douglas Bridges)