Don’t Get Knocked Off the Curve: Fault Injection on Elliptic Curve Cryptosystems

A strategic and technically grounded understanding of how fault injection can undermine the security of elliptic curve cryptosystems, and how to effectively protect against it through thoughtful implementation, validation, and testing.

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Elliptic Curve Cryptography (ECC) is a core component in securing digital systems, widely used in applications ranging from internet communications to embedded devices. It supports key cryptographic protocols such as the Elliptic Curve Digital Signature Algorithm (ECDSA) and Elliptic Curve Diffie-Hellman (ECDH), both of which rely on the presumed difficulty of underlying mathematical problems. However, while ECC is mathematically strong, its real-world implementations often expose critical vulnerabilities when faced with fault injection attacks. These attacks exploit the behavior of hardware or software under abnormal or manipulated operating conditions to recover secrets or bypass security controls.

This white paper presents a comprehensive overview of how fault injection attacks compromise ECC-based systems, focusing specifically on ECDSA and ECDH implementations. It explores how attackers can use faults to exploit weaknesses in the control flow, data handling, or parameter validation of cryptographic computations. These techniques do not break the underlying mathematics of ECC but instead manipulate its execution to extract or infer sensitive values such as private keys or nonces.

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