CEILIDH is a public key cryptosystem based on the discrete logarithm problem in algebraic torus.
This idea was first introduced by Alice Silverberg and Karl Rubin in 2003; Silverberg named CEILIDH after her cat.
[1][2] The main advantage of the system is the reduced size of the keys for the same security over basic schemes.[which?]
This Scheme is based on the Diffie-Hellman key agreement.
This scheme is based on the ElGamal encryption.
If the computational Diffie-Hellman assumption holds the underlying cyclic group
[3] If the decisional Diffie-Hellman assumption (DDH) holds in
, then CEILIDH achieves semantic security.
[3] Semantic security is not implied by the computational Diffie-Hellman assumption alone.
CEILIDH encryption is unconditionally malleable, and therefore is not secure under chosen ciphertext attack.
, one can easily construct a valid encryption