We examine the relationship between correctness definitions for Fully Homomorphic Encryption (FHE) and the associated security definitions. We show that reactive notions of correctness imply IND-CPA-D and sIND-CPA-D security. But that to obtain both IND-CPA-D and sIND-CPA-D security we need to use a randomized version of the evaluation procedure. Such randomized evaluation procedures cause problems in real life deployments of FHE solutions, so we then go on to show how one can de-randomize the evaluation procedure and still obtain sIND-CPA-D security in the random oracle model for the specific FHE scheme of TFHE.
We examine the relationship between correctness definitions for Fully Homomorphic Encryption (FHE) and the associated security definitions. We show that reactive notions of correctness imply IND-CPA-D and sIND-CPA-D security. But that to obtain both IND-CPA-D and sIND-CPA-D security we need to use a randomized version of the evaluation procedure. Such randomized evaluation procedures cause problems in real life deployments of FHE solutions, so we then go on to show how one can de-randomize the evaluation procedure and still obtain sIND-CPA-D security in the random oracle model for the specific FHE scheme of TFHE.
This paper proposes a generic construction of CCA-secure fully homomorphic encryption (FHE) scheme.First, we introduce a new primitive called multi-identity fully homomorphic encryption, which works in the multi-identity setting; that is, homomorphic evaluation can performed on ciphertexts created with different identities.Then, we propose an IND-sID-CPA secure multi-identity leveled FHE scheme over lattice.Finally, we present CCA-secure FHE from our proposed multi-identity FHE scheme and strongly EUF-CMA secure signature.The security analysis shows that our FHE scheme is CCA2-secure when the evaluation key is unavailable to the adversary, and remains CCA1-secure when the evaluation key is exposed in the standard model.
Multi-key fully homomorphic encryption (MKFHE), a generalization of fully homomorphic encryption (FHE), enables a computation over encrypted data under multiple keys. The first MKFHE schemes were based on the NTRU primitive, however these early NTRU based FHE schemes were found to be insecure due to the problem of over-stretched parameters. Recently, in the case of standard (non-multi key) FHE a secure version, called FINAL, of NTRU has been found. In this work we extend FINAL to an MKFHE scheme, this allows us to benefit from some of the performance advantages provided by NTRU based primitives. Thus, our scheme provides competitive performance against current state-of-the-art multi-key TFHE, in particular reducing the computational complexity from quadratic to linear in the number of keys.
We consider a setting of two-party computation between a server and a client where every message received by the server is encrypted by a fully homomorphic encryption (FHE) scheme and its decryption key is held by the client only. Akavia and Vald (IACR ePrint Archive, 2021) revisited the privacy problem in such protocols against malicious servers and revealed (as opposed to a naive expectation) that under certain condition, a malicious server can recover the client's input even if the underlying FHE scheme is IND-CPA secure. They also gave some sufficient conditions for the FHE scheme to ensure the privacy against malicious servers. However, their argument did not consider the possibility that a query from a malicious server to a client involves an invalid ciphertext. In this paper, we show, by giving a concrete example, that if such an invalid query is just rejected by the client, then the sufficient conditions in Akavia and Vald's result do not in general ensure the privacy against malicious servers. We also propose another option to handle an invalid query in a way that the client returns a random ciphertext (without explicitly rejecting the query), and show that such a protocol is private against malicious servers if the underlying FHE scheme is IND-CPA secure, sanitizable (in the sense of Ducas and Stehlé, EUROCRYPT 2016), and circular secure.
1 (State Key Laboratory of Mathematical Engineering and Advanced Computing , Zhengzhou 450001) Abstract: Fully homomorphic is an encryption scheme that allows for data to be stored and processed in an encrypted format, which gives the cloud provider a solution to host and process data without even knowing what the message is. In previous identity-based homomorphic encryption scheme, computing efficiency is complicated and expensive. In this work, based on Regev’s work, we propose a sampling trapdoor one-way function in arbitrary cyclotomic rings [ ] ( ) / 1 n R X x = + Z . Then construct a leveled identity-based homomorphic encryption scheme from ring learning with errors, which has advantage in computational efficiency and key management, by using user’s identity as the unique public key. This scheme is proved IND-CPA secure in the random oracle model, relied to hardness of decision ring learning with errors problem.
Abstract. Fully homomorphic encryption (FHE) is a form of public-key encryption that enables arbitrary computation over encrypted data. The past few years have seen several realizations of FHE under differ-ent assumptions, and FHE has been used as a building block in many cryptographic applications. Adaptive security for public-key encryption schemes is an important se-curity notion proposed by Canetti et al. It is intended to ensure security when encryption is used within an interactive protocol and parties may be adaptively corrupted by an adversary during the course of the protocol execution. Due to the extensive applications of FHE to protocol design, it is natural to understand whether adaptively secure FHE is achievable. In this paper we show two contrasting results in this direction. First, we show that adaptive security is impossible for FHE satisfying the (stan-dard) compactness requirement. On the other hand, we show a construc-tion of adaptively secure FHE that is not compact, but that does achieve circuit privacy.
Fully homomorphic encryption (FHE) is a form of public-key encryption that allows the computation of arbitrary functions on encrypted data without decrypting the data. As a result, it is a useful tool with numerous applications. Certificateless encryption (CLE) is a type of public-key encryption that combines the advantages of PKI-based public-key encryption with those of identity-based encryption (IBE). Thus, certificateless fully homomorphic encryption (CLFHE) has aroused considerable research interest. Recently, Chen, Hu, and Lian proposed a leveled certificateless homomorphic encryption (CLHE) scheme and proved its semantic security based on the learning with errors (LWE) problem in the random oracle model. However, their scheme supports only homomorphic addition, but not homomorphic multiplication. In this work, we construct two leveled CLFHE schemes using the approximate eigenvector method presented by Gentry, Sahai, and Waters. Based on the hardness of the LWE problem, we prove that one scheme satisfies adaptive semantic security and anonymity in the random oracle model, whereas the other satisfies selective semantic security and anonymity in the standard model.