Discovery of Elliptic Curve Cryptographic Private Key in O(n)

TL;DR

This paper introduces an algorithm capable of discovering elliptic curve cryptographic private keys in worst-case linear time, challenging assumptions about the security of such cryptosystems.

Contribution

The paper presents a novel algorithm that reduces the complexity of private key discovery in elliptic curve cryptography to O(n).

Findings

Private keys can be recovered in linear time.

The algorithm impacts the perceived security of elliptic curve cryptography.

Potential vulnerabilities in ECC implementations are highlighted.

Abstract

An algorithm is presented that in context of public key use of Elliptic Curve Cryptography allows discovery of the private key in worst case O(n).