Boneh et al.’s k-Element Aggregate Extraction Assumption Is Equivalent to the Diffie-Hellman Assumption
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In Eurocrypt 2003, Boneh et al. presented a novel cryptographic primitive called aggregate signatures. An aggregate signature scheme is a digital signature that supports aggregation: i.e. given k signatures on k distinct messages from k different users it is possible to aggregate all these signatures into a single short signature.
Applying the above concept to verifiably encrypted signatures, Boneh et al. introduced a new complexity assumption called the k-Element Aggregate Extraction Problem.
In this paper we show that the k-Element Aggregate Extraction Problem is nothing but a Computational Diffie-Hellman Problem in disguise.
Keywordsaggregate signatures Diffie-Hellman problem complexity assumption
- 3.Boneh, D., Gentry, C., Lynn, B., Shacham, H.: Aggregate and Verifiably Encrypted Signatures from Bilinear Maps, Cryptology ePrint Archive, Report 2002/175 (2002), http://eprint.iacr.org/