  We study cryptography based on operator theory, and propose quantum no-key
(QNK) protocols from the perspective of operator theory, then present a
framework of QNK protocols. The framework is expressed in two forms:
trace-preserving quantum operators and natural presentations. Then we defined
the information-theoretical security of QNK protocols and the security of
identification keys. Two kinds of QNK protocols are also proposed. The first
scheme is constructed based on unitary transformation, and the other is
constructed based on two multiplicative commutative sets.
