Consider a scenario where a server S shares a symmetric key kU with each user U. Building on a 2-party solution of Bohli et al., we describe an authenticated 3-party key establishment which remains secure if a computational Bilinear Diffie Hellman problem is hard or the server is uncorrupted. If the BDH assumption holds during a protocol execution, but is invalidated later, entity authentication and integrity of the protocol are still guaranteed. Key establishment protocols based on hardness assumptions, such as discrete logarithm problem (DLP) and integer factorization problem (IFP) are vulnerable to quantum computer attacks, whereas the protocols based on other hardness assumptions, such as conjugacy search problem and decomposition search problem can resist such attacks. The existing protocols based on the hardness assumptions which can resist quantum computer attacks are only passively secure. Compilers are used to convert a passively secure protocol to an actively secure protoc ol. Compilers involve some tools such as, signature scheme and a collision-resistant hash function. If there are only passively secure protocols but not a signature scheme based on same assumption then the application of existing compilers requires the use of such tools based on different assumptions. But the introduction of new tools, based on different assumptions, makes the new actively secure protocol rely on more than one hardness assumptions. We offer an approach to derive an actively secure two-party protocol from a passively secure two-party protocol without introducing further hardness assumptions. This serves as a useful formal tool to transform any basic algebric method of public key cryptography to the real world applicaticable cryptographic scheme. In a recent preprint, Vivek et al. propose a compiler to transform a passively secure 3-party key establishment to a passively secure group key establishment. To achieve active security, they apply this compiler to Joux's / protoc ol and apply a construction by Katz and Yung, resulting in a 3-round group key establishment. In this reserach, we show how Joux's protocol can be extended to an actively secure group key establishment with two rounds. The resulting solution is in the standard model, builds on a bilinear Diffie-Hellman assumption and offers forward security as well as strong entity authentication. If strong entity authentication is not required, then one half of the participants does not have to send any message in the second round, which may be of interest for scenarios where communication efficiency is a main concern. / by Kashi Neupane. / Thesis (Ph.D.)--Florida Atlantic University, 2012. / Includes bibliography. / Electronic reproduction. Boca Raton, Fla., 2012. Mode of access: World Wide Web.
| Identifer | oai:union.ndltd.org:fau.edu/oai:fau.digital.flvc.org:fau_3886 |
| Contributors | Neupane, Kashi., Charles E. Schmidt College of Science, Department of Mathematical Sciences |
| Publisher | Florida Atlantic University |
| Source Sets | Florida Atlantic University |
| Language | English |
| Detected Language | English |
| Type | Text, Electronic Thesis or Dissertation |
| Format | ix, 83 p., electronic |
| Rights | http://rightsstatements.org/vocab/InC/1.0/ |
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