In this paper, a practical quantum public-key encryption model is proposed by studying the recent quantum public-key encryption. This proposed model makes explicit stipulations on the generation, distribution, authentication, and usage of the secret keys, thus forms a black-box operation. Meanwhile, this proposed model encapsulates the process of encryption and decryption for the users, and forms a blackbox client-side. In our models, each module is independent and can be replaced arbitrarily without affecting the proposed model. Therefore, this model has a good guiding significance for the design and development of the quantum public key encryption schemes.
In this paper, a practical quantum public-key encryption model is proposed by studying the recent quantum public-key encryption. This proposed model makes explicit stipulations on the generation, distribution, authentication, and usage of the secret keys, thus forms a black-box operation. Meanwhile, this proposed model encapsulates the process of encryption and decryption for the users, and forms a blackbox client-side. In our models, each module is independent and can be replaced arbitrarily without affecting the proposed model. Therefore, this model has a good guiding significance for the design and development of the quantum public key encryption schemes.
Abstract Asymmetric encryption has some important applications in the field of communication. In classical computers, most public key encryption schemes are designed based on computational assumption. In other words, they can ensure computational security. When the computing power is large enough, it will pose a threat to these encryption schemes. We propose a quantum public key encryption scheme which based on properties of quantum physics. Our scheme realizes encryption and decryption with few resources and does not rely on any computational assumption. The key in our scheme consists of classical bits and qubits. Where the private key are classical bit and public key are qubits. The public key are generated through private key. We analyze the performance and security of the scheme. Our scheme ensures the information-theoretic secure and can be implemented easily.
Proving whether it is possible to build IND-CCA public-key encryption (PKE) from IND-CPA PKE in a black-box manner is a major open problem in theoretical cryptography. In a significant breakthrough, Gertner, Malkin and Myers showed in 2007 that shielding black-box reductions from IND-CCA to IND-CPA do not exist in the standard model. Shielding means that the decryption algorithm of the IND-CCA scheme does not call the encryption algorithm of the underlying IND-CPA scheme. In other words, it implies that every tentative construction of IND-CCA from IND-CPA must have a re-encryption step when decrypting. This result was only proven with respect to classical algorithms. In this work we show that it stands in a post-quantum setting. That is, we prove that there is no post-quantum shielding black-box construction of IND-CCA PKE from IND-CPA PKE. In the type of reductions we consider, i.e. post-quantum ones, the constructions are still classical in the sense that the schemes must be computable on classical computers, but the adversaries and the reduction algorithm can be quantum. This suggests that considering quantum notions, which are stronger than their classical counterparts, and allowing for quantum reductions does not make building IND-CCA public-key encryption easier.
The invention of public-key cryptography (PKC) by Diffie and Hellman in 1976 is one of two milestones marking the beginning of modern cryptography. The security of a PKC system requires that it should be infeasible to compute the private key from a given public key, which in turn is typically guaranteed by the difficulty in solving some cryptographic-friendly mathematical problems. Among those problems, the integer factorization and discrete logarithm problems play pivotal roles in the development of public-key cryptography. In particular, the assumption that there is no polynomial time (classical) algorithm that solves the above two problems constitutes the basis for the security of almost all currently used public-key cryptosystems, such as RSA and ElGamal. However, Shor [1] found an efficient quantum solving algorithm for the integer factorization and discrete logarithm problems in 1994, which would destroy the security basis for most real deployed PKC systems if large-scale quantum computers become available. The rapid development of quantum technology in recent years suggests that we are getting closer to the quantum crisis of current PKC systems. As a response to the quantum crisis, the research community has made many efforts to post-quantum cryptography (PQC) that are believed to resist quantum computer attacks. Lattice-based cryptography is one of the main directions in this area, and has become the most promising PQC candidate for standardization. The research of lattice-based cryptography dates back to the seminal work of Ajtai [2], which first based the security of cryptographic primitives on the difficulty of solving some lattice problems such as the approximate shortest vector problem and the closest vector problem. After more than two decades of development, lattice-based cryptography has gained substantial progress. In theory, we have witnessed the construction of many powerful cryptographic primitives that were not known before. In practice, the public key size of lattice-based cryptosystems has been significantly reduced from several gigabytes to a few kilobytes. For current applications and standardization, key exchanges, public-key encryptions (PKEs) and signatures are the most desired lattice-based cryptosystems, where the first two are often used to ensure information secrecy, while the last provides information authentication. Note that public-key encryptions are equivalent to two-round key exchanges, also known as the key encapsulation mechanism (KEM). In the following, we focus on lattice-based PKEs/KEMs. The design principle of lattice-based PKEs/KEMs follows two approaches: a trapdoor one-way function and an approximate commutative one-way function. In the first approach, a trapdoor one-way function f and its trapdoor f−1 are generated as the public key and private key. A plaintext m is encrypted as c = f(m), and the ciphertext is decrypted as m = f−1(c). The NTRU scheme and its variants follow such an approach. In the second approach, an approximate commutative function fs and a random input a are generated, the public key is (a, b = fs(a)) and the private key is s. A plaintext m is encrypted as c1 = gr(a), c2 = gr(b) + E(m), where r is a random element, g is an approximate commutative one-way function and E is the encoding of an error-correction code. The ciphertext (c1, c2) is decrypted as m = D(c2 − fs(c1)), where D is the decoding of an error-correction code. The correctness of decryption is guaranteed by the approximate commutative property (gr(b) = gr(fs(a)) ≈ fs(gr(a)) = fs(c1)) and the error-correction code. Learning with errors (LWE) problem-based PKE/KEM schemes and their variants follow such an approach. The standardization of PQC has received substantial support from national funding agencies, such as the European Union projects PQCrypto and SAFEcrypto. The USA National Institute of Standard and Technology (NIST) started the post-quantum standardization project in 2012, organized a worldwide ‘competition’ in 2016 and plans to deliver draft standards before 2024. After two rounds of evaluation, seven schemes were accepted as the round-three candidates on 22 July 2020, of which five are lattice-based schemes. In 2017, the International organization for standardization started a study project of post-quantum cryptography named SD8. Most LWE-based PKE schemes such as Kyber and LAC follow the Lindner-Peikert framework [3] up to the choices of ring structure, noise distribution and parameters. As the size of noise in lattice-based PKEs/EKMs is typically larger than the lower bits of the ciphertext, many schemes often artificially drop a few lower bits to optimize the practical performance without significantly increasing the final decryption noise. Kyber [4] is one of the most promising PKE/KEM candidates in the NIST PQC standardization, whose security is provably based on the difficulty of so-called module LWE (MLWE) problems. The use of MLWE allowed Kyber to obtain additional flexibility and security advantages, while keeping the same efficiency as those based on the ring-LWE problems. The strategy of dropping some lower bits is used to compress both the public-key and ciphertext sizes. For a targeted 128-bit quantum security, the public-key and ciphertext sizes of Kyber is around a single kilobyte. LAC [5] uses several techniques to reduce the modulus as small as possible: it uses a byte-level modulus, embeds powerful error-correcting codes to maximize the noise-modulus rate, provides a different style of modulus to avoid potential attacks for special polynomial ring structures and optimizes the polynomial multiplication algorithm of the bit-level secret and noise. Based on these techniques, LAC reduces the public key to 544–1056 bytes and the ciphertext to 664–1464 bytes. Meanwhile, it achieves similar computational performance compared with NTT technique schemes. By observing the asymmetries in lattice-based cryptosystems, Zhang and Yu et al. [6] proposed asymmetric MLWE and asymmetric MSIS problems, which yield further size-optimized KEMs and signature schemes to those from standard counterparts. Compared to the seven NIST round-three candidates at Category III security, their KEM scheme has parameters (public key + ciphertext size) smaller than Classic McEliece, CRYSTALS-Kyber, NTRU and Saber; their signature scheme has parameters (public key + signature size) smaller than CRYSTALS-Dilithium and Rainbow, but slightly larger than FALCON, where CRYSTALS-Kyber, NTRU, Saber, CRYSTALS-Dilithium and FALCON are lattice-based schemes. One important application of lattice-based PKEs/KEMs is to build authenticated key exchange (AKE), which could provide additional authentication to the established session key. There are several generic ways to construct AKE from lattice-based PKEs/KEMs. In the PKE setting, Xue and Lu et al. [7] proposed a more compact KEM-based framework via a new primitive named ‘2-key KEM’, which shares some item between different ciphertexts. In the only password setting, Zhang and Yu [8] presented a two-round PAKE framework from the splittable-PKEs that can be instantiated from lattices. The only known AKE that does not rely on lattice-based PKEs/KEMs was given in Ref. [9], which has two-round messages and provides implicit authentication. This work was supported by the National Natural Science Foundation of China (6197239 to X.L.; 62022018 and 61932019 to J.Z.) and the National Key Research and Development Program of China (2018YFB0804105 to J.Z.). Conflict of interest statement. None declared.
We construct a quantum public key encryption scheme from oneway functions in the random oracle model. While our construction only has indistinguishability against restricted adversaries, who perform individual attacks and can only make classical queries to the random oracle, it possesses two practical advantages that were not achieved in previous works. First, legitimate participants can discard noisy quantum public keys. Second, the scheme only requires products of single-qubit states, and it does not require quantum computing or quantum memory for legitimate participants. Although the security does not hold against adversaries capable of large-scale quantum computation, we believe that our protocol is well-suited for the near-term stage of the quantum era.
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 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,