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In Eurocrypt 2003, Boneh et al. presented a novel crypto- graphic primitive called aggregate signatures. An aggregate signature scheme is a digital signature that supports aggregation: i.e. given k sig- natures on k distinct messages from k dieren t users it is possible to aggregate all these signatures into a single short signature. Applying the above concept to veriably encrypted signatures, Boneh et al. introduced a new complexity assumption called the k-Element Ag- gregate Extraction Problem. In this paper we show that the k-Element Aggregate Extraction Problem is nothing but a Computational Die-Hellman Problem in disguise.

Boneh et al.’s k-Element Aggregate Extraction Assumption Is Equivalent to the Diffie-Hellman Assumption