### Concrete Security Treatment of Public-Key Cryptosystem againstAdaptive Chosen Cipher-Text Attack Using PQK Public-Key Cryptosystem

#### Abstract

We propose a new public key cryptosystem which named PQK that based on the decisional Diffie-Hellman problem. The scheme is provably secure against adaptive chosen cipher-text attack under the hardness assumption of the decisional Diffie-Hellman problem. Compared with the RSA public key scheme, our scheme has nice features: (1) our scheme is provably secure against adaptive chosen cipher-text attack under the intractability paradigm, (2) the PQK is secure against other attacks such as common modulus attack and low exponent attack which the RSA is still suffered from these attacks, and (3) it is faster than, in the decryption process, the RSA cryptosystem.

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