• Symmetric and public key Cryptography, elliptic curve based schemes, algebraic cryptanalysis of block and stream ciphers.
• Feedback compensation design for high bandwidth analog systems.
• Finite state systems and control of their behaviors.
• High performance computation in cryptology.

• EE720 Introduction to number theory and cryptography
• EE635 Applied linear algebra

• Ph.D. (Electrical Engineering) 1990 IIT Bombay.
• M.E. (Electrical Engineering) 1983 VJTI Bombay.
• B.Tech. (Electrical Power) 1981 KREC Surathkal.

Department of Electrical Engineering
IIT Bombay, Powai
Mumbai 400 076, India
Email : vrs[AT]ee.iitb.ac.in
Phone (Internal(O)) : (0091 22) - 2576 7492
Fax: (0091 22) - 25723707

1. This is an article which generalizes the well known Boole-Shannon expansion over certain orthonormal terms and derives a condition for consistency of Boolean equations over general finite Boolean algebras. An algorithm for decomposition and solution of a system of Boolean equations shall be announced based on this theory. See the article here an unpublished article
2. This article develops a systems theory approach for stabilization and H-infinity based sensitivity reduction of linear time invariant active multiport circuits. In active circuit theory concepts of short circuit and open circuit stability have been known since the past for single port circuits. This article extends these to multiport case and also formulates the problem of stabilization. The resulting theory is a natural extension of the algebraic stabilization theory of feedback control systems for circuits. See this unpublished article here http://www.ee.iitb.ac.in/~vrs/AnalogCircuitDesign.pdf
3. Trapdoor one way function associated with the exponential function. http://eprint.iacr.org/2011/131 I show here that just as computing the exponential Q=[m]P given P on an elliptic curves and m is a polynomial time problem, if Q and m are given computation of P is also a polynomial time problem. This problem is equivalent to solving equations over the elliptic curve group.
4. Boolean equation approach to discrete log problem (DL) and other results appear as part of this presentation I show here using the elimination theory of Boolean equations that over the fields of char 2 the DL, Diffie Hellman Problem (DHP) and Decisional DHP are computationally equivalent as all of them can be transformed in polynomial time to a satisfiability (SAT) problem of Boolean equations. In particular this means that if the SAT problem corresponding the DHP is easy to solve then the DL problem is also easy to solve. A detailed article on this work is under preparation and shall be announced soon (along with analogous results for the DL problem on elliptic curves over fields of char 2).
5. Defining and proving the Jacobian condition on polynomial maps in prime fields. The Jacobian condition is defined for functions over prime fields and it is shown that the condition is true in n=1 case for functions in prime fields F_p for all p. Then it is also shown that the condition is true for n=2 on the binary filed i.e. for maps F_2xF_2–>F_2xF_2. see this unpublished article Unfortunately the computations become unmanageable for n>2 even for F_2. I believe n=2 case is not explicitly reported elsewhere and is certainly known to be an open problem for R,C.