Smart move

Prerequisites & Requirements

• Elliptic Curve Cryptography (ECC): A solid understanding of the Elliptic Curve Discrete Logarithm Problem (ECDLP) and how scalar multiplication works over prime fields.

What will you learn?

• Smart's Attack (SSSA): Learn how to exploit anomalous elliptic curves over quotient rings (like $\mathbb{Z}/p^n\mathbb{Z}$) by lifting them to the $p$-adic field ($\mathbb{Q}_p$) and using formal groups to efficiently solve the ECDLP.

Tools

• SageMath & Python Shell: Leveraging SageMath's advanced algebraic computing capabilities within a Python script to perform the complex $p$-adic calculations required for the exploit.