Abstract The functional encryption scheme designed using the lattice can realize fine-grained encryption and it can resist quantum attacks. Unfortunately, the sizes of the keys and ciphertexts in cryptographic applications based on learning with errors are large, which makes the algorithm inefficient. Therefore, we construct a functional encryption for inner product predicates scheme by improving the learning with errors scheme of Agrawal et al. [Asiacrypt 2011], and its security relies on the difficulty assumption of ring learning with errors. Our construction can reduce the sizes of the keys and ciphertexts compared with the learning with errors scheme.
Abstract The functional encryption scheme designed using the lattice can realize fine-grained encryption and it can resist quantum attacks. Unfortunately, the sizes of the keys and ciphertexts in cryptographic applications based on learning with errors are large, which makes the algorithm inefficient. Therefore, we construct a functional encryption for inner product predicates scheme by improving the learning with errors scheme of Agrawal et al. [Asiacrypt 2011], and its security relies on the difficulty assumption of ring learning with errors. Our construction can reduce the sizes of the keys and ciphertexts compared with the learning with errors scheme.
Functional encryption is a powerful primitive: given an encryption Enc(x) of a value x and a secret key skf corresponding to a circuit f, it enables efficient computation of f(x) without revealing any additional information about x. Constructing functional encryption schemes with succinct ciphertexts that guarantee security for even a single secret key (for a general function f) is an important open problem with far reaching applications, which this paper addresses. Our main result is a functional encryption scheme for any general function f of depth d, with succinct ciphertexts whose size grows with the depth d rather than the size of the circuit for f. We prove the security of our construction based on the intractability of the learning with error (LWE) problem. More generally, we show how to construct a functional encryption scheme from any public-index predicate encryption scheme and fully homomorphic encryption scheme. Previously, the only known constructions of functional encryption were either for specific inner product predicates, or for a weak form of functional encryption where the ciphertext size grows with the size of the circuit for f. We demonstrate the power of this result, by using it to construct a reusable circuit garbling scheme with
Abstract Functional encryption (FE) is a novel paradigm for encryption scheme which allows tremendous flexibility in accessing encrypted information. In FE, a user can learn specific function of encrypted messages by restricted functional key and reveal nothing else about the messages. Inner product encryption (IPE) is a special type of functional encryption where the decryption algorithm, given a ciphertext related to a vector x and a secret key related to a vector y, computes the inner product x·y. In this paper, we construct an efficient private-key functional encryption (FE) for inner product with simulation-based security, which is much stronger than indistinguishability-based security, under the External Decisional Linear assumption in the standard model. Compared with the existing schemes, our construction is faster in encryption and decryption, and the master secret key, secret keys and ciphertexts are shorter.
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.
Abstract We propose a novel variant of functional encryption which supports ciphertext updates, dubbed ciphertext-updatable functional encryption. Such a feature further broadens the practical applicability of the functional encryption paradigm and allows for fine-grained access control even after a ciphertext is generated. Updating ciphertexts is carried out via so-called update tokens which a dedicated party can use to convert ciphertexts. However, allowing update tokens requires some care for the security definition. Our contribution is threefold: We define our new primitive with a security notion in the indistinguishability setting. Within CUFE, functional decryption keysandciphertexts are labeled with tags such that only if the tags of the decryption key and the ciphertext match, then decryption succeeds. Furthermore, we allow ciphertexts to switch their tags to any other tag via update tokens. Such tokens are generated by the holder of the main secret key and can only be used in the desired direction. We present a generic construction of CUFE for any functionality as well as predicates different from equality testing on tags which relies on the existence of indistinguishability obfuscation (iO). We present a practical construction of CUFE for the inner-product functionality from standard assumptions (i.e., LWE) in the random-oracle model. On the technical level, we build on the recent functional encryption schemes with fine-grained access control and linear operations on encrypted data (Abdalla et al., AC’20) and introduce an additional ciphertext updatability feature. Proving security for such a construction turned out to be non-trivial, particularly when revealing keys for the updated challenge ciphertext is allowed. Overall, such construction enriches the set of known inner-product functional encryption schemes with the additional updatability feature of ciphertexts.
Ring Learning With Errors (Ring-LWE) is one of the basic schemes used to develop cryptographic algorithms that are resistant to quantum attacks, offering better computational efficiency compared to standard Learning With Errors (LWE). Ring-LWE uses the algebraic characteristics of polynomial rings to create a robust and fast encryption system. This study implements and evaluates the Ring-LWE algorithm in the context of public key exchange and encryption. Simulations are performed with various security parameters, including modulus size and error rate, to test the resistance to brute force attacks and lattice-based attacks. The experimental results show that the Ring-LWE algorithm can achieve a balance between security and computational efficiency, with shorter processing time than conventional LWE while maintaining a high level of security even in the face of quantum computers. From this study, it can be concluded that Ring-LWE is an excellent choice for application in post-quantum security systems, especially in encrypted communication and digital authentication applications. The next step can be directed at optimizing resource utilization and testing against various types of attacks.
The recent promising results on the hardness of lattice problems have inspired the construction of several Attribute-based Encryption (ABE) schemes from the quantum resistant perspective. However, these schemes are insufficient enough for supporting real-world applications due to inherent quadratic overhead problem in the use of Learning With Error (LWE). To solve this problem, this paper proposed a Ciphertext-Policy Attribute-Based Encryption (CP-ABE) scheme from a more lightweight ideal lattice classes- Ring-Learning with Errors (Ring-LWE), that further called as CP-ABER-LWEscheme. Compared to existing R-LWE based ABE scheme, the proposed CP-ABER-LWEis capable to handle a monotone access structure and enjoys collusion resistance properties. We exploited Linear Secret Scheme (LSSS) to express a monotone access structure. For resist to collusion attack, we applied the private key randomization technique to blind the user's private key. The proposed scheme CP-ABER-LWEis further proven to be secure under the Decision Ring-LWEd,q,χproblem in the selective set model.