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            <funder>This work was supported in part by the European Community’s Seventh Framework Programme (FP7/2007-2013 Grant Agreement no. 339563 – CryptoCloud), the European Community’s Horizon 2020 Project FENTEC (Grant Agreement no. 780108), the Google PhD fellowship, and the French FUI ANBLIC Project. This work was partially done while the third author was visiting ENS, Paris, and UC Berkeley, California.</funder>
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              <p>We introduce Dynamic Decentralized Functional Encryption (DDFE), a generalization ofFunctional Encryption which allows multiple users to join the system dynamically, without relying on atrusted third party or on expensive and interactive Multi-Party Computation protocols.This notion subsumes existing multi-user extensions of Functional Encryption, such as Multi-Input, Multi-Client, and Ad Hoc Multi-Input Functional Encryption.We define and construct schemes for various functionalities which serve as building-blocks for latter primitivesand may be useful in their own right, such as a scheme for dynamically computing sums in any Abeliangroup. These constructions build upon simple primitives in a modular way, and have instantiations fromwell-studied assumptions, such as DDH or LWE.Our constructions culminate in an Inner-Product scheme for computing weighted sums on aggregatedencrypted data, from standard assumptions in prime-order groups in the Random Oracle Model.</p>
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