Efficient Fully Homomorphic Encryption with Circularly Secure Key Switching Process

Fully homomorphic encryption (FHE) has important applications in cloud computing. However, almost all fully homomorphic encryption schemes share two common flaws that they all use large-scale secret keys and some operations inefficient. In this paper, the “special b” variant of the Learning With Errors problem (bLWE) is presented, and helps us construct the first circularly secure key switching process which can replace the key switching process and similar re-linearization process used by the existing FHE schemes. Then, we present an efficient FHE. Compared with Brakerski’s scheme, our scheme reduces L secret keys to one and is more efficient. Finally, we prove the chosen-plaintext attack (CPA) security of the fully homomorphic scheme and the circular security of key switching process in standard model under the learning with errors problem (LWE) assumption

Extend FHEW to General Case

When talking about FHE, refresh process is a little different from bootstrapping process. Bootstrapping always means that a scheme homomorphic decrypting its process, while refresh imply that use another scheme, always in large scale, to perform its decryption process. In EUROCRYPT’2015, Ducas and Micciancio proposed a FHE which can perform refresh process in less than a second, called DM14, while the scheme only support bite plaintext space, which is cumbersome for many applications. Extending DM14 to a large plaintext space becomes an open problem. In order to solve it, we improved the msbExtract process to endure a large base, by mapping the element to position. As a result, we constructed an efficient FHE with large plaintext space and quickly refresh process. We implemented our scheme in computer, and made a comparison between our performance and DM14. The result is that the running time is almost same, when extend the plaintext space from 2 to 8

Faster Bootstrapping with Multiple Addends

As an important cryptographic primitive in cloud computing and outsourced computation, fully homomorphic encryption (FHE) is an animated area of modern cryptography. However, the efficiency of FHE has been a bottleneck that impeding its application. According to Gentry’s blueprint, bootstrapping, which is used to decrease ciphertext errors, is the most important process in FHE. However, bootstrapping is also the most expensive process that affecting the efficiency of the whole system. Firstly, we notice that, hundreds of serial homomorphic additions take most of the time of bootstrapping. We made use of the properties of Boolean circuit to reduce the number of serial homomorphic additions by two-thirds, and thus constructed an efficient FHE scheme with bootstrapping in 10ms. Secondly, the most expensive parts in our bootstrapping, EHCM and addition operations of multiple matrices, can be accelerated by parallel. This parallel may accelerate the bootstrapping. At last, we found a set of more efficient combination of parameters. As a result, our security parameter level is 128 bits and the correctness is elevated, compared with TFHE scheme in ASIACRYPT 2016. Experiments show that the running time of our bootstrapping is 10ms, which is only 52 percent of TFHE, and is less than CGGI17

Efficient Multi-key FHE with short extended ciphertexts and less public parameters

Multi-Key Full Homomorphic Encryption (MKFHE) can perform arbitrary operations on encrypted data under different public keys (users), and the final ciphertext can be jointly decrypted by all involved users. Therefore, MKFHE has natural advantages and application value in security multi-party computation (MPC). The MKFHE scheme based on Brakerski-Gentry-Vaikuntanathan (BGV) inherits the advantages of BGV FHE scheme in aspects of encrypting a ring element, the ciphertext/plaintext ratio, and supporting the Chinese Remainder Theorem (CRT)-based ciphertexts packing technique. However some weaknesses also exist such as large ciphertexts and keys, and complicated process of generating evaluation keys. In this paper, we present an efficient BGV-type MKFHE scheme. Firstly, we construct a nested ciphertext extension for BGV and separable ciphertext extension for Gentry-Sahai-Waters (GSW), which can reduce the size of the extended ciphertexts about a half. Secondly, we apply the hybrid homomorphic multiplication between RBGV ciphertext and RGSW ciphertext to the generation process of evaluation keys, which can significantly reduce the amount of input/output ciphertexts and improve the efficiency. Finally, we construct a directed decryption protocol which allows the evaluated ciphertext to be decrypted by any target user, thereby enhancing the ability of data owner to control their own plaintext, and abolish the limitation in current MKFHE schemes that the evaluated ciphertext can only be decrypted by users involved in homomorphic evaluation

Two round multiparty computation via Multi-key fully homomorphic encryption with faster homomorphic evaluations

Multi-key fully homomorphic encryption (MKFHE) allows computations on ciphertexts encrypted by different users (public keys), and the results can be jointly decrypted using the secret keys of all the users involved. The NTRU-based scheme is an important alternative to post-quantum cryptography, but the NTRU-based MKFHE has the following drawbacks, which cause it inefficient in scenarios such as secure multi-party computing (MPC). One is the relinearization technique used for key switching takes up most of the time of the scheme’s homomorphic evaluation, the other is that each user needs to decrypt in sequence, which makes the decryption process complicated. We propose an efficient leveled MKFHE scheme, which improves the efficiency of homomorphic evaluations, and constructs a two-round (MPC) protocol based on this. Firstly, we construct an efficient single key FHE with less relinearization operations. We greatly reduces the number of relinearization operations in homomorphic evaluations process by separating the homomorphic multiplication and relinearization techniques. Furthermore, the batching technique and a specialization of modulus can be applied to our scheme to improve the efficiency. Secondly, the efficient single-key homomorphic encryption scheme proposed in this paper is transformed into a multi-key vision according to the method in LTV12 scheme. Finally, we construct a distributed decryption process which can be implemented independently for all participating users, and reduce the number of interactions between users in the decryption process. Based on this, a two-round MPC protocol is proposed. Experimental analysis shows that the homomorphic evaluation of the single-key FHE scheme constructed in this paper is 2.4 times faster than DHS16, and the MKFHE scheme constructed in this paper can be used to implement a two-round MPC protocol effectively, which can be applied to secure MPC between multiple users under the cloud computing environment

Multi-key Fully Homomorphic Encryption Scheme with Compact Ciphertexts

Multi-Key fully homomorphic encryption (MKFHE) allows computations on data encrypted by different parties. One disadvantage of previous MKFHE schemes is that the ciphertext size increases linearly or squarely with respect to the number of parties. It incurs a heavy communication and computation burden for the homomorphic evaluation, especially when the number of involved parties is large. In this paper, we propose the first method to construct MKFHE scheme while keeping the size of the ciphertext and corresponding evaluation key to be independent of the number of parties during the homomorphic evaluation. Specifically, we construct efficient compact MKFHE schemes with various advantages. On the one hand, we show how to construct compact MKFHE schemes which support the homomorphic encryption of ring elements and are friendly to floating point numbers. On the other hand, we give a compact MKFHE scheme that supports high efficient bootstrapping. In our paper, we show a novel method to reduce the cost of generating these evaluation keys from a quadratic time to a linear time with respect to the number of parties

A New Group Location Privacy-Preserving Method Based on Distributed Architecture in LBS

Nowadays, the location privacy problem has become an important problem for the users who enjoy the location-based services (LBSs). Researchers have focused on the problem of how to protect the location privacy of user efficiently for a long time. On one hand, many achievements adopt the centralized structure in which there is an additional center server. Additionally, some other researchers adopt the distributed structure to overcome the disadvantages brought by the center server in the centralized anonymous system structure. On the other hand, the existing methods of solving the problem are always to protect the individual user’s location privacy in LBSs, without considering the user group’s location privacy. This kind of methods is not very applicable to the status of a number of users who formed a group to complete a LBS task together by collaborative computing. In order to solve the problem of location privacy protection for a user group in the untrusted mobile social networks, a location privacy protection method based on the distributed structure is discussed in this paper. In the scheme, the special homomorphic features of BGN cryptosystem are cleverly used so that it can solve the group’s three classical location service applications simultaneously, namely, group nearest neighbor query, optimal group collection point determination, and group friend’s distance query, by only one security policy. If there are k users who formed the group, it could achieve k-anonymity without exposing the coordinate of each individual user or using any anonymous areas. Furthermore, theoretical and experimental analysis proves that the proposal can efficiently protect each user’s location privacy in the group through taking full advantage of the collaborative computing and communication capabilities of the mobile terminals. It can resist the existing distance interaction attack and collusion attack and can realize the secure and efficient fine-grained controllable location privacy protection for the user group