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)