Constructing Identity-Based Key Distribution Systems over Elliptic Curves

Hisao SAKAZAKI  Eiji OKAMOTO  Masahiro MAMBO  

Publication
IEICE TRANSACTIONS on Fundamentals of Electronics, Communications and Computer Sciences   Vol.E81-A    No.10    pp.2138-2143
Publication Date: 1998/10/25
Online ISSN: 
DOI: 
Print ISSN: 0916-8508
Type of Manuscript: Special Section PAPER (Special Section on Information Theory and Its Applications)
Category: Security
Keyword: 
ID-based key distribution systems,  elliptic curve,   message recovery signature,  

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Summary: 
A key distribution system is a system in which users securely generate a common key. One kind of identity-based key distribution system was proposed by E. Okamoto. Its security depends on the difficulty of factoring a composite number of two large primes like RSA public-key cryptosystem. Another kind of identity-based key distribution system was proposed by K. Nyberg, R. A. Rueppel. Its security depends on the difficulty of the discrete logarithm problem. On the other hand, Koblitz and Miller described how a group of points on an elliptic curve over a finite field can be used to construct a public key cryptosystem. In 1997, we proposed an ID-based key distribution system over an elliptic curve, as well as those over the ring Z/nZ. Its security depends on the difficulty of factoring a composite number of two large primes. We showed that this system over an elliptic curve is more suitable for the implementation than those over the ring Z/nZ. In this paper, we apply the Nyberg-Rueppel ID-based key distribution system to an elliptic curve. It provides relatively small block size and high security. This public key distribution system can be efficiently implemented. However the Nyberg-Rueppel's scheme requires relatively large data transmission. As a solution to this problem, we improve the scheme. This improved scheme is very efficient since data transferred for the common key generation is reduced to half of those in the Nyberg-Rueppel's scheme.