Authors
Essam Ghadafi, Jens Groth
Publication date
2017/11/18
Book
International Conference on the Theory and Application of Cryptology and Information Security
Pages
66-96
Publisher
Springer International Publishing
Description
We study non-interactive computational intractability assumptions in prime-order cyclic groups. We focus on the broad class of computational assumptions which we call target assumptions where the adversary’s goal is to compute concrete group elements.
Our analysis identifies two families of intractability assumptions, the q-Generalized Diffie-Hellman Exponent (q-GDHE) assumptions and the q-Simple Fractional (q-SFrac) assumptions (a natural generalization of the q-SDH assumption), that imply all other target assumptions. These two assumptions therefore serve as Uber assumptions that can underpin all the target assumptions where the adversary has to compute specific group elements. We also study the internal hierarchy among members of these two assumption families. We provide heuristic evidence that both families are necessary to cover the full class of target assumptions. We also …
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