The following articles have been accepted for publication and are waiting to be published. They are listed in the order of their submission date. 

Trisha Sabadra

Abtract: The widely used Diffie-Hellman (DH) and RSA cryptosystems can be broken in subexponential time, which increases security risks. In contrast, breaking Elliptic Curve Cryptography (ECC) requires exponential running time using Pollard’s Rho, achieving equivalent security to RSA with smaller keys and reduced computing power. However, Shor’s algorithm showed that all current public-key cryptosystems, including ECC, can be broken in polynomial time on quantum computers. This has made it crucial to explore quantum-resistant encryption methods. Super-singular Isogeny Diffie-Hellman (SIDH), based on the difficulty of computing isogenies between supersingular elliptic curves, made it to the fourth round of NIST's standardization effort for post-quantum cryptography. However, in 2022, SIDH was broken by an efficient key recovery attack with a classical computer based on Kani's reducibility criterion.

Vivaan Daga

Abtract: We present an exposition of the Banach-Tarski paradox and several related results. All of of the material presented here is classical. Our aim is to distill the key results and to provide short, clear proofs in an accessible manner.