We present a quantum public-key cryptography protocol for quantum message transmission. The private key of this protocol includes three classical matrices: a generator matrix of a Goppa code, an invertible matrix and a permutation matrix. The public key is product of these three matrices. The encryption and decryption algorithms are merely quantum computations related with the transformations between bases of the quantum registers. The security of this protocol is based on the hypothesis that there is no effective algorithm of NP-complete problem.
We present a quantum public-key cryptography protocol for quantum message transmission. The private key of this protocol includes three classical matrices: a generator matrix of a Goppa code, an invertible matrix and a permutation matrix. The public key is product of these three matrices. The encryption and decryption algorithms are merely quantum computations related with the transformations between bases of the quantum registers. The security of this protocol is based on the hypothesis that there is no effective algorithm of NP-complete problem.
Public-key cryptosystems for quantum messages are considered from two aspects: public-key encryption and public-key authentication. Firstly, we propose a general construction of quantum public-key encryption scheme, and then construct an information-theoretic secure instance. Then, we propose a quantum public-key authentication scheme, which can protect the integrity of quantum messages. This scheme can both encrypt and authenticate quantum messages. It is information-theoretic secure with regard to encryption, and the success probability of tampering decreases exponentially with the security parameter with regard to authentication. Compared with classical public-key cryptosystems, one private-key in our schemes corresponds to an exponential number of public-keys, and every quantum public-key used by the sender is an unknown quantum state to the sender.
We propose a quantum authentication and digital signature protocol whose security is founded on the Quantum Merlin Arthur~(QMA)-completeness of the consistency of local density matrices. The protocol functions as a true public-key cryptography system, where the public key is a set of local density matrices generated from the private key, a global quantum state. This construction uniquely eliminates the need for trusted third parties, pre-shared secrets, or authenticated classical channels for public key distribution, making a significant departure from symmetric protocols like quantum key distribution. We provide a rigorous security analysis, proving the scheme's unforgeability against adaptive chosen-message attacks by quantum adversaries. The proof proceeds by a formal reduction, demonstrating that a successful forgery would imply an efficient quantum algorithm for the QMA-complete Consistency of Quantum Marginal Problem~(QMP). We further analyze the efficiency of verification using partial quantum state tomography, establishing the protocol's theoretical robustness and outlining a path towards practical implementation
Abstract. This paper presents a new paradigm of cryptography, quantum public-key cryptosystems. In quantum public-key cryptosystems, all parties including senders, receivers and adversaries are modeled as quantum (probabilistic) poly-time Turing (QPT) machines and only classical channels (i.e., no quantum channels) are employed. A quantum trapdoor one-way function, f, plays an essential role in our system, in which a QPT machine can compute f with high probability, any QPT machine can invert f with negligible probability, and a QPT machine with trapdoor data can invert f. This paper proposes a concrete scheme for quantum public-key cryptosystems: a quantum public-key encryption scheme or quantum trapdoor one-way function. The security of our schemes is based on the computational assumption (over QPT machines) that a class of subset-sum problems is intractable against any QPT machine. Our scheme is very efficient and practical if Shor’s discrete logarithm algorithm is efficiently realized on a quantum machine.
Transmitting message in secret is getting more and more important nowadays. In the classical world, the message we sent run the risk of being intercepted by an attacker. As a result, we have to encrypt the message, or send it using a private channel. However, if we transmit messages via such methods, there are still some ways to decipher the information. For example, a powerful computer can be used to decrypt the message or try to steal the message from the private channel. In quantum cryptography, entanglement can be used as a secure channel to transmit information with absolute secrecy. From this perspective, quantum entanglement pairs are equivalent to a quantum private key. However, like the classical key distribution problem, the entanglement has to be shared before it can be used. In this paper, we propose a protocol that can be used to distribute such entanglement pairs securely, so they can be subsequently used to transmit messages with perfect security. The security of this protocol is based on the laws of nature, instead of unproven mathematical hard problems.
We present a classification of quantum public-key encryption protocols. There are six elements in quantum public-key encryption: plaintext, ciphertext, public-key, private-key, encryption algorithm and decryption algorithm. According to the property of each element which is either quantum or classical, the quantum public-key encryption protocols can be divided into 64 kinds. Among 64 kinds of protocols, 8 kinds have already been constructed, 52 kinds can be proved to be impossible to construct and the remaining 4 kinds have not been presented effectively yet. This indicates that the research on quantum public-key encryption protocol should be focus on the existed kinds and the unproposed kinds.
Public key cryptography is extensively used for encryption, signing contracts and secure exchanges over the unreliable network.The findings of Shor in 1994, of a powerful algorithm which was based on quantum mechanics for computing discrete logarithms and factoring large integers sabotaged the security presumptions upon which the currently used public key cryptographic protocols are based, like ElGamal, RSA and ECC.However, few cryptosystems, known as post quantum cryptosystems, while not currently in wide use are considered to be resistant to such attacks.In this paper, a quantum version of ElGamal Cryptosystem is proposed whose security relies on the commutative rotation transformations and measurements in computational basis of qubits.An understanding of the new scheme over the quantum channels is provided.The proposed cryptosystem allows the party to send messages in the form of qubits over a quantum channel.Also the proposed protocol provides an opportunity for two parties to exchange keys which is considered as one of the major concerns while developing post quantum cryptosystems.