Dynamic Group Diffie-Hellman Key Exchange under Standard Assumptions

Authenticated Diffie-Hellman key exchange allows two principals communicating over a public network, and each holding public /private keys, to agree on a shared secret value. In this paper we study the natural extension of this cryptographic problem to a group of principals. We begin from existing formal security models and refine them to incorporate major missing details (e.g., strong-corruption and concurrent sessions). Within this model we define the execution of a protocol for authenticated dynamic group Diffie-Hellman and show that it is provably secure under the decisional Diffie-Hellman assumption. Our security result holds in the standard model and thus provides better security guarantees than previously published results in the random oracle model

Public key exchange using semidirect product of (semi)groups

In this paper, we describe a brand new key exchange protocol based on a semidirect product of (semi)groups (more specifically, on extension of a (semi)group by automorphisms), and then focus on practical instances of this general idea. Our protocol can be based on any group, in particular on any non-commutative group. One of its special cases is the standard Diffie-Hellman protocol, which is based on a cyclic group. However, when our protocol is used with a non-commutative (semi)group, it acquires several useful features that make it compare favorably to the Diffie-Hellman protocol. Here we also suggest a particular non-commutative semigroup (of matrices) as the platform and show that security of the relevant protocol is based on a quite different assumption compared to that of the standard Diffie-Hellman protocol.Comment: 12 page

The Twin Diffie-Hellman Problem and Applications

We propose a new computational problem called the \emph{twin Diffie-Hellman problem}. This problem is closely related to the usual (computational) Diffie-Hellman problem and can be used in many of the same cryptographic constructions that are based on the Diffie-Hellman problem. Moreover, the twin Diffie-Hellman problem is at least as hard as the ordinary Diffie-Hellman problem. However, we are able to show that the twin Diffie-Hellman problem remains hard, even in the presence of a decision oracle that recognizes solutions to the problem --- this is a feature not enjoyed by the Diffie-Hellman problem in general. Specifically, we show how to build a certain ``trapdoor test\u27\u27 that allows us to effectively answer decision oracle queries for the twin Diffie-Hellman problem without knowing any of the corresponding discrete logarithms. Our new techniques have many applications. As one such application, we present a new variant of ElGamal encryption with very short ciphertexts, and with a very simple and tight security proof, in the random oracle model, under the assumption that the ordinary Diffie-Hellman problem is hard. We present several other applications as well, including: a new variant of Diffie and Hellman\u27s non-interactive key exchange protocol; a new variant of Cramer-Shoup encryption, with a very simple proof in the standard model; a new variant of Boneh-Franklin identity-based encryption, with very short ciphertexts; a more robust version of a password-authenticated key exchange protocol of Abdalla and Pointcheval

User Collusion Avoidance Scheme for Privacy-Preserving Decentralized Key-Policy Attribute-Based Encryption

Decentralized attribute-based encryption (ABE) is a variant of multi-authority based ABE whereby any attribute authority (AA) can independently join and leave the system without collaborating with the existing AAs. In this paper, we propose a user collusion avoidance scheme which preserves the user's privacy when they interact with multiple authorities to obtain decryption credentials. The proposed scheme mitigates the well-known user collusion security vulnerability found in previous schemes. We show that our scheme relies on the standard complexity assumption (decisional bilienar Deffie-Hellman assumption). This is contrast to previous schemes which relies on non-standard assumption (q-decisional Diffie-Hellman inversion)

User collusion avoidance scheme for privacy-preserving decentralized key-policy attribute-based encryption

Decentralized attribute-based encryption (ABE) is a variant of multi-authority based ABE whereby any attribute authority (AA) can independently join and leave the system without collaborating with the existing AAs. In this paper, we propose a user collusion avoidance scheme which preserves the user's privacy when they interact with multiple authorities to obtain decryption credentials. The proposed scheme mitigates the well-known user collusion security vulnerability found in previous schemes. We show that our scheme relies on the standard complexity assumption (decisional bilienar Deffie-Hellman assumption). This is contrast to previous schemes which relies on non-standard assumption (q-decisional Diffie-Hellman inversion)

Pairing-based identification schemes

We propose four different identification schemes that make use of bilinear pairings, and prove their security under certain computational assumptions. Each of the schemes is more efficient and/or more secure than any known pairing-based identification scheme

A SECURE KEY AGREEMENT PROTOCOL

In this paper we propose a secure protocol for an authenticated key agreement based on the Diffie-Hellman key agreement, which works in an elliptic curve group We prove that our protocol meets the security attributes under the assumption that the elliptic curve discrete logarithm problem is secure