## Cryptology ePrint Archive: Report 2018/974

Adaptively Secure and Succinct Functional Encryption: Improving Security and Efficiency, Simultaneously

Fuyuki Kitagawa and Ryo Nishimaki and Keisuke Tanaka and Takashi Yamakawa

Abstract: Functional encryption (FE) is advanced encryption that enables us to issue functional decryption keys where functions are hardwired. When we decrypt a ciphertext of a message $m$ by a functional decryption key where a function $f$ is hardwired, we can obtain $f(m)$ and nothing else. We say FE is selectively or adaptively secure when target messages are chosen at the beginning or after function queries are sent, respectively. In the weakly-selective setting, function queries are also chosen at the beginning. We say FE is single-key/collusion-resistant when it is secure against adversaries that are given only-one/polynomially-many functional decryption keys, respectively. We say FE is sublinearly-succinct/succinct when the running time of an encryption algorithm is sublinear/poly-logarithmic in the function description size, respectively.

In this study, we propose a generic transformation from weakly-selectively secure, single-key, and sublinearly-succinct (we call building block'') PKFE for circuits into adaptively secure, collusion-resistant, and succinct (we call fully-equipped'') one for circuits. We assume only the existence of the building block PKFE for circuits. That is, our transformation relies on neither concrete assumptions such as learning with errors nor indistinguishability obfuscation (IO). This is the first generic construction of fully-equipped PKFE that does not rely on IO.

As side-benefits of our results, we obtain the following primitives from the building block PKFE for circuits: (1) laconic oblivious transfer (2) succinct garbling scheme for Turing machines (3) selectively secure, collusion-resistant, and succinct PKFE for Turing machines (4) low-overhead adaptively secure traitor tracing (5) key-dependent-message secure and leakage-resilient public-key encryption. We also obtain a generic transformation from simulation-based adaptively secure garbling schemes that satisfy a natural decomposability property into adaptively indistinguishable garbling schemes whose online complexity does not depend on the output length.

Category / Keywords: foundations / Functional encryption, Adaptive security, Succinctness, Adaptive garbled circuit, Laconic oblivious transfer

Date: received 12 Oct 2018, last revised 13 Feb 2019

Contact author: ryo nishimaki at gmail com,kitagaw1@is titech ac jp,takashi yamakawa ga@hco ntt co jp

Available format(s): PDF | BibTeX Citation

Note: Fixing minor typos (2/14/2019). Improving the presentation (2/12/2019). Add an explanation about transforming laconic OT into updatable laconic OT (11/20/2018).

Short URL: ia.cr/2018/974

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