Elliptical Curve Cryptography (ECC) is a public-key cryptography system that uses elliptical curves over finite fields to provide the same security capabilities of systems like [[RSA]], but with the benefit of significantly smaller keys. They are widely used now and have been a standard approach for cryptographic systems, but are theoretically breakable using [[Quantum Computers]]. Newer [[Post-Quantum Cryptography]] approaches are meant to address this limitation. See [[ECC Keys and Curves]] for an overview. # Uses * Encryption/decryption ([[ECIES]]) * Signing/verification ([[ECDSA]]) * Key exchange ([[ECDH]]) # Serialization Formats This list is not comprehensive. * [[PEM Key Encoding]] * [[DER Key Encoding]] * [[X9.62 Key Encoding]] # Other Resources * [Elliptic Curve Points | Desmos](https://www.desmos.com/calculator/ialhd71we3) Interactive graph for exploring elliptical curves. * [Elliptic Curve Cryptography (ECC) | Practical Cryptography for Developers](https://cryptobook.nakov.com/asymmetric-key-ciphers/elliptic-curve-cryptography-ecc) * [Elliptic curve point multiplication - Wikipedia](https://en.wikipedia.org/wiki/Elliptic_curve_point_multiplication)