RSA and primality testing | Jay Mehta | Sardar Patel University, Vallabh Vidyanagar | CLD 2024

Speaker: Jay Mehta, Assistant Professor, Department of Mathematics, Sardar Patel University, Vallabh Vidyanagar, Anand, Gujarat

Title: RSA and primality testing

Abstract:

The RSA cryptosystem named after its proposors Ron Rivest, Adi Shamir and Leonard Adleman is a public-key cryptosystem is one of the oldest, popular, and widely used secure cryptosystem. The security of RSA is based on the factoring problem, i.e., factorization of an integer into primes. On the other hand, for its implementation, large primes need to be generated. How to determine whether a large integer chosen is prime or not? In this talk we describe the RSA cryptosystem and discuss a couple of primality tests, one due to Fermat and the other due to Miller-Rabin. We shall see that Fermat's result has limitations and so the property of primes given by Miller-Rabin is preferable.
The talk is elementary in nature, suitable for all B.Sc. and M.Sc. students in Mathematics and requires minimal prerequisites like some basic knowledge of number theory (primes and congruences).

Brief Profile:

M.Sc. from: Department of Mathematics, Sardar Patel University in 2008.
Participated in MTTS: Level 2 at ICT Mumbai, 2007.
Exams Qualified: CSIR NET JRF - Dec. 2008, GATE - February 2008 (with AIR 201), NBHM PhD Written Test - January 2009.
PhD from: Harish-Chandra Research Institute (HRI), Prayagraj (Allahabad) 2009-2015 in Number Theory.
Postdoctoral: The Institute of Mathematical Sciences (IMSc), Chennai for 1 year (June 2015 - June 2016).
Present Designation and Affiliation: Assistant Professor, Department of Mathematics, Sardar Patel University, Vallabh Vidyanagar, Anand, Gujarat since 2016.
Area of Interest: Number Theory and Cryptography.
Associated with MTTS activities: since 2018.