Pairing-based cryptosystems and key agreement protocols.

For a long time, pairings on elliptic curves have been considered to be destructive in elliptic curve cryptography. Only recently after some pioneering works, particularly the well-known Boneh-Franklin identity-based encryption (IBE), pairings have quickly become an important tool to construct novel cryptographic schemes. In this thesis, several new cryptographic schemes with pairings are proposed, which are both efficient and secure with respect to a properly defined security model, and some relevant previous schemes are revisited. IBE provides a public key encryption mechanism where a public key can be an arbitrary string such as an entity identifier and unwieldy certificates are unnecessary. Based on the Sakai-Kasahara key construction, an IBE scheme which is secure in the Boneh-Franklin IBE model is constructed, and two identity-based key encapsulation mechanisms are proposed. These schemes achieve the best efficiency among the existing schemes to date. Recently Al-Riyami and Paterson introduced the certificateless public key encryption (CL-PKE) paradigm, which eliminates the need of certificates and at the same time retains the desirable properties of IBE without the key escrow problem. The security formulation of CL-PKE is revisited and a strong security model for this type of mechanism is defined. Following a heuristic approach, three efficient CL-PKE schemes which are secure in the defined strong security model are proposed. Identity-based two-party key agreement protocols from pairings are also investigated. The Bellare-Rogaway key agreement model is enhanced and within the model several previously unproven protocols in the literature are formally analysed. In considering that the user identity may be sensitive information in many environments, an identity-based key agreement protocol with unilateral identity privacy is proposed

General Certificateless Encryption and Timed-Release Encryption

While recent timed-release encryption (TRE) schemes are implicitly supported by a certificateless encryption (CLE) mechanism, the security models of CLE and TRE differ and there is no generic transformation from a CLE to a TRE. This paper gives a generalized model for CLE that fulfills the requirements of TRE. This model is secure against adversaries with adaptive trapdoor extraction capabilities, decryption capabilities for arbitrary public keys, and partial decryption capabilities. It also supports hierarchical identifiers. We propose a concrete scheme under our generalized model and prove it secure without random oracles, yielding the first strongly-secure security-mediated CLE and the first TRE in the standard model. In addition, our technique of partial decryption is different from the previous approach

Further Observations on Certificate-Base Encryption and its Generic Construction from Certificateless Public Key Encryption

Certificate-based encryption (CBE) is a new asymmetric encryption paradigm which was introduced to solve the certificate management problem in traditional public key encryption (PKI). It combines PKE and identity-based encryption (IBE) while preserving some of their most attractive features. CBE provides an efficient implicit certificate mechanism which eliminates the third-party queries and simplifies the certificate revocation problem in the traditional PKI. It also solves the key escrow problem and key distribution problem inherent in IBE. In this paper, we introduce the key replacement attack and the malicious-but-passive certifier attack into CBE, and define a class of new security models for CBE under different security levels according to the power of the adversaries against CBE. Our new security models are more elaborated and stronger compared with other existing ones. Then, we propose a generic construction of CBE from certificateless public key encryption and prove its security under the proposed security models in the standard model. We also show a concrete conversion using the proposed generic construction

Still Wrong Use of Pairings in Cryptography

Several pairing-based cryptographic protocols are recently proposed with a wide variety of new novel applications including the ones in emerging technologies like cloud computing, internet of things (IoT), e-health systems and wearable technologies. There have been however a wide range of incorrect use of these primitives. The paper of Galbraith, Paterson, and Smart (2006) pointed out most of the issues related to the incorrect use of pairing-based cryptography. However, we noticed that some recently proposed applications still do not use these primitives correctly. This leads to unrealizable, insecure or too inefficient designs of pairing-based protocols. We observed that one reason is not being aware of the recent advancements on solving the discrete logarithm problems in some groups. The main purpose of this article is to give an understandable, informative, and the most up-to-date criteria for the correct use of pairing-based cryptography. We thereby deliberately avoid most of the technical details and rather give special emphasis on the importance of the correct use of bilinear maps by realizing secure cryptographic protocols. We list a collection of some recent papers having wrong security assumptions or realizability/efficiency issues. Finally, we give a compact and an up-to-date recipe of the correct use of pairings.Comment: 25 page

Efficient Certificateless Public Key Encryption

In [3] Al-Riyami and Paterson introduced the notion of Certificateless Public Key Cryptography and presented an instantiation. In this paper, we revisit the formulation of certificateless public key encryption and construct a more efficient scheme and then extend it to an authenticated encryption

Certificateless Key Insulated Encryption: Cryptographic Primitive for Achieving Key-escrow free and Key-exposure Resilience

Certificateless encryption (CLE) alleviates the heavy certificate management in traditional public key encryption and the key escrow problem in the ID-based encryption simultaneously. Current CLE schemes assumed that the user’s secret key is absolutely secure. Unfortunately, this assumption is too strong in case the CLE is deployed in the hostile setting and the leakage of secret key is inevitable. In this paper, we present a new concept called an certificateless key insulated encryption scheme (CL-KIE). We argue that this is an important cryptographic primitive that can be used to achieve key-escrow free and key-exposure resilience. We also present an efficient CL-KIE scheme based on bilinear pairing. After that, the security of our scheme is proved under the Bilinear Diffie-Hellman assumption in the random oracle model. Certificateless encryption (CLE) alleviates the heavy certificate management in traditional public key encryption and the key escrow problem in the ID-based encryption simultaneously. Current CLE schemes assumed that the user’s secret key is absolutely secure. Unfortunately, this assumption is too strong in case the CLE is deployed in the hostile setting and the leakage of the secret key is inevitable. In this paper, we present a new concept called a certificateless key insulated encryption scheme (CL-KIE). We argue that this is an important cryptographic primitive that can be used to achieve key-escrow free and key-exposure resilience. We also present an efficient CL-KIE scheme based on bilinear pairing. After that, the security of our scheme is proved under the Bilinear DiffieHellman assumption in the random oracle model