Elliptic Curve Cryptosystems

1987/01/01 by Neal Koblitz · 4 citations
Computer Science · #Cryptography and Residue Arithmetic #Cryptography and Data Security #Coding theory and cryptography

paper · doi:10.2307/2007884

openalex publication_date 1987/01/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/04

Abstract

We discuss analogs based on elliptic curves over finite fields of public key cryptosystems which use the multiplicative group of a finite field. These elliptic curve cryptosystems may be more secure, because the analog of the discrete logarithm problem on elliptic curves is likely to be harder than the classical discrete logarithm problem, especially over \text GF(2ⁿ). We discuss the question of primitive points on an elliptic curve modulo p, and give a theorem on nonsmoothness of the order of the cyclic subgroup generated by a global point.

Citations

• Use of Elliptic Curves in Cryptography
• Primitive points on elliptic curves
• New directions in cryptography

Cited by

• Evaluation of discrete logarithms in a group of 𝑝-torsion points of an elliptic curve in characteristic 𝑝
• Cryptography in a Quantum World
• A complete classification of quantum public-key encryption protocols
• Elliptic-curve cryptography [wikipedia]