Lagrange Interpolation: The 250-Year-Old Math Enabling Modern Cryptography

Lagrange interpolation transforms scattered data points into polynomials with elegant mathematical efficiency—a technique now essential to zero-knowledge proof systems that underpin modern cryptographic security. Unlike brute-force equation solving, this method provides a computational shortcut that reduces overhead dramatically. For developers building or understanding ZK systems, grasping this foundational technique is critical to understanding how sensitive data can be encoded without revelation.