Academic History

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.

Educational Background

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

Research Interests

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.


  1. NBHM Research grant for three years (2010-2013)
  2. NBHM Travel grant for travel to Istanbul (2011)
  3. DST travel grant to attend Groups St Andrews 2013, 3-11 August 2013
  4. PI for a SERB research grant for three years (2014-2017)
  5. NBHM research grant for three years (2015-2018)

  1. SERB Matrices grant for three years (ongoing)

Research Students

  1. Jay Shah M.S. IISER Pune 2012
  2. Rahul Kumar, M.S. IISER Pune 2012
  3. Hardik Gajera, M.S. IISER Pune 2013
  4. Preeti, M.S. IISER Pune 2015
  5. Krishna Hariram, M.S. IISER Pune 2015
  6. Upendra Kapshikar, M.S. IISER Pune 2018 (Best Thesis Award)

  1. Pralhad Shinde, Ph. D. IISER Pune 2018
  2. Prabhat Kushwaha, Ph. D. IISER Pune 2017

Significant Publications

Here is a list of some of my significant publications. The files of all recent publications are uploaded in arXiv .

Algorithms in linear algebraic groups

Advances in applied Clifford algebras, 2020 (with Sushil Bhunia, Pralhad Shinde and Anupam Singh).

arXiv preprint

Initial minors -- a conjecture to solve the elliptic curve discrete logarithm problem

Recent preprint, available on arXiv (with Ansari Abdullah and Vivek M. Mallick).

arXiv preprint

The MOR Cryptosystem in Classical Groups with a Gaussian Elimination Algorithm for Symplectic and Orthogonal Groups

Book Chapter, Modern Cryptography - Theory, Technology, Adaptation and Integration, IntechOpen, 2019 (with Sushil Bhunia, Pralhad Shinde and Anupam Singh)

A Las Vegas algorithm to solve the elliptic curve discrete logarithm problem

In Proceedings of Progress in Cryptology –INDOCRYPT 2018, LNCS, vol 11356, 215-227 (with Vivek Mallick and Ansari Abdullah).

A probabilistic baby-step giant-step algorithm

In Proceedings of the 14th International Joint Conference on e-Business and Telecommunications (ICETE 2017) - Volume 4: SECRYPT, pages 401-406 (with Prabhat Kushwaha)

Bilinear Cryptography Using Groups of Nilpotency Class 2

In: O’Neill M. (eds) Cryptography and Coding. IMACC 2017. Lecture Notes in Computer Science, vol. 10655 (with Pralhad Shinde)

Gaussian elimination in unitary groups with an application to cryptography

Journal of algebra combinatorics discrete structures andapplications 4(3) 247-260, 2017 (with Anupam Singh)

The MOR cryptosystem and finite p-groups

Contemporary Mathematics Vol. 633, 81-95, 2015

Are matrices useful in public-key cryptography

International Mathematical Forum Vol. 8, no. 39, 1939-1953, 2013

The discrete logarithm problem in the group of non-singular circulant matrices

Groups-Complexity-Cryptology 2(2010), 83-89

The Diffie-Hellman key exchange and non-abelian nilpotent groups

Israel Journal of mathematics, 165, 2008, 161-187

Bounded variation implies regulated: a constructive proof

Journal of Symbolic Logic 66, 2001, no. 4, 1695-1700 (with Douglas Bridges)

Get in touch

  • Use snail mail. Well, nobody does that anymore.
  • Email me at or ayanm[!]
  • Call me at my office number +91-20-25908081. Please use the telephone as a last resort.