We use theta groups to study $2 $-isogenies between Kummer lines, with a particular focus
on the Montgomery model. This allows us to recover known formula, along with more …

This paper introduces 4 way vectorization of Montgomery ladder on any Montgomery form
elliptic curve. Our algorithm takes 2M^ 4+ 1S^ 4 (M^ 4: A vector of four field multiplications …

Recently, some studies have constructed one-coordinate arithmetics on elliptic curves. For
example, formulas of the $ x $-coordinate of Montgomery curves, $ x $-coordinate of …

Digital signatures are a vital part of the digital world. The trust factor in the digital world is
ensured with a digital signature. Over the evolution, the purpose remained constant, but the …

Digital signatures, essential for establishing trust in the digital realm, have evolved in their
application and importance alongside emerging technologies such as the Internet of Things …

Isogeny-based cryptography has been the hotspot in recent years owing to its resistance to
quantum computing attacks. Unfortunately, efficiency is the main bottleneck that limits its …

Isogenies between elliptic curves play a very important role in elliptic curve related
cryptosystems and cryptanalysis. It is widely known that different models of elliptic curves …

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This work considers the problem of fast and secure scalar multiplication using curves of
genus one defined over a field of prime order. Previous work by Gaudry and Lubicz in 2009 …

This work considers the problem of fast and secure scalar multiplication using curves of
genus one defined over a field of prime order. Previous work by Gaudry and Lubicz (Finite …