Name
Abstract | ||
|---|---|---|
Three decades ago, Montgomery introduced a new elliptic curve model for use in Lenstrau0027s 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 Montgomeryu0027s x-only arithmetic and Ladder algorithm, x-only Diffie–Hellman, y-coordinate recovery, and 2-dimensional and Euclidean differential addition chains such as Montgomeryu0027s PRAC algorithm. |
Year | DOI | Venue |
|---|---|---|
2017 | 10.1007/s13389-017-0157-6 | Journal of Cryptographic Engineering |
Keywords | Field | DocType |
Montgomery curve, Montgomery ladder, Elliptic curve cryptography, Scalar multiplication | Discrete mathematics,Supersingular elliptic curve,Lenstra elliptic curve factorization,Algebra,Arithmetic,Montgomery curve,Elliptic curve cryptography,Hessian form of an elliptic curve,Curve25519,Schoof's algorithm,Mathematics,Tripling-oriented Doche–Icart–Kohel curve | Journal |
Volume | Issue | ISSN |
abs/1703.01863 | 3 | 2190-8516 |
Citations | PageRank | References |
6 | 0.47 | 22 |
Authors | ||
2 | ||
Name | Order | Citations | PageRank |
|---|---|---|---|
| Craig Costello | 1 | 348 | 18.74 |
| Benjamin Smith | 2 | 30 | 5.54 |