IACR News item: 15 October 2013
Sarah Meiklejohn, Hovav Shacham
ePrint ReportIn this paper, we describe, characterize, and exploit this surprising structure. It is our thesis that the additional structure available in these curves will give rise to novel cryptographic constructions, and we initiate the study of such constructions. Both the subgroup hiding and SXDH assumptions appear to hold in the new setting; in addition, we introduce custom-tailored assumptions designed to capture the trapdoor nature of the projection maps into $G_1$ and $G_2$. Using the old and new assumptions, we describe an extended variant of the Boneh-Goh-Nissim cryptosystem that allows a user, at the time of encryption, to restrict the homomorphic operations that may be performed. We also present a variant of the Groth-Ostrovsky-Sahai NIZK, and new anonymous IBE, signature, and encryption schemes.
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