In the quantum era, the advent of quantum computers poses significant threats to the security of current cryptosystems. Therefore, designing quantum-resistant cryptoschemes becomes important to guarantee information security. This work concentrates on the development of the post-quantum public key encryption (PKE) scheme. Non-commutative cryptography (NCC) has entered the field of post-quantum cryptography. We utilize the TSPEM problem with asymmetric structures (which serve as a potential candiate for resisting quantum attacks) to construct two PKE schemes which are demonstrated to be CPA security under the DTSPEM assumption. By representing the plaintext as a matrix, these schemes can effectively encrypt a significant amount of information in a single operation. Assuming an equal amount of messages for encryption, the proposed schemes acheive superior efficiency compared to existing PKE schemes. Structurally, our systems exhibit a level of synchronization and coexistence due to the distinct public keys $ (P) $ and ciphertexts $ (C_{1}) $. The efficiency analysis is conducted by comparing known schemes from the aspect of specific cryptographic indicators. Generally, the proposed ones offer several advantages including provable security, high efficiency, potential quantum-resistant, and relative ease of implementation; along with synchronization and coexistence. Our investigation has established the feasibility of constructing PKE schemes based on the TSPEM problem, specifically for asymmetric communication scenarios. The preliminary results pave the way for further exploration of the TSPEM problem$ ' $s potential in developing other cryptosystems suitable for quantum computing environments.
In the quantum era, the advent of quantum computers poses significant threats to the security of current cryptosystems. Therefore, designing quantum-resistant cryptoschemes becomes important to guarantee information security. This work concentrates on the development of the post-quantum public key encryption (PKE) scheme. Non-commutative cryptography (NCC) has entered the field of post-quantum cryptography. We utilize the TSPEM problem with asymmetric structures (which serve as a potential candiate for resisting quantum attacks) to construct two PKE schemes which are demonstrated to be CPA security under the DTSPEM assumption. By representing the plaintext as a matrix, these schemes can effectively encrypt a significant amount of information in a single operation. Assuming an equal amount of messages for encryption, the proposed schemes acheive superior efficiency compared to existing PKE schemes. Structurally, our systems exhibit a level of synchronization and coexistence due to the distinct public keys (P) and ciphertexts (C1). The efficiency analysis is conducted by comparing known schemes from the aspect of specific cryptographic indicators. Generally, the proposed ones offer several advantages including provable security, high efficiency, potential quantum-resistant, and relative ease of implementation; along with synchronization and coexistence. Our investigation has established the feasibility of constructing PKE schemes based on the TSPEM problem, specifically for asymmetric communication scenarios. The preliminary results pave the way for further exploration of the TSPEM problem′s potential in developing other cryptosystems suitable for quantum computing environments.
Quantum public-key encryption (PKE), where public-keys and/or ciphertexts can be quantum states, is an important primitive in quantum cryptography. Unlike classical PKE (e.g., RSA or ECC), quantum PKE can leverage quantumsecure cryptographic assumptions or the principles of quantum mechanics for security. It has great potential in providing for secure cryptographic systems under potentially weaker assumptions than is possible classically. In addition, it is of both practical and theoretical interest, opening the door to novel cryptographic systems not possible with classical information alone. While multiple quantum PKE schemes have been proposed, they require a large number of qubits acting coherently, and are not practical on current noisy quantum devices. In this paper, we design a practical quantum PKE scheme, taking into account the constraints of current NISQ devices. Specifically, we design a PKE scheme with quantum-classical public keys and classical ciphertexts, that is noise-resilient and only requires a small number of qubits acting coherently. In addition, our design provides tradeoffs in terms of efficiency and the number of qubits that are required.
The emergence of quantum computer will threaten the security of existing public-key cryptosystems, including the Diffie Hellman key exchange protocol, encryption scheme and etc, and it makes the study of resistant quantum cryptography very urgent. This motivate us to design a new key exchange protocol and encryption scheme in this paper. Firstly, some acknowledged mathematical problems was introduced, such as ergodic matrix problem and tensor decomposition problem, the two problems have been proved to NPC hard. From the computational complexity prospective, NPC problems have been considered that there is no polynomial-time quantum algorithm to solve them. From the algebraic structures prospective, non-commutative cryptography has been considered to resist quantum. The matrix and tensor operator we adopted also satisfied with this non-commutative algebraic structures, so they can be used as candidate problems for resisting quantum from perspective of computational complexity theory and algebraic structures. Secondly, a new problem was constructed based on the introduced problems in this paper, then a key exchange protocol and a public key encryption scheme were proposed based on it. Finally the security analysis, efficiency, recommended parameters, performance evaluation and etc. were also been given. The two schemes has the following characteristics, provable security, security bits can be scalable, to achieve high efficiency, quantum resistance, and etc.
Abstract The rapid progress of quantum computing threatens widely deployed public-key cryptosystems such as RSA and Diffie–Hellman, accelerating the transition toward post-quantum cryptography (PQC). During this migration, hybrid key encapsulation mechanisms (KEMs) that combine classical and post-quantum primitives are strongly recommended by standardization bodies and cybersecurity agencies. However, existing hybrid designs mainly focus on combining post-quantum KEMs with Diffie–Hellman–style constructions, while the systematic integration of standardized classical public-key encryption (PKE) schemes with post-quantum KEMs remains largely unexplored. In this work, we introduce two generic hybrid constructions, and , that combine a classical PKE scheme with a post-quantum KEM satisfying ciphertext second-preimage resistance (C2PRI). We prove that both constructions achieve IND-CCA security in the standard model. The refined construction additionally relies on a new security notion of the classical PKE scheme, termed partial ciphertext second-preimage resistance (PC2PRI), which captures second-preimage resistance when a designated ciphertext component is fixed. This new property enables shared-key derivation from only a designated PKE ciphertext component in . Finally, we provide a systematic analysis of the PC2PRI property for several standardized classical encryption schemes, including ECIES, PSEC, and SM2.
Quantum public-key encryption [Gottesman; Kawachi et al., Eurocrypt'05] generalizes public-key encryption (PKE) by allowing the public keys to be quantum states. Prior work indicated that quantum PKE can be constructed from assumptions that are potentially weaker than those needed to realize its classical counterpart. In this work, we show that quantum PKE can be constructed from any quantum-secure one-way function. In contrast, classical PKE is believed to require more structured assumptions. Our construction is simple, uses only classical ciphertexts, and satisfies the strong notion of CCA security.
The need for secure communication in the advent of fully developed quantum computers is underscored by the ongoing standardization of Post-Quantum Cryptography algorithms (PQC). However, due to the complexity and long processing time of PQC algorithms, it is impractical to use them directly in most applications. Therefore, a practical implementation, especially in applications that may be vulnerable to quantum attacks, is essential. This paper proposes PQC-based and PQC-AES (Advanced Encryption Standard) hybrid Public Key Encryption (PKE) protocols to secure the communication of application data transmitted between two parties. The parties securely exchange their PQC keys using a PQC Key Encapsulation Mechanism (KEM) scheme. In the PQC-based PKE, the exchanged PQC public keys (asymmetric key cryptography) are used to encrypt data for network transmission. To decrypt the encrypted data, each party uses their private PQC secret key, known only to them, enabling secure end-to-end communication. In the PQC-AES hybrid PKE, a two-way shared secret key is used to generate a symmetric key (symmetric key cryptography) for encryption and decryption. The performance of the proposed protocols is evaluated through experiments with PQC algorithms in a client-server file transfer application. The evaluation results highlight the necessity of considering security, latency, and other metrics when implementing PQC algorithms in various applications. It is confirmed that KYBER1024 and BIKE-L1 achieved similar throughput in comparison to using the conventional AES-256 key encryption algorithm without extensive overheads in the wireless network for a smaller load (e.g., 1 KB size), while the PQC-AES hybrid cryptography protocol may be suitable for applications where the data size is larger,
The production of quantum computers with fast processing power and practical use will adversely affect the foundations of secure communication, especially for public-key cryptosystems (PKCs). Potential problems and solution scenarios are created early to design quantum-resistant PKCs. In this paper, the emergence of the concept of post-quantum cryptography (PQC) and early precautionary actions are explained. In addition, cryptosystem families that are known/believed to be secure in the presence of quantum computers are discussed. Based on these classes, the selected encryption/key encapsulation (KEM) and signature schemes of the NIST PQC process are expressed. Finally, some open problems for the post-quantum era are summarized.