The first short signature scheme is proposed by Boneh, Lynn, and Shacham (BLS). This scheme uses the properties of bilinear pairings on certain elliptic curves. The main problem in BLS scheme is the use of special hash function. To deal with this problem, many cryptographic schemes were proposed with cryptographic hash functions such as MD5, SHA-1. In this paper, we propose a new and efficient short signature scheme from the bilinear pairings. Our scheme is constructed by Bilinear Inverse-Square Die-Hellman Problem (BISDHP) and does not require any special hash function. The exact security proofs are also explained in the random oracle model. We give the implementation and comparison results of the BLS and ZSS (Zhang, Safavi, and Susilo) schemes. Furthermore, We use this signature scheme to construct a ring signature scheme.
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