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

Anonymous and Adaptively Secure Revocable IBE with Constant Size Public Parameters

In Identity-Based Encryption (IBE) systems, key revocation is non-trivial. This is because a user's identity is itself a public key. Moreover, the private key corresponding to the identity needs to be obtained from a trusted key authority through an authenticated and secrecy protected channel. So far, there exist only a very small number of revocable IBE (RIBE) schemes that support non-interactive key revocation, in the sense that the user is not required to interact with the key authority or some kind of trusted hardware to renew her private key without changing her public key (or identity). These schemes are either proven to be only selectively secure or have public parameters which grow linearly in a given security parameter. In this paper, we present two constructions of non-interactive RIBE that satisfy all the following three attractive properties: (i) proven to be adaptively secure under the Symmetric External Diffie-Hellman (SXDH) and the Decisional Linear (DLIN) assumptions; (ii) have constant-size public parameters; and (iii) preserve the anonymity of ciphertexts---a property that has not yet been achieved in all the current schemes

On the Anonymity of Identity-Based Encryption

Anonymity of identity-based encryption (IBE) means that given a ciphertext, one cannot distinguish the target identity from a random identity. In this paper, we thoroughly discuss the anonymity of IBE systems. We found that the current definition of anonymity is obscure to describe some IBE systems, such as Gentry IBE system. Furthermore, current definition cannot express the degree of anonymity. So we divide the degree of anonymity into weak anonymity and strong anonymity based on indistinguishability between different games. For weakly anonymous IBE systems, the target identity in a ciphertext cannot be distinguished from a random identity. For strongly anonymous IBE systems, the whole ciphertext cannot be distinguished from a random tuple. We also discuss the type of anonymity and divide it into two types. Type 1 means that a random tuple can be seen as a valid ciphertext, while type 2 cannot. Based on our new definitions, we show that three famous IBE systems, Gentry IBE system, Boyen-Waters IBE system, and Lewko IBE system, have strong but different types of anonymity

Tightly Secure Hierarchical Identity-Based Encryption

We construct the first tightly secure hierarchical identity-based encryption (HIBE) scheme based on standard assumptions, which solves an open problem from Blazy, Kiltz, and Pan (CRYPTO 2014). At the core of our constructions is a novel randomization technique that enables us to randomize user secret keys for identities with flexible length. The security reductions of previous HIBEs lose at least a factor of Q, which is the number of user secret key queries. Different to that, the security loss of our schemes is only dependent on the security parameter. Our schemes are adaptively secure based on the Matrix Diffie-Hellman assumption, which is a generalization of standard Diffie-Hellman assumptions such as k-Linear. We have two tightly secure constructions, one with constant ciphertext size, and the other with tighter security at the cost of linear ciphertext size. Among other things, our schemes imply the first tightly secure identity-based signature scheme by a variant of the Naor transformation

Novel Techniques for Secure Use of Public Cloud Computing Resources

The federal government has an expressed interest in moving data and services to third party service providers in order to take advantage of the flexibility, scalability, and potential cost savings. This approach is called cloud computing. The thesis for this research is that efficient techniques exist to support the secure use of public cloud computing resources by a large, federated enterprise. The primary contributions of this research are the novel cryptographic system MA-AHASBE (Multi-Authority Anonymous Hierarchical Attribute-Set Based Encryption), and the techniques used to incorporate MA-AHASBE in a real world application. Performance results indicate that while there is a cost associated with enforcing the suggested security model, the cost is not unreasonable and the benefits in security can be significant. The contributions of this research give the DoD additional tools for supporting the mission while taking advantage of the cost efficient public cloud computing resources that are becoming widely available

Are These Pairing Elements Correct? Automated Verification and Applications

Using a set of pairing product equations (PPEs) to verify the correctness of an untrusted set of pairing elements with respect to another set of trusted elements has numerous cryptographic applications. These include the design of basic and structure-preserving signature schemes, building oblivious transfer schemes from “blind” IBE, finding new verifiable random functions and keeping the IBE/ABE authority “accountable” to the user. A natural question to ask is: are all trusted-untrusted pairing element groups in the literature PPE testable? We provide original observations demonstrating that the answer is no, and moreover, it can be non-trivial to determine whether or not there exists a set of PPEs that can verify some pairing elements with respect to others. Many IBE schemes have PPE-testable private keys (with respect to the public parameters), while others, such as those based on dual-system encryption, provably do not. To aid those wishing to use PPE-based element verification in their cryptosystems, we devised rules to systematically search for a set of PPEs that can verify untrusted elements with respect to a set of trusted elements. We prove the correctness of each rule and combine them into a main searching algorithm for which we also prove correctness. We implemented this algorithm in a new software tool, called AutoPPE. Tested on over two dozen case studies, AutoPPE found a set of PPEs (on schemes where they exist) usually in just a matter of seconds. This work represents an important step towards the larger goal of improving the speed and accuracy of pairing-based cryptographic design via computer automation

Efficient Adaptively Secure IBBE from Standard Assumptions

This paper describes the first construction of efficient identity-based broadcast encryption (IBBE) schemes which can be proved secure against adaptive-identity attacks based on standard assumptions. The constructions are obtained by extending the currently known most efficient identity-based encryption scheme proposed by Jutla and Roy in 2013. Ciphertext size and user storage compare favourably to previously known constructions. The new constructions fill both a practical and a theoretical gap in the literature on efficient IBBE schemes