New secure applications of bilinear maps in cryptography
(2006)
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Details
- Authors
- Supervisors
- Quisquater, Jean-Jacques
- Abstract
- Nowadays, the design of new cryptographic schemes follows the modern methodology of provable security. This approach requires to first clearly set out a formal model for the security of the scheme. Next, a ``reductionist'' proof is needed to show that the only way to break the scheme with a significant probability is either to attack an insecure component or to solve a computationally hard mathematical problem. Pairings are bilinear mappings defined over groups wherein the discrete logarithm problem is hard. They are usually instantiated with carefully chosen elliptic curves. For the last couple of years, they have been found to provide plenty of applications in the design of cryptographic protocols. The most salient examples were probably the appearance of tripartite key agreement protocols, identity-based encryption schemes, where any arbitrary public identifier can be used as a public key, and digital signature schemes producing short signatures. This thesis deals with pairing-based cryptographic protocols ensuring the same functionalities as the latter two kinds of primitives. In a first part, we deal with efficiency and (provable) security issues in identity based encryption (IBE) schemes and related concepts. We show two efficient variants of the Boneh-Franklin IBE and discuss the feasibility of using such schemes to construct of certificateless public key encryption systems. A second part describes new digital signatures supporting identity-based public keys. One of these new constructions can be modified at a very low cost to simultaneously ensure the confidentiality of authenticated messages. The resulting signature/encryption scheme is supported by security proofs and enjoys an impressive efficiency for such a scheme. The last part of this work considers several constructions to jointly achieve signature and encryption in a traditional public-key setting. For each of them, we give security reductions in a suitable model of security.
- Affiliations
UCLouvain FSA/ELEC - DƩpartement d'ƩlectricitƩ
Citations
Libert, B. (2006). New secure applications of bilinear maps in cryptography. https://hdl.handle.net/2078.5/98057