arXiv subjects

Goutam Paul

Publications and source records attributed to Goutam Paul.

59 records · Page 4Linked to original sources

arXiv2013

Designing Parity Preserving Reversible Circuits

Making a reversible circuit fault-tolerant is much more difficult than classical circuit and there have been only a few works in the area of parity-preserving reversible logic design. Moreover, all of these designs are ad hoc, based on some pre-defined parity preserving reversible gates as building blocks. In this paper, we for the first time propose a novel and systematic approach towards parity preserving reversible circuits design. We provide some related theoretical results and give two algorithms, one from reversible specification to parity preserving reversible specification and another from irreversible specification to parity preserving reversible specification. We also evaluate the effectiveness of our approach by extensive experimental results.

cs.AR↗

arXiv2010

Image Sterilization to Prevent LSB-based Steganographic Transmission

Sterilization is a very popular word used in biomedical testing (like removal of all microorganisms on surface of an article or in fluid using appropriate chemical products). Motivated by this biological analogy, we, for the first time, introduce the concept of sterilization of an image, i.e., removing any steganographic information embedded in the image. Experimental results show that our technique succeeded in sterilizing around 76% to 91% of stego pixels in an image on average, where data is embedded using LSB-based steganography.

cs.MM↗

arXiv2009

Revisiting Fermat's Factorization for the RSA Modulus

We revisit Fermat's factorization method for a positive integer $n$ that is a product of two primes $p$ and $q$. Such an integer is used as the modulus for both encryption and decryption operations of an RSA cryptosystem. The security of RSA relies on the hardness of factoring this modulus. As a consequence of our analysis, two variants of Fermat's approach emerge. We also present a comparison between the two methods' effective regions. Though our study does not yield a new state-of-the-art algorithm for integer factorization, we believe that it reveals some interesting observations that are open for further analysis.

cs.CR↗

arXiv2009

On Necessary and Sufficient Number of Cops in the Game of Cops and Robber in Multidimensional Grids

We theoretically analyze the Cops and Robber Game for the first time in a multidimensional grid. It is shown that for an $n$-dimensional grid, at least $n$ cops are necessary to ensure capture of the robber. We also present a set of cop strategies for which $n$ cops are provably sufficient to catch the robber. Further, for two-dimensional grid, we provide an efficient cop strategy for which the robber is caught even by a single cop under certain conditions.

cs.DM↗

arXiv2009

Some Conjectures on the Number of Primes in Certain Intervals

In this paper, we make some conjectures on prime numbers that are sharper than those found in the current literature. First we describe our studies on Legendre's Conjecture which is still unsolved. Next, we show that Brocard's Conjecture can be proved assuming our improved version of Legendre's Conjecture. Finally, we sharpen the Bertrand's Postulate for prime numbers. Our results are backed by extensive empirical investigation.

math.NT↗