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Contemporary Mathematics

A quantum Public-Key Cryptosystem without Quantum Storage for Public-Key

Xiaoyu Li, Zhipeng Fang

Published Nov 9, 2025• 0 citations
Publisher

Abstract

A quantum public-key cryptosystem without quantum storage for public-keys is provided. In traditional quantum public-key cryptosystems the public key of a user is a set of quantum systems. There is a key mangement center (KMC) which needs to keep the public keys of all users for a long time to satisfy communication requirments between users. But it's very difficult to keep quantum systems for a long time beacuse quantum system will undergo decoherence with time. This is a big obstacle for quantum public-key crytosystems when they are applied in practice. This quantum public-key cryptosystem can solve this problem. A user keeps a state sequence and a binary string in the key management center called the source key which is only a piece of classical information. If one user A wants to have another user B to get a secret message, KMC creates a sequence of quantum systems according to the latter one's source key, which is just the user's (public key, private key) pair. Then the two users can acomplish secure communications with KMC's assistance. On the otherhand users can also perform message authentication on the messages to guarantee that the messages can't be forged or distorted. In this cryptosystem KMC needs no quantum storage for public keys, which greatly reduces the technical difficulities of key management and secret communication. Moreover any two users needn't keep a quantum channel between them. Therefore to realize and apply this quantum public-key cryptosystem is much more easier than traditional quantum public-key cryptosystems.

DOI
10.37256/cm.6620257498

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A quantum public-key cryptosystem without quantum storage for public-keys is provided. In traditional quantum public-key cryptosystems the public key of a user is a set of quantum systems. There is a key mangement center (KMC) which needs to keep the public keys of all users for a long time to satisfy communication requirments between users. But it's very difficult to keep quantum systems for a long time beacuse quantum system will undergo decoherence with time. This is a big obstacle for quantum public-key crytosystems when they are applied in practice. This quantum public-key cryptosystem can solve this problem. A user keeps a state sequence and a binary string in the key management center called the source key which is only a piece of classical information. If one user A wants to have another user B to get a secret message, KMC creates a sequence of quantum systems according to the latter one's source key, which is just the user's (public key, private key) pair. Then the two users can acomplish secure communications with KMC's assistance. On the otherhand users can also perform message authentication on the messages to guarantee that the messages can't be forged or distorted. In this cryptosystem KMC needs no quantum storage for public keys, which greatly reduces the technical difficulities of key management and secret communication. Moreover any two users needn't keep a quantum channel between them. Therefore to realize and apply this quantum public-key cryptosystem is much more easier than traditional quantum public-key cryptosystems.
A quantum public-key cryptosystem without quantum channels between any two users using non-orthogonal states is provided in this paper. Every user keeps a set of quantum particles in non-orthogonal states in a key management center (KMC) as the public key while he or she keeps the states of them as the private key. By the help of KMC users can accomplish secret communication and message authentication. The laws of quantum physics guarantee the unconditional security of this cryptosystem. No entangled states or complex quantum operations are needed. On the other hand there are no quantum channels needed to connecting any two users. So the public-key cryptosystem is easier to carry out and more robust in practice.
In most of the traditional quantum public-key cryptosystems the public key held by the key management center (KMC) is a group of quantum systems. The public key will be destroyed after a secret communication process. So users must reconstruct the public key with KMC after every communication process or keep many copies of public key in the beginning. It’s an obstacle for the quantum cryptosystem to apply in practice. A quantum public-key cryptosystem with reusable (public key privtate key) pair using the bell states is provided in this paper. Every user shares a set of entangled quantum systems in the Bell states with KMC as his or her (public key, private key) pair. Two users can acomplish secret comminications by the help of KMC. Moreover the states of the quantum systems turn back to their original states. The user’s (public key, private key) pair is unchanged so that they are reusable. It’s unnecessary for users to reconstruct the public key with KMC or save many copies of public key in KMC. So this public-key cryptosystem is of much lower management expenses. It’s easier to realized in practice than most of traditional quantum public-key cryptosystems.
In this paper we provide a quantum public-key cryptosystem using non-orthogonal states. A user Alice uses a set of particles which are in non-orthogonal quantum states as the public key kept by a key management center (KMC) while the she keeps the states of the particles secret as the private key. By the help of KMC any other user can send encrypted message to Alice. Any one including KMC except Alice can’t get the message. On the other hand digital signature can also be achieved by this public-key cryptosystem. There are no entangled states and complex operations needed in our cryptosystem. So it’s easier to carry out in practice and more robust against possible attacks.
In most traditional quantum public-key cryptosystems, the public key held by the key management center (KMC) is a group of quantum systems. The public key is destroyed after a secret communication process, and so users must reconstruct the public key with the KMC after every communication process or hold many copies of the public key in the beginning. This requirement is an obstacle to the practical application of such quantum cryptosystems. This paper describes a quantum public-key cryptosystem with reusable keys using entangled states. Each user shares a set of entangled quantum systems with the KMC as that individual user’s (public key, private key) pair. Two users can exchange secret communications with the help of the KMC. Moreover, the states of the quantum systems revert to their original states. The user’s (public key, private key) pair is unchanged so that the keys are reusable. It is unnecessary for users to reconstruct the public key with the KMC or save many copies of the public key in the KMC. As a result, this public-key cryptosystem is much less expensive to manage and easier to realize in practice than most traditional quantum public-key cryptosystems.
A public-key cryptosystem using orthogonal product states is presented. It is based on the non-locality of some orthogonal product states in an untangled two-particle quantum system. Every user creates a group of two-particle quantum systems and shares them with a key management center (KMC) in which the first particle of the two-particle systems are held by the user and the second particle of the two-particle systems are held by KMC. This is the user's (private key, public key) pair. Two users can exchange secret message by this cryptosystem. The laws of quantum physics guarantees that this cryptosystem has unconditional security. There are no entangled states needed in this public-key cryptosystem. Moreover both users and KMC needn't perform complex quantum operations except quantum measurements on a particle or a two-particle system. So the public-key cryptosystem is feasible to implement by today's technology. One orthogonal product quantum system contributes three bits to the key. So the cryptosystem has a high channel capacity.
In this paper we provide a quantum public-key cryptosystem based on super dense coding technology. A user Alice shares a set of Einstein-Podolsky-Rosen (EPR) pairs with a key management center (KMC) in which the particles hold by Alice are the private key and the particle hold by KMC are the public key. By the help of the key management center any other user can send encrypted message to Alice. Any one including KMC except Alice can't recover the message. On the other hand digital signature can also be achieved by this public-key cryptosystem. In the cryptosystem one EPR pair can be used to encrypt two bits of the plain text. So it's efficient. Finally we prove that our cryptosystem is robust against possible attacks.