Efficient signature schemes with tight reductions to the Diffie-Hellman problems

TitleEfficient signature schemes with tight reductions to the Diffie-Hellman problems
Publication TypeJournal Articles
Year of Publication2007
AuthorsGoh EJ, Jarecki S, Katz J, Wang N
JournalJournal of Cryptology
Pagination493 - 514
Date Published2007///

We propose and analyze two efficient signature schemes whose security is tightly related to the Diffie-Hellman problems in the random oracle model. The security of our first scheme relies on the hardness of the computational Diffie-Hellman problem; the security of our second scheme - which is more efficient than the first-is based on the hardness of the decisional Diffie-Hellman problem, a stronger assumption. Given the current state of the art, it is as difficult to solve the Diffie-Hellman problems as it is to solve the discrete logarithm problem in many groups of cryptographic interest. Thus, the signature schemes shown here can currently offer substantially better efficiency (for a given level of provable security) than existing schemes based on the discrete logarithm assumption. The techniques we introduce can also be applied in a wide variety of settings to yield more efficient cryptographic schemes (based on various number-theoretic assumptions) with tight security reductions.