A public key cryptosystem based on quantum stabilizer codes

Abstract

We introduce a public key cryptosystem for the transmission of classical data using quantum information. In the protocol, a public key and a private key are chosen corresponding to stabilizer groups, i.e. commutative subgroups of the n-qubit Pauli group not containing the negative identity operator. A quantum state called the "tableau" is prepared by the receiver as a stabilizer state for the private key. The tableau is sent to the sender, who encodes the message by passing the state through a quantum circuit. The encoded state is returned to the receiver who decodes the message by performing a quantum measurement. We study the security properties of this protocol, proving that it is secure against brute force attacks. We also analyze a potential letter frequency attack, showing that such an attack is successful if the receiver reuses the private key too much, and can be thwarted by simply varying the choice of private key.