Cryptography is not for secure the sensitive data but now days it is compulsory in many applications like IoT, Cloud Platform, business systems and so on. A new area of advanced information technology called quantum-computing uses the unique characteristics of quantum physics to solve complex problems, which are beyond the powers of even the most robust classical/powerful computers. Security is the major concern in the area of quantum computing environment. Quantum cryptography, in addition, merely practices the ideologies of quantum mechanism to encrypt/decrypt data and transmit it in a way that cannot be hacked by anyone. This chapter explores the area of quantum public key cryptography, which seeks to create cryptographic building blocks that can withstand attacks from a quantum computing-enabled adversary. Chapter begins with fundamental principles of quantum mechanics, cryptography, quantum cryptography, quantum public key cryptography and, core families of quantum-resistant public key schemes.