International Association for Cryptologic Research

International Association
for Cryptologic Research


Xiong Fan

Affiliation: Cornell University


FE for Inner Products and Its Application to Decentralized ABE
In this work, we revisit the primitive functional encryption (FE) for inner products and show its application to decentralized attribute-based encryption (ABE). Particularly, we derive an FE for inner products that satisfies a stronger notion, and show how to use such an FE to construct decentralized ABE for the class $$\{0,1\}$$-$$\mathsf {LSSS} $$ against bounded collusions in the plain model. We formalize the FE notion and show how to achieve such an FE under the LWE or DDH assumption. Therefore, our resulting decentralized ABE can be constructed under the same standard assumptions, improving the prior construction by Lewko and Waters (Eurocrypt 2011). Finally, we also point out challenges to construct decentralized ABE for general functions by establishing a relation between such an ABE and witness encryption for general NP statements.
Making Public Key Functional Encryption Function Private, Distributively
Xiong Fan Qiang Tang
We put forth a new notion of distributed public key functional encryption. In such a functional encryption scheme, the secret key for a function f will be split into shares $$\mathsf {sk}_i^f$$ skif. Given a ciphertext $$\mathsf {ct} $$ ct that encrypts a message x, a secret key share $$\mathsf {sk}_i^f$$ skif, one can evaluate and obtain a shared value $$y_i$$ yi. Adding all the shares up can recover the actual value of f(x), while partial shares reveal nothing about the plaintext. More importantly, this new model allows us to establish function privacy which was not possible in the setting of regular public key functional encryption. We formalize such notion and construct such a scheme from any public key functional encryption scheme together with learning with error assumption.We then consider the problem of hosting services in the untrusted cloud. Boneh, Gupta, Mironov, and Sahai (Eurocrypt 2014) first studied such application and gave a construction based on indistinguishability obfuscation. Their construction had the restriction that the number of corrupted clients has to be bounded and known. They left an open problem how to remove such restriction. We resolve this problem by applying our function private (distributed) public key functional encryption to the setting of hosting service in multiple clouds. Furthermore, our construction provides a much simpler and more flexible paradigm which is of both conceptual and practical interests.Along the way, we strengthen and simplify the security notions of the underlying primitives, including function secret sharing.