Lattice-Based Key-Aggregate (Searchable) Encryption in Cloud Storage

Abstract

In cloud storage, selectively sharing encrypted data is becoming increasingly important. One key design challenge is the management of encryption keys. Traditionally, a large quantity of encryption keys have to be managed by the data owner, and an equally large number of keyword trapdoors must be sent to the cloud for the purpose of searching over the shared data, which are cumbersome in terms of secure communication and management. Recently, key-aggregate (searchable) encryption schemes have been introduced to alleviate the problem. However, they were only designed under the Bilinear Diffie-Hellman Exponent assumption in the prior works. Lattice-based key-aggregate (searchable) encryption schemes are valuable, because they have security against quantum computing attacks, average-case to worse-case equivalence as well as simplicity and potential efficiency. Here we propose a key-aggregate encryption scheme and a key-aggregate searchable encryption scheme which are both based on a lattice problem (i.e., the Learning with Errors problem). Some key techniques are employed during the construction of the schemes. A basis delegation algorithm is designed to generate the aggregate key without increasing the lattice dimension. The encryption algorithms of the two schemes are trickily devised to make the encrypted files decryptable or searchable. To overcome the problem of general matrix multiplication failing to satisfy commutative law, a hash function is designed by using diagonalizable matrices to make the encrypted file decryptable and the trapdoor adjustable. We present the schemes' correctness proof, formal security analysis as well as performance analysis, which confirm that they are provably secure and practically efficient. To the best of our knowledge, the former is the first lattice-based key-aggregate encryption scheme and the latter is the first lattice-based key-aggregate searchable encryption scheme. We also demonstrate their application to cloud storage for searchable group data sharing by combining the two schemes. INDEX TERMS Cloud storage, searchable data sharing, key-aggregate encryption, key-aggregate searchable encryption, lattice-based problem, the learning with errors problem.

R-OO-KASE: Revocable Online/Offline Key Aggregate Searchable Encryption

“…2|G| Table 5, we can observe that none of the existing KASE schemes listed in the table provide revocation of delegated rights, conjunctive keywords search using a single trapdoor and energy-efficient encryption as well as decryption algorithms for resource-limited devices. Additionally, as shown in Table 5, the KASE schemes [4,13,23,24,31,32,34,35] do not support search over multiowners' data using a single trapdoor. On the other hand, the KASE schemes proposed in [18][19][20][21][22] provide the solution to search over multi-owners' data using a single trapdoor.…”

“…Yao et al propose the first lattice-based KASE scheme in [32]. The lattice-based KASE [32] scheme provides security against quantum computing attacks and potential efficiency.…”

“…Yao et al propose the first lattice-based KASE scheme in [32]. The lattice-based KASE [32] scheme provides security against quantum computing attacks and potential efficiency. Padhya et al [23] propose a revocable KASE scheme with Break-The-Glass access control.…”

“…Comparative analysis: communication overhead n number of documents that belongs to the data owner, | ������ ⃗ KW| number of keywords attached with the ciphertext, | �� ⃗ Q| number of keywords in the query set, q size prime number in lattice-based KASE scheme[32], mXn size of matrix in lattice-based KASE scheme[32], |G| size of a element in group G, |G T | size of a element in group G T…”

P 2 KASE A 2 —privacy‐preserving key aggregate searchable encryption supporting authentication and access control on multi‐delegation

“…The key aggregate searchable encryption (KASE) scheme [5 ] is more extended in scope, in which a DO delegates search rights over a selected dataset using an aggregate key and the user can search over shared data by submitting a single aggregate trapdoor to the cloud. The KAE schemes [4, 6–11 ] and KASE schemes [5, 12–23 ] focus on the list of data that the DO wants to share with other users rather than focusing on the role or the attributes of recipients. This data‐centric characteristic of the KAE and the KASE helps them to reduce the number of keys required for group data sharing, as compared to the user‐centric data sharing schemes [1–3 ].…”