Chosen-Ciphertext Secure Key-Encapsulation Based on Gap Hashed Diffie-Hellman.
Eike Kiltz · 2007
We propose a practical key encapsulation mechanism with a simple and intuitive design concept. Security against chosen-ciphertext attacks can be proved in the standard model under a new assumption, the Gap Hashed Diffie-Hellman (GHDH) assumption. The security reduction is tight and simple. Secure key encapsulation, combined with an appropriately secure symmetric encryption scheme, yields a hybrid public-key encryption scheme which is secure against chosen-ciphertext attacks. The implied encryption scheme is very efficient: compared to the previously most efficient scheme by Kurosawa and Desmedt [Crypto 2004] it has 128 bits shorter ciphertexts, between 25-50% shorter public/secret keys, and it is slightly more efficient in terms of encryption/decryption speed. Furthermore, our scheme enjoys (the option of) public verifiability of the ciphertexts and it inherits all practical advantages of secure hybrid encryption. Our results extend to key encapsulation mechanisms based on the class of Gap Hashed Multi-Diffie-Hellman (GHMDH) assumptions which is a natural generalization of GHDH.