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

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. Key-words: aggregate signatures, Diffie-Hellman problem, complexity assumption.