Algebraic Geometry: Elliptic Curves and Cryptography

Quantum computation platforms are likely to revolutionize many areas of information system designs. But unfortunately, cryptography appears to be vulnerable. Bruce Schneier famously stated that we need to protect our systems with mathematics. Algebraic geometry is a field with a lot of promise for future cybersecurity systems.  

#EllipticCurves (#ECC) are algebraic equations that can be used to construct efficient cryptosystems with fewer bits. The underlying mathematical issue is the difficulty of solving discrete log problems (ECDLP) for points on the curve, thus making the function a good candidate for a cryptographic system. In addition, elliptic curves can also be a foundation for the isogeny-based system that is believed to be quantum resistant—for example, the supersingular Diffie-Hellman algorithm. 

#algebraicgeometry #diffiehellman

https://ieeexplore.ieee.org/abstract/document/9667324