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.