Work

Montgomery curves and their arithmetic

Year: 2017

Type: preprint

Abstract: Three decades ago, Montgomery introduced a new elliptic curve model for use in Lenstra's ECM factorization algorithm. Since then, his curves and the algorithms associated with them have become foundational in the implementation of elliptic curve cryptosystems. This article surveys the theory and cryptographic applications of Montgomery curves over non-binary finite fields, including Montgomery's x-only arithmetic and Ladder algorithm, x-only Diffie--Hellman, y-coordinate recovery, and 2-dimensional and Euclidean differential addition chains such as Montgomery's PRAC algorithm.

Source: arXiv (Cornell University)

DOI: 10.48550/arxiv.1703.01863

Authors: Costello, Craig, Smith, Benjamin

Institutions: Microsoft (United States), Institut national de recherche en sciences et technologies du numérique, Laboratoire d'Informatique de l'École Polytechnique

Language: English

Topic: Cryptography and Residue Arithmetic

Subfield: Information Systems

Field: Computer Science

Domain: Physical Sciences

Open Access status: green

OpenAlex ID: W2950873340

Cites: 1

Cited by:

Related to: 20