TY - JOUR
T1 - Efficient signature schemes with tight reductions to the Diffie-Hellman problems
JF - Journal of Cryptology
Y1 - 2007
A1 - Goh,E. J
A1 - Jarecki,S.
A1 - Katz, Jonathan
A1 - Wang,N.
AB - 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.
VL - 20
CP - 4
M3 - 10.1007/s00145-007-0549-3
ER -