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.
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.
Abstract—Sahai and Waters introduced a fuzzy id-based encryption (FIBE) scheme in which an identity was viewed as a set of descriptive attributes, and any user with a private key for an identity ID was allowed to decrypt a ciphertext encrypted with an identity ID ′ , if and only if the identity ID and ID ′ were close to each other as measured by the “set overlap ” distance metric. After that, Shweta Agrawal, Xavier Boyen, Vinod Vaikuntanathan, Panagiotis Voulgaris and Hoeteck Weeto constructed a fuzzy id-based encryption scheme from the hardness of the Learning With Errors ( LWE) problem. The two schemes both had more longer public and private keys, and it was not very efficient. This paper gives more efficient fuzzy id-based encryption scheme from lattice, in which the public keys are greatly reduced, and there are two vectors corresponding to each bit of the identity by using of the algorithm Sampleleft introduced by Shweta Agrawal, Dan Boneh and Xavier Boyen, and only a trapdoor basis is the secret key. Furthermore, the scheme is dealing with N bit − information and is also secure from the hardness of the Learning With Errors ( LWE) problem, and all these greatly raise efficiency.
—In order to provide access control on encrypted data, Attribute-based encryption (ABE) defines each user using a set of attributes. Fuzzy identity-based encryption (FIBE) is a variant of ABE that allows for a threshold access structure for users. To address the potential threat posed by future quantum computers, this paper presents a postquantum fuzzy IBE scheme based on lattices. However, current lattice-based ABE schemes face challenges related to computational complexity and the length of ciphertext and keys. This paper aims to improve the performance of an existing fuzzy IBE scheme by reducing key length and computational complexity during the encryption phase. While negative attributes are not utilized in our scheme, we prove its security under the learning with error (LWE) hard problem assumption in the selective security model. These improvements have significant implications for the field of ABE.
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.
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.
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.
Certificateless signcryption can simultaneously provide certificateless signature and encryption. In recent years, many certificateless signcryption schemes have been proposed. However, these schemes are based on traditional mathematical theory and not have the ability of resisting the quantum computing attacks. Up to now, lattice-based certificateless signature or encryption schemes have been proposed; however, these schemes only have one function and cannot fulfill two functions of certificateless signature and encryption at the same time. In consideration of this reason, in this article, a certificateless signcryption scheme from lattice (L-CLSS) is constructed. L-CLSS has three advantages. First, in the random oracle model, it is provably indistinguishable against adaptive ciphertext-chosen attacks under the intractability of the learning with errors (LWE) problem and unforgeable against adaptive message-chosen attacks under the hardness of small integer solution (SIS) problem. Second, comparison with the cryptographic algorithms under the difficulty of large integer decomposition, L-CLSS can resist the quantum computing attacks. Third, L-CLSS has higher computation efficiency and a lower communication cost than the existing schemes.