Attacks on Elliptic Curve Cryptography Implementations in Sage Math

This paper presents a summary of the various attacks that have been discovered on the implementation of Elliptic Curve Cryptography (ECC) in SageMath, a widely used open-source mathematics software. ECC is a popular method for providing secure communication and is used in a variety of applications, such as secure key exchange, digital signatures, and more. However, the implementation of ECC in real life has been found to have several vulnerabilities that could potentially be exploited by attackers. This paper will look at the various attacks that have been found and how they affect the safety of ECC-based systems.

Keywords

Discrete Log Problem, Elliptic Curve, Cryptography, Pohlig Hellman, Singular Curve, Smart Attack, P-Adic, Hensel Lifting, Weil Pairing, Tate Pairing, Frey-Rück Attack, Supersingular Curves, MOV Attack, ECDLP, Lattice, Nonce, Digital Signatures.

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