Research Experiences

University of Tehran, Iran

For my Bachelor’s project (Fall 2023), I extensively studied classic and modern primality tests and their underlying number theoretical foundations. Some notable areas I studied are the Fast Fourier Transform (FFT) algorithm for fast operation on numbers, the Tonelli–Shanks algorithm for computing square roots in rings, the Miller-Rabin primality test with the extension that is based on the extended Riemann hypothesis (ERH), Lucas and Grantham’s Frobenius primality tests, Succinct Certificates, and AKS. Furthermore, I studied more about Elliptic Curves and the tests based on them, like ECM, Shanks–Mestre method, Schoof method, Goldwasser–Kilian primality test, and Atkin–Morain primality test (ECPP). My primary reference was the Prime Numbers book, a wonderful book by R. Crandall and C. Pomerance.
Under the guidance of Prof. Ghadermarzi, whose expertise lies in pure number theory, I received invaluable support in comprehending the theoretical nuances crucial to understanding these algorithms.

EPFL, Switzerland

During the summer of 2023, as a participant at the Summer@EPFL, I was a research assistant at the LASEC lab under the supervision of Dr. Foutsa.
I was working on primality testing and factorization methods. I was mainly studying the General Number Field Sieve algorithm, and then we tried to find a factorization method with the help of the doubling formula in the Montgomery Curves.
Since I had pretty trouble finding good resources for my research, I provide my presentation slides and some helpful materials that helped me during my research: