Abstract
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.
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Goh, EJ., Jarecki, S., Katz, J. et al. Efficient Signature Schemes with Tight Reductions to the Diffie-Hellman Problems. J Crypto 20, 493–514 (2007). https://doi.org/10.1007/s00145-007-0549-3
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DOI: https://doi.org/10.1007/s00145-007-0549-3