With the rapid development of cloud computing, it raises real questions on privacy protection, which greatly limits the use of cloud computing.However, fully homomorphic encryption (FHE) can make cloud computing consistent with privacy.In this paper, we propose a simpler FHE scheme based on ring LWE problem, with a smaller size of ciphertext and a lower noise-expansion factor for homomorphic multiplication.Then based on our optimized RLWE-based FHE scheme, we propose a fast single-database private information retrieval protocol, combining with batching and number theoretic transform technology.
With the rapid development of cloud computing, it raises real questions on privacy protection, which greatly limits the use of cloud computing.However, fully homomorphic encryption (FHE) can make cloud computing consistent with privacy.In this paper, we propose a simpler FHE scheme based on ring LWE problem, with a smaller size of ciphertext and a lower noise-expansion factor for homomorphic multiplication.Then based on our optimized RLWE-based FHE scheme, we propose a fast single-database private information retrieval protocol, combining with batching and number theoretic transform technology.
Fully Homomorphic Encryption (FHE) is a powerful encryption system in cloud computing that allows homomorphic computations on encrypted data without decrypting them. Multi-key fully homomorphic encryption (MFHE), as an extension to FHE, allows homomorphic computations on ciphertexts encrypted under different keys. However, most MFHE schemes require a Common Random/Reference String (CRS), while the few that do not are based on the Learning With Errors (LWE) problem, which means that they can only deal with single bit plaintext. Consequently, MFHE schemes based on the Ring Learning With Errors (RLWE) problem are more desirable, as they can handle polynomial plaintext. Requiring the CRS seems to weaken the semantic definition of MFHE, where all users generate their own keys independently. In this paper, we study the RLWE-based MFHE in the CRS model and propose the first RLWE-based MFHE without a CRS. To this end, we remove the CRS by designing a relinearization algorithm without a CRS. Like previous MFHE schemes, our RLWE-based MFHE without CRS has a simple 1-round threshold decryption, which implies a 3-round secure MPC protocol in the plain model from the RLWE assumption.
A multi-bit somewhat homomorphic encryption scheme based on Learning With Errors over Rings (RLWE) assumption is provided, which use canonical embedding to transform elements over a ring into vectors, thus the operation of polynomial multiplication can be performed within O(nlog n) scalar operations, and cipher text size is reduced as well. CPA security of this scheme can be reduced into RLWE assumption. Moreover, an efficient private information retrieval protocol that employs this scheme is presented.
The idea of computing on encrypted data without decryption dates back to the notion of privacy homomorphisms introduced by Rivest, Adleman, and Dertouzos (1978). Their proposals built using the elegant structure of Chinese Remainder Theorem (CRT), were later shown to be insecure under simple known-plaintext attacks. Subsequent CRT-based fully homomorphic encryption (FHE) over the integers addresses this algebraic transparency by injecting noise and basing security on approximate common divisor–type assumptions, but the resulting designs are burdened by large public keys and costly ciphertext refresh procedures. In this work, we develop a new CRT-based FHE scheme whose security relies on the Ring-LWE (RLWE) hardness assumption. For this purpose, we introduce the CRT-RLWE problem. We show that the problem is at least as hard as the RLWE, thereby positioning our construction within the established post-quantum security landscape of RLWE-based cryptography. Our scheme retains an explicit CRT embedding, separating a message component modulo a prime-power plaintext modulus and an auxiliary CRT component, while using RLWE-style key and ring arithmetic for compactness and efficiency. Finally, we make it fully homomorphic by using a new bootstrapping procedure, that adopts the recryption paradigm for BGV/BFV schemes utilizing the linear transformation and digit extraction techniques.
Fully Homomorphic Encryption (FHE) provides a good solution to directly operate on the ciphertext, and the decryption result is equivalent to the corresponding operation on the plaintext. As a technique suitable for distributed environments, multi-key Fully Homomorphic Encryption (MKFHE) scheme is the most common variant of the FHE scheme since it allows encrypted data to be computed under different keys. Unfortunately, the existing dynamic MKFHE schemes based on learning with errors (LWE) still suffer from the inefficiency of long public keys, which typically grow cube in size along the lattice dimension. Moreover, there current constructions fail to provide reliable and fast algorithms to simultaneously expand ciphertexts with multiple additional keys. In order to solve the above problems, a new faster dynamic MKFHE scheme with shorter public key in asymmetric key setting from LWE is proposed in this paper, in which the size of the public key is further reduced from O~(n3(K+L)2) to O~(n2(K+L)2). In addition, our scheme cleverly adopts the dual-user cooperation method in distributed system to realize the ciphertext expansion locally, thereby reducing the computing overhead of the cloud server. More interestingly, we design a flexible parallel ciphertext expansion algorithm for the first time based on the basic algorithm. This algorithm realizes the ciphertext expansion when multiple keys are added at the same time, thus significantly improving the computational efficiency of ciphertext expansion in the dynamic MKFHE scheme. Finally, the CPA-secure of our scheme based on standard LWE assumptions is proven.
A fully homomorphic encryption (FHE) scheme allows a client to encrypt and delegate its data to a server that performs computation on the encrypted data that the client can then decrypt. While FHE gives confidentiality to clients' data, it does not protect the server's input and computation. Nevertheless, FHE schemes are still helpful in building delegation protocols that reduce communication complexity, as the ciphertext's size is independent of the size of the computation performed on them. We can further extend FHE by a property called circuit privacy, which guarantees that the result of computing on ciphertexts reveals no information on the computed function and the inputs of the server. Thereby, circuit private FHE gives rise to round optimal and communication efficient secure two-party computation protocols. Unfortunately, despite significant efforts and much work put into the efficiency and practical implementations of FHE schemes, very little has been done to provide useful and practical FHE supporting circuit privacy. In this work, we address this gap and design the first randomized bootstrapping algorithm whose single invocation sanitizes a ciphertext and, consequently, serves as a tool to provide circuit privacy. We give an extensive analysis, propose parameters, and provide a C++ implementation of our scheme. Our bootstrapping can sanitize a ciphertext to achieve circuit privacy at an 80-bit statistical security level in between 1.3 and 0.9 seconds, depending which Gaussian sampling algorithm is used, and whether the parameter set targets a fast Fourier or a number theoretic transform-based implementation. In addition, we can perform non-sanitized bootstrapping in around 0.27 or 0.14 seconds. Crucially, we do not need to increase the parameters to perform computation before or after sanitization takes place. For comparison's sake, we revisit the Ducas-Stehlé washing machine method. In particular, we give a tight analysis, estimate efficiency, review old, and provide new parameters.
Private Information Retrieval (PIR) enables users to retrieve records from a database without revealing their query targets to the server. While lattice-based PIR schemes have gained attention due to their quantum-resistance properties, existing approaches face significant challenges in terms of computational overhead and noise management. Current state-of-the-art solutions like SealPIR, OnionPIR, and SPIRAL suffer from three main limitations: (1) complex ciphertext query expansion requiring iterative homomorphic operations,(2) substantial computational costs due to polynomial operations in ring-LWEbased schemes, and (3) inefficient conversion between heterogeneous ciphertexts that increases both communication overhead and noise growth. In this paper, we propose a novel coefficient extraction-based PIR scheme that addresses these challenges through two key innovations: A direct coefficient extraction technique that eliminates iterative homomorphic operations; a unified algebraic structure across RLWE, LWE, and LWEGSW schemes for seamless ciphertext conversion. Compared to existing approaches, our scheme achieves: significant reduction in computational overhead through optimized homomorphic operations compared to baseline approaches; substantially decreased communication costs via efficient ciphertext structure design- Better controlled noise growth allowing smaller parameter settings; maintained security based on standard RLWE/LWE hardness assumptions. These improvements make our scheme particularly suitable for practical PIR applications requiring both efficiency and strong security guarantees.