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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. The main advantage of the system is the reduced size of the keys for the same security over basic schemes.["which?]

The name CEILIDH comes from the Scots Gaelic word "ceilidh which means a traditional Scottish Gathering.

Contents

Algorithms[edit]

Parameters[edit]

Key agreement scheme[edit]

This Scheme is based on the "Diffie-Hellman key agreement.

is the identity, thus we have : which is the shared secret of Alice and Bob.

Encryption scheme[edit]

This scheme is based on the "ElGamal encryption.

Security[edit]

The CEILIDH scheme is based on the ElGamal scheme and thus has similar security properties.

If the "computational Diffie-Hellman assumption holds the underlying cyclic group , then the encryption function is "one-way.[1]

If the "decisional Diffie-Hellman assumption (DDH) holds in , then CEILIDH achieves "semantic security.[1] Semantic security is not implied by the computational Diffie-Hellman assumption alone.[2] See "decisional Diffie-Hellman assumption for a discussion of groups where the assumption is believed to hold.

CEILIDH encryption is unconditionally "malleable, and therefore is not secure under "chosen ciphertext attack. For example, given an encryption of some (possibly unknown) message , one can easily construct a valid encryption of the message .

See also[edit]

References[edit]

  1. ^ a b CRYPTUTOR, "Elgamal encryption scheme Archived 2009-04-21 at the "Wayback Machine."
  2. ^ M. Abdalla, M. Bellare, P. Rogaway, "DHAES, An encryption scheme based on the Diffie-Hellman Problem" (Appendix A)

External links[edit]

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