From Cryptomania to Obfustopia Through Secret-Key Functional Encryption

International audienceFunctional encryption lies at the frontiers of the current research in cryptography; some variants have been shown sufficiently powerful to yield indistinguishability obfuscation (IO), while other variants have been constructed from standard assumptions such as LWE. Indeed, most variants have been classified as belonging to either the former or the latter category. However, one mystery that has remained is the case of secret-key functional encryption with an unbounded number of keys and ciphertexts. On the one hand, this primitive is not known to imply anything outside of minicrypt, the land of secret-key cryptography, but, on the other hand, we do no know how to construct it without the heavy hammers in obfustopia. In this work, we show that (subexponentially secure) secret-key functional encryption is powerful enough to construct indistinguishability obfuscation if we additionally assume the existence of (subexponentially secure) plain public-key encryption. In other words, secret-key functional encryption provides a bridge from cryptomania to obfustopia. On the technical side, our result relies on two main components. As our first contribution, we show how to use secret-key functional encryption to get “exponentially efficient indistinguishability obfuscation” (XIO), a notion recently introduced by Lin et al. (PKC’16) as a relaxation of IO. Lin et al. show how to use XIO and the LWE assumption to build IO. As our second contribution, we improve on this result by replacing its reliance on the LWE assumption with any plain public-key encryption scheme. Lastly, we ask whether secret-key functional encryption can be used to construct public-key encryption itself and therefore take us all the way from minicrypt to obfustopia. A result of Asharov and Segev (FOCS’15) shows that this is not the case under black-box constructions, even for exponentially secure functional encryption. We show, through a non-black-box construction, that subexponentially secure-key functional encryption indeed leads to public-key encryption. The resulting public-key encryption scheme, however, is at most quasi-polynomially secure, which is insufficient to take us to obfustopia

From Cryptomania to Obfustopia through Secret-Key Functional Encryption

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The Birth of Cryptographic Obfuscation -- A Survey

The first candidate indistinguishability obfuscator (iO) of Garg et al. (FOCS 2013) changed the previously pessimistic attitude towards general-purpose cryptographic obfuscation. The potential realizability of such a powerful tool motivated a plethora of applications, including solutions for long-standing open problems, from almost all areas of cryptography. At the same time, the question of whether iO is realizable under standard assumptions is still open. In this work, we review the rapid development of candidate constructions and organize the results of the first four years since the breakthrough. Our goal is to give a bird\u27s-eye view of the infancy of cryptographic obfuscation, providing insight into the most important ideas and techniques