The emergence of practical quantum computers will threaten the classical computers, which makes the resistant quantum cryptography become so important and urgent, where lattice-based cryptography attracts widespread attention for its feature of resistant quantum and ease of implementation. The lattice problem LWE enjoys its provable security, related to worst-case and other characteristics, these make LWE become a hot topic in lattice-based cryptography. Lattice-based cryptography currently has commonly occurring decryption errors, such as GGH NTRU. The LWE problem was introduced by Regev in 2005, and he proposed a single-bit encryption scheme based on LWE, subsequently multi-bit encryption scheme based on LWE was constructed by Peikert, etc. The decryption errors still exist. This paper is based on this, we propose a multi-bit encryption scheme without decryption errors based on LWE and SIS problem. Lastly, this paper gave the property of the scheme under the homomorphic operations, and the application in the IBE scheme without identity information leakage. This scheme has the advantages of resistant quantum, provable security, multi-bit, no decryption errors, strong extensibility and easy to implement.
The emergence of practical quantum computers will threaten the classical computers, which makes the resistant quantum cryptography become so important and urgent, where lattice-based cryptography attracts widespread attention for its feature of resistant quantum and ease of implementation. The lattice problem LWE enjoys its provable security, related to worst-case and other characteristics, these make LWE become a hot topic in lattice-based cryptography. Lattice-based cryptography currently has commonly occurring decryption errors, such as GGH NTRU. The LWE problem was introduced by Regev in 2005, and he proposed a single-bit encryption scheme based on LWE, subsequently multi-bit encryption scheme based on LWE was constructed by Peikert, etc. The decryption errors still exist. This paper is based on this, we propose a multi-bit encryption scheme without decryption errors based on LWE and SIS problem. Lastly, this paper gave the property of the scheme under the homomorphic operations, and the application in the IBE scheme without identity information leakage. This scheme has the advantages of resistant quantum, provable security, multi-bit, no decryption errors, strong extensibility and easy to implement.
Due to the threat of future quantum computers, it is necessary to develop cryptographic schemes that are resistant to quantum attacks. Lattice based cryptographic schemes have resistance to quantum attacks and security under worst-case assumptions that are difficult to solve. To solve the problems of large size of public and private keys, low encryption efficiency, and large noise growth in identity based encryption schemes, an adaptive secure identity based all homomorphic encryption scheme based on Learning with Errors (LWE) is constructed. This scheme uses {0,1} matrices to store plaintext, significantly improving encryption efficiency compared to single bit encryption schemes. It uses key conversion technology to achieve homomorphic operations and modulus conversion technology to reduce noise. It also converts IDs into bit sequences to construct an encryption scheme for adaptive security. Compared to selective security that only provides security guarantees for specific types of attacks, adaptive security is suitable for general scenarios, providing higher security guarantees and being able to cope with more challenging attack situations. It has been proven through the LWE problem that the security of our proposed scheme satisfies IND-ID-CPA. Finally, the experimental results indicate that this scheme introduces less noise, and has higher encryption efficiency and performance.
Cryptographically Relevant Quantum Computers (CRQCs) are no longer hypothetical; they present significant challenges to current IT infrastructure by potentially breaking existing encryption schemes within minutes. This paper introduces an innovative and efficient method for achieving quantum-resistant encryption through lattice-based cryptography. We specifically tackle the challenge of encrypting extremely small units of data, such as a single letter or a single-bit message, by constructing a multidimensional lattice. Our proposed technique leverages the Short Vector Problem (SVP) in lattice-based cryptography and incorporates the Learning with Errors (LWE) methodology for data encryption and decryption. We demonstrate the feasibility and robustness of this approach using a real-time messaging application that provides quantum-resistant end-to-end encryption. Our work has the potential for deployment in strategic applications, securing information from the “harvest now, decrypt later” threat, even in the presence of quantum technologies.
Since the introduction of the ring learning with errors (R-LWE) by Lyubashevsky, Peikert and Regev, many efficient and secure applications were founded in cryptography. In this paper, we mainly present an efficient public-key encryption scheme based on the R-LWE assumption. It is very simple to describe and analyze. As well as it can achieve security against certain key-dependent message (KDM) attacks. Namely, this efficient encryption scheme can securely encrypt its own secret key. The security of this scheme follows from the already proven hardness of the R-LWE problem since the R-LWE assumption is reducible to worst-case problems on the ideal lattice. Besides, the scheme enjoys a high level efficiency and low cost since the operations of the scheme are very simple and fast. The cost of both the encryption and decryption is only polylog(n) bit per message symbol.
With the development of quantum theory, traditional encryption algorithms are facing enormous challenges. Once quantum computers are available, existing encryption systems will no longer be secure. The lattice cipher is proven by theory to be a new type of encryption scheme, which can resist quantum algorithm. It has the property of fast computing speed and small space occupation, hence, it has become a hot issue in today??s research. The identity-based encryption scheme can improve the utilization of storage space and facilitate user public key management. Consequently, this paper based on the hard problem of learning with errors (LWE), constructs an identity-based matrix encryption scheme at first, then applies the improved key switching technology to reduce the dimension of homomorphic ciphertext to normal, and uses the mode conversion technique to reduce noise, realizing matrix homo-morphic operation, and getting an identity-based matrix (level) fully homomorphic encryption scheme. The scheme uses matrices as the storage structure, which has greatly improved the processing capability compared to other single-bit schemes. The scheme not only satisfies the addition and Hadamard product of the matrix, but also supports matrix dot multiplication. The experimental results show that compared with other methods, the improved key switching technology in this paper inputs less noise. Through the difficulty of the LWE problem, it is proven that the scheme satisfies IND-sID-CPA (indistinguishability-selective identity-chosen plaintext attack).
The advent of quantum computing poses a significant existential threat to the security foundations of current public-key cryptography, most notably the widely adopted RSA algorithm. Shor's algorithm, specifically, can efficiently break the mathematical problems underlying RSA and elliptic curve cryptography, necessitating a paradigm shift towards quantum-resistant solutions. This paper explores lattice-based cryptography as the leading candidate for this post-quantum era. We delve into the fundamental mathematical principles of lattices, including hard problems like the Shortest Vector Problem (SVP), Closest Vector Problem (CVP), Short Integer Solution (SIS), and Learning With Errors (LWE), which form the bedrock of their security. The paper reviews prominent lattice-based schemes such as NTRU, CRYSTALS-Kyber, CRYSTALS-Dilithium, and Falcon, highlighting their construction, security properties, and performance characteristics. We analyze their resilience against both classical and quantum attacks, discuss their progress in the NIST Post-Quantum Cryptography Standardization process, and evaluate their practical implications and implementation challenges. The discussion emphasizes the provable security, versatility, and efficiency of lattice-based methods, positioning them as the robust and essential successor to RSA for safeguarding digital communications and data in a quantum-enabled future.
Due to their conjectured resistance to quantum cryptanalysis, strong worst-case/average-case security guarantees, ease of implementation and increasing practicality, lattice-based cryptography is one of the hottest and fastest moving areas in mathematical cryptography today. In this paper, we give a fuzzy certificateless identity-based encryption scheme from lattice, whose security is based on the hardness of the Learning With Errors (LWE) problem. In the scheme, the user can choose his own secret key that the KGC cannot obtain, which is an efficient approach to mitigate the key escrow problem in fuzzy identity-based encryption scheme.