Master Elliptic Curve Point Addition with Step-by-Step Algebraic Derivation 📈

Learn how to calculate elliptic curve point addition using pure algebra—no geometry required! This presentation provides a complete step-by-step derivation of the point addition formulas from first principles, explaining where λ² - x₁ - x₂ comes from and why we use these specific formulas. Starting with the line through two points, we substitute into the curve equation, apply Vieta's formulas to the resulting cubic, and derive the complete formulas for computing P + Q. Includes a fully worked example with real numbers on the curve y² = x³ - 2x, showing every calculation explicitly and verifying the result. Perfect for understanding the mathematical foundation of elliptic curve cryptography used in Bitcoin, TLS, and other security systems. Whether you're studying cryptography, implementing ECC, or just curious about the mathematics, this presentation demystifies point addition and shows you the elegant algebra that makes it all work.