Provably Secure Public Key Cryptosystem Based on Chebyshev Polynomials

Abstract

Chebyshev polynomials based public key cryptosystem (CPPKC), proposed by L. Kocarev in 2003, has emerged as a new research field in cryptography and attracted a lot of attentions in recent years. Although provable security in traditional public key cryptosystem has already been developed about twenty years, no relevant security proof research has been found about CPPKC. Aiming at the disability of CPPKC to resist against the adaptive chosen ciphertext attack, we construct a provably secure CPPKC, namely PS-CPPKC, which is designed utilizing the benefits of hash function and its security proof is completed under the Cheybshev Diffie-Hellman problem (CDHP) assumption by probabilistic analyses and computation in random oracle model. This is our primary exploration and it shows that provable security theory can combine well with CPPKC.