Quantum Secret Sharing Evolves: KTYC Protocol Enhances Cryptography Security

Quantum Secret Sharing (QSS) is a branch of cryptography that uses quantum mechanics principles to ensure higher security than traditional Secret Sharing (SS). Proposed by Hillery et al., QSS can share secrets and check for eavesdropping simultaneously, unlike SS. Since its inception, various QSS protocols have been developed, including the KTYC protocol in 2023, which uses a novel structure and single qubits. Despite a security loophole in the KTYC protocol, improvements have been made, resulting in a qubit efficiency higher than the original QSS protocol. These advancements make QSS more secure and practical for real-world applications.

What is Quantum Secret Sharing?

Quantum Secret Sharing (QSS) is a branch of cryptography that has been gaining significant attention in recent years. Cryptography, the art of writing and solving coded messages, has always played a crucial role in human society. Over time, many branches of cryptography have been developed, one of which is Secret Sharing (SS), proposed independently by Shamir and Blakley in 1979. In SS, a dealer’s secret is split into several pieces, each held by an agent. No subset of agents can recover the secret, but the entire set can.

Twenty years later, Hillery et al. proposed the first QSS protocol, generalizing SS into the quantum scenario. The major difference between SS and QSS lies in what their respective securities rely on. SS’s security relies on the high complexity of underlying mathematical problems, such as the factorization of large numbers. In contrast, QSS’s security relies on fundamental theories in quantum mechanics, such as the Heisenberg uncertainty principle and the quantum no-cloning theorem.

Another difference is the number of actions carried out. SS can only carry out the action of sharing secrets, but not that of checking eavesdropping, while QSS can carry out both actions simultaneously. This makes QSS demonstrate higher security, ensuring the unconditional security of the protocol, which SS can’t.

How has Quantum Secret Sharing Evolved?

Since the proposal of the first QSS protocol, the field has received widespread attention, and numerous other protocols have been proposed. For instance, in 2003, Bagherinezhad and Karimipour utilized reusable GHZ states as secure carriers to propose a QSS protocol. In 2006, Deng et al. proposed a circular QSS protocol, where the quantum information carrier can circularly run.

In 2009, Gu et al. proposed a high-capacity three-party QSS protocol with quantum superdense coding, where almost all Einstein-Podolsky-Rosen pairs can be used for carrying useful information. In 2012, Tsai et al. proposed a multiparty QSS protocol based on two special entangled states. In 2017, Song et al. proposed a tn threshold d-level QSS protocol, where the d-level secret can be reconstructed only if at least t shares are collected.

Two kinds of special QSS have received much attention recently. One is dynamic quantum secret sharing (DQSS), where agents can be added or deleted, and the secret or sub-secrets can be updated. The other is semi-quantum secret sharing (SQSS), where only the dealer is quantum, and all agents are classical.

What is the KTYC Protocol?

In 2023, Kuo et al. proposed a multiparty QSS protocol based on a novel structure and single qubits, known as the KTYC protocol. This protocol ensures the independence of each agent and grants them equal privileges. However, a security loophole exists in the n-party n>4 secret sharing case in the KTYC protocol. Two dishonest agents can collude to obtain part of Alice’s secret messages without the help of the other agents.

How Does the KTYC Protocol Work?

The KTYC protocol works as follows: Each agent prepares a sequence composed of S*N qubits, where S represents the length of the secret and N the number of agents. Each qubit is randomly in one of the four states.

What are the Improvements to the KTYC Protocol?

Despite the security loophole in the KTYC protocol, improvements have been proposed to overcome this issue. By calculating the qubit efficiency of the three-party case, it is equal to 1/8, which is higher than that in Hillery et al.’s protocol. This improved protocol and security analysis can help to further advance the field of Quantum Secret Sharing, making it more secure and practical for real-world applications.