Pairing-Based Cryptography Sample Clauses

Pairing-Based Cryptography. ‌ Bilinear pairings of algebraic curves were originally used as cryptographic tools for re- ducing the discrete logarithm problem in weak elliptic curves [41, 24]. In 2000, however, Joux [32] showed that pairings also could have a positive use in cryptography by con- structing a tripartite Xxxxxx-Xxxxxxx key agreement protocol based on the Weil pairing. The message flows of the protocol are identical to the elliptic curve-based Xxxxxx-Xxxxxxx protocol, but use the Weil pairing in computing the session key. As there is no way of efficiently computing discrete logarithms on elliptic curves, it is possible to maintain a high level of security while using short keys. Boneh and Franklin [9] extended the idea by Joux and constructed an identity-based encryption scheme based on the properties of bilinear pairings on elliptic curves. The scheme was the first fully functional, efficient and provably secure identity-based encryp- tion scheme, and was shortly followed by the BLS short signature scheme [10]. Since the introduction of these two important applications of pairings, many new pairing-based cryptographic protocols have been designed and analyzed (see [23] for a survey). A lot of the work concerning pairing-based cryptography is on the realization and effi- cient implementation of pairings. Such implementations may, for instance, be done using the Weil pairing or the Xxxx pairing. Although both involve fairly complex mathematics, they can be dealt with abstractly. Most key agreement protocols use a modified pairing in order to avoid sending two points per participant. For more detailed information about pairings and their use in cryptographic protocols, see [33, 26].