Message Authentication Scheme Based on Quantum Error-correction Codes

Pla Information

This paper presents a quantum public-key cryptosystem by using quantum Calderbank-Shor-Steane(CSS) error correcting codes and the NPC problem related with decoding general linear codes. It uses classical key to encrypt quantum message, and its security relies on the fact that NPC problem can not be solved on quantum Turing machines. Based on this public-key cryptosystem, this paper also gives a message authentication scheme and proves its security.

Jothi Rangasamy, Dillibabu Shanmugam

Sofia Zebboudj, Abdellah Akilal

Yfke Dulek, Garazi Muguruza, Florian Speelman

When sending quantum information over a channel, we want to ensure that the message remains intact. Quantum error correction and quantum authentication both aim to protect (quantum) information, but approach this task from two very different directions: error-correcting codes protect against probabilistic channel noise and are meant to be very robust against small errors, while authentication codes prevent adversarial attacks and are designed to be very sensitive against any error, including small ones. In practice, when sending an authenticated state over a noisy channel, one would have to wrap it in an error-correcting code to counterbalance the sensitivity of the underlying authentication scheme. We study the question of whether this can be done more efficiently by combining the two functionalities in a single code. To illustrate the potential of such a combination, we design the threshold code, a modification of the trap authentication code which preserves that code's authentication properties, but which is naturally robust against depolarizing channel noise. We show that the threshold code needs polylogarithmically fewer qubits to achieve the same level of security and robustness, compared to the naive composition of the trap code with any concatenated CSS code. We believe our analysis opens the door to combining more general error-correction and authentication codes, which could improve the practicality of the resulting scheme.

Tao Shang, Jianwei Liu

Julio R. Gea-Banacloche

A method is proposed to hide messages in arbitrary quantum data files. The messages may act as “watermarks,” to secure the authenticity and/or integrity of the data. With the help of classical secret keys, they can be made unreadable by other parties and to reveal whether thay have been tampered with. The basic idea is to encode the data using a quantum error-correcting code and hide the message as (correctible) errors, deliberately inserted, which can be read out from the error syndrome. Also discussed briefly is a “reverse encoding,” which would involve putting the actual data in the error syndrome, and letting the encoded qubit itself carry the message.