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Secure channel free public key encryption with multiple keywords search

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Ma, Yang (2020) Secure channel free public key encryption with multiple keywords search. Doctoral thesis, London Metropolitan University.

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Abstract

With a further exploration of modern cryptography, people realize that Public Key Infrastructure (PKI) is not perfect but has its limitations. One of the limitations is that PKI completely depends on the Certification Authority (CA) to obtain a digital certificate, but this online trusted third party might be compromised by the cyber attacks. Therefore, Shamir proposed a definition of Identity Based Encryption (IBE) which only relies on user’s identity to generate the public key instead of CA. Although the blueprint of IBE was presented in 1984, the first secure and reliable IBE system has been introduced until 2001. Meanwhile, some applications of IBE, such as Public Key Encryption with Keyword Search (PEKS), have been came up with since then.

PEKS is one of the most technologically advanced crypto-systems to address searchable encryption. It enables individuals to search encrypted documents appending with a keyword without deriving any information. The first PEKS scheme was formalized by BDOP in 2004, but a secure channel must be established in order to transfer the Trapdoor query to the third party. Comparing with the original PEKS scheme, the later PEKS approaches remove secure channels and become much secure and efficient as time goes by. However, no matter what happened, Multiple Keywords Search and Keyword Guessing Attack are still two main research interests for the consideration. This PhD research aims to propose a few PEKS schemes in order to solve both Single and Multiple Keyword(s) Search issues and resist Off-line Keyword Guessing Attack (OKGA) and/or Inside Keyword Guessing Attack (IKGA). The focus of this research is listed on the three following parts:

Many current Public Key Encryption with Multiple Keywords Search (MPEKS) schemes suffers OKGA. Therefore, this research firstly defines a formal MPEKS scheme to solve OKGA, which is called “Trapdoor-indistinguishable Secure Channel Free Public Key Encryption with Multi-keywords Search (tSCF-MPEKS)”. More specially, the new scheme allows users to search both Single and Multiple Keyword(s) and also has the characters of Ciphertext Indistinguishability and Trapdoor Indistinguishability so that it proves to be semantic secure under Random Oracle Models by Bilinear Diffie-Hellman (BDH) and 1-Bilinear Diffie-Hellman Inversion(1-BDHI) assumptions for preventing OKGA. Besides, the efficiency and performance of tSCF-MPEKS is presented from both the theoretical analysis and the practical analysis.

IKGA in MPEKS schemes is still an intractable problem up to now. But, this PhD research solves IKGA by applying User Authentication technique. More specially, the second proposed PEKS scheme, namely “Robust Secure Channel Free Public Key Encryption with Multi-keywords Search (rSCF-MPEKS)”, not only addresses both the Single and Multiple Keyword(s) Search problems but also satisfies Ciphertext Indistinguishability and Trapdoor Indistinguishability properties and incorporates with User Authentication, therefore, it proves to be semantic secure under Random Oracle Models by BDH assumption for resisting IKGA. Besides, OKGA is also resisted in the proposed scheme. In addition, the performance of rSCF-MPEKS is also analyzed by the theoretical analysis and the computer simulation.

Thirdly, almost all current PEKS and MPEKS schemes cannot deal with imprecise keywords, such as “latest”, “newest”, etc. The research incorporates with Fuzzy Logic (Artificial Intelligence) technique to PEKS and then proposes a formal statement of “Public Key Encryption with Multi-keywords Search using Mamdani System (m-PEMKS)”. Its concrete construction, correctness and security verification are then proposed in the following section of the thesis. The new approach solves Fuzzy Keyword Search problem and proves to be semantic secure under Random Oracle Models by BDH and 1-BDHI assumptions so that it could resist OKGA. Besides, the performance of m-PEMKS is presented by the theoretical analysis and the computer simulation.

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