Research activities include designing and developing algorithms for Cryptography, Computational Number Theory, Error-free Computation, Graph Theory, Digital Signal Processing, Image Processing, Computer Graphics, Linear Algebra, and Linear Programming problems. The main results obtained are summarized below.

A new public key cryptosystem is designed for secure communication. The encryption and decryption procedures of the proposed system are computationally less intensive as opposed to the existing public key cryptosystems, and hence it can be used in high data bit rate communication systems.

Also, a symmetric key cryptosystem that uses nonlinear operations and can be realized using linear feedback shift registers is proposed.

A modification to ElGamal.s public key cryptosystem is suggested to electronically exchange the keys.

An algorithm which is a modification of Derome and Chang and Hwang methods to generate RSA keys is proposed. This algorithm is an alternative to popularly used Euclid.s algorithm.

Most of the general purpose factoring algorithms that include continued fraction algorithm and quadratic sieve algorithms, factor a given number n by constructing a quadratic congruence x2.y2 mod n. a theory that estimates the number of such congruencies, the number of solutions of each congruence and generalizes the Euler.s totient function is proposed.

A new factorization algorithm that does away with the concept of smooth number and uses sieve techniques to find nontrivial solutions of the sets of congruencies, x2.y2 mod n and x4.y2 mod n, is proposed. Also, it uses a simple trick to amortize the computation of Pollard.s observation by half.

Improved the algorithm of Corno et al for finding the maximum clique in a graph using binary decision diagrams (BDD's).

An algorithm to compute a symmetrizer of a matrix is proposed; which is a generalization of the existing algorithms. Existing algorithms are applicable only to Hessenberg matrices, whereas our algorithm is applicable to any arbitrary matrix. Also, proved in this context is a result that states that there exists no positive definite symmetrizer if the non-symmetric matrix has complex eigenvalues.

A definition that defines a symmetric matrix to be equivalent to a non-symmetric matrix, if both the matrices have the same set of eigenvalues, is proposed. An algorithm to compute an equivalent symmetric matrix is also proposed. Therefore, this algorithm tries to solve the problem of computing eigenvalues of a non-symmetric matrix.

The problem of solving a system of linear equations is considered and an algorithm is proposed. This algorithm is concise and is applicable even if the system is under or over determined.

A new definition for a center of a polytope is suggested and an algorithm is designed to compute it. This definition does not introduce non-linearity unlike the definition found in the literature. Hence, approximation is not required to compute a center. The centering algorithm is applied to compute an initial feasible solution of the linear programming problem, without increasing the dimensionality of the problem.

Angular projection matrix which may be interpreted as a generalization of orthogonal projection matrix is defined. This definition is made use of to derive Karmarkar.s affine algorithm. Also, an entirely different algorithm based on the new definition of a center of a polytope, to solve linear programming problems, is designed.

A new transformation called Householder transform in Cm is obtained. This transformation generalizes the ordinary Householder transformation in that, it is applicable even if the inner product of a pair of vectors is not real. The new transformation is applied to solve the subspace rotation problem that arises in the Direction of Arrival estimation.

Designed two fully polynomial time approximation algorithms for the 0-1 multiple choice knapsack problem. These algorithms produce a (1+.) approximate solution and runs in O(nm/.) time, where n is the number of items and m is the number of multiple choice classes. The best algorithm known to date has the time complexity O(nlogn+nm/.).

An algorithm to convert residue numbers to rational numbers is proposed, wherein the residue numbers are represented as ordered pairs. The algorithm defines an extended set of Farey fractions that we termed generalized set of Farey fractions. Also, obtained is a bound on the elements of the inverse of a matrix and a bound on the elements of the solution vector, wherein the elements of the matrix as well as that of the right hand side vector ar assumed to be rational numbers.

The ordered pair representation of residue numbers is extended to polynomial case choosing the elements of the base vector as irreducible polynomials. An arithmetic on these numbers called floating-point-like modular arithmetic for polynomials is suggested and an application of the arithmetic to matrix processors is also studied. A result that gives a bound on the degree of the elements of the inverse of a matrix, whose elements are rational functions, is obtained.

Residue arithmetic algorithms, basic linear algebra algorithms to compute eigenvalues and to solve system of linear equations, algorithm to compute center of a polytope, algorithms to solve linear programming problem, multi-precision arithmetic, a primality test, algorithms to compute multiplicative inverse of an element in a finite field, public key cryptosystems, our new factorization algorithm and several other algorithms are implemented in Pascal and C languages.

He has also led a group which designed and developed a video codec confirming to H.261 standard for video telephony and video conferencing applications. In this project, he was personally involved in implementing the encoding and decoding algorithms of binary double error correcting BCH codes in C as well as in ADSP assembly language by exploiting the intrinsic properties of shift register sequences, Galois field theory in general and the concerned polynomial arithmetic. Also, involved in the implementation of motion estimation cum compensation algorithms in C and then in ADSP assembly language to meet the real time requirement.

He was also in a 3D-Graphics project, wherein we have designed and developed a computer graphics package. He was in particular, involved in the implementation of Non Uniform Rational B-spline (NURBS) curve and surface tessellation using the Cox deBoor algorithm and in the implementation of lighting and shading algorithms by Gourad and Phong.

A package that generates check digits for identification numbers was developed. Also, it analyses the number of single errors, adjacent transposition errors, twin errors etc that it can detect.

Also was developed a security toolkit that allows documents to be encrypted, secure file transfers and secure chats over the LAN using various private key and public key algorithms. Also, it sniffs the data going through the network. Further, it allows you to securely exchange the keys over a public channel to be used in a symmetric key cryptosystem. More details of this project here.