SafeGCD in secp256k1: Enhancing Bitcoin's Security Against Side-Channel Attacks

The SafeGCD algorithm is one of Bitcoin’s silent guardians — a constant-time mathematical design that protects private keys from side-channel attacks.

In this video, we’ll explore the inner workings of SafeGCD, as implemented in the libsecp256k1 cryptographic library — built for speed, security, and reliability.

You’ll learn:

⚙️ What makes SafeGCD different from the traditional Euclidean algorithm

⏱️ How constant-time execution prevents timing leaks and side-channel vulnerabilities

🧠 The mathematical reasoning behind its design

💻 How secp256k1 integrates SafeGCD to ensure cryptographic safety without sacrificing performance

🔐 Why this optimization is critical for maintaining Bitcoin’s uncompromising security

By the end, you’ll see how a simple idea — computing a GCD securely — becomes a cornerstone of Bitcoin’s cryptographic resilience.