There Is No Diffie-Hellman but Elliptic Curve Diffie-Hellman
a year ago
- #Cryptography
- #Elliptic Curves
- #Category Theory
- The article explores why elliptic curves are used in Diffie-Hellman key exchange instead of other groups like the Monster Group.
- Diffie-Hellman requires a group where private and public keys can be distinguished, which is not possible with groups alone due to isomorphism.
- The concept of group objects in category theory is introduced to provide the necessary structure for Diffie-Hellman.
- Algebraic groups, specifically elliptic curves, are identified as suitable group objects for cryptographic purposes.
- Finite field Diffie-Hellman is shown to be a special case of elliptic curve Diffie-Hellman, emphasizing the centrality of elliptic curves in cryptography.