{"id":168210,"date":"2012-03-01T00:00:00","date_gmt":"2012-03-01T00:00:00","guid":{"rendered":"https:\/\/www.microsoft.com\/en-us\/research\/msr-research-item\/functional-re-encryption-and-collusion-resistant-obfuscation\/"},"modified":"2018-10-16T20:10:18","modified_gmt":"2018-10-17T03:10:18","slug":"functional-re-encryption-and-collusion-resistant-obfuscation","status":"publish","type":"msr-research-item","link":"https:\/\/www.microsoft.com\/en-us\/research\/publication\/functional-re-encryption-and-collusion-resistant-obfuscation\/","title":{"rendered":"Functional Re-encryption and Collusion-Resistant Obfuscation"},"content":{"rendered":"

We introduce a natural cryptographic functionality called functional re-encryption<\/em>. Informally, this functionality, for a public-key encryption scheme and a function F<\/em> with n<\/em> possible outputs, transforms (\u201cre-encrypts\u201d) an encryption of a message m<\/em> under an \u201cinput public key\u201d pk<\/span> into an encryption of the same message m<\/em> under one of the n<\/em> \u201coutput public keys\u201d, namely the public key indexed by F<\/em>(m<\/em>).<\/p>\n

In many settings, one might require that the program implementing the functional re-encryption functionality should reveal nothing about both the input secret key sk<\/span> as well as the function F<\/em>. As an example, consider a user Alice who wants her email server to share her incoming mail with one of a set of n<\/em> recipients according to an access policy specified by her function F<\/em>, but who wants to keep this access policy private from the server. Furthermore, in this setting, we would ideally obtain an even stronger guarantee: that this information remains hidden even when some of the n<\/em> recipients may be corrupted.<\/p>\n

To formalize these issues, we introduce the notion of collusion-resistant obfuscation<\/em> and define this notion with respect to average-case secure obfuscation (Hohenberger et al.<\/em> – TCC 2007). We then provide a construction of a functional re-encryption scheme for any function F<\/em> with a polynomial-size domain and show that it satisfies this notion of collusion-resistant obfuscation. We note that collusion-resistant security can be viewed as a special case of dependent auxiliary input security (a setting where virtually no positive results are known), and this notion may be of independent interest.<\/p>\n

Finally, we show that collusion-resistant obfuscation of functional re-encryption for a function F<\/em> gives a way to obfuscate F<\/em> in the sense of Barak et al.<\/em> (CRYPTO 2001), indicating that this task is impossible for arbitrary (polynomial-time computable) functions F<\/em>.<\/p>\n","protected":false},"excerpt":{"rendered":"

We introduce a natural cryptographic functionality called functional re-encryption. Informally, this functionality, for a public-key encryption scheme and a function F with n possible outputs, transforms (\u201cre-encrypts\u201d) an encryption of a message m under an \u201cinput public key\u201d pk into an encryption of the same message m under one of the n \u201coutput public keys\u201d, […]<\/p>\n","protected":false},"featured_media":0,"template":"","meta":{"msr-url-field":"","msr-podcast-episode":"","msrModifiedDate":"","msrModifiedDateEnabled":false,"ep_exclude_from_search":false,"_classifai_error":"","footnotes":""},"msr-content-type":[3],"msr-research-highlight":[],"research-area":[13561,13558],"msr-publication-type":[193716],"msr-product-type":[],"msr-focus-area":[],"msr-platform":[],"msr-download-source":[],"msr-locale":[268875],"msr-post-option":[],"msr-field-of-study":[],"msr-conference":[],"msr-journal":[],"msr-impact-theme":[],"msr-pillar":[],"class_list":["post-168210","msr-research-item","type-msr-research-item","status-publish","hentry","msr-research-area-algorithms","msr-research-area-security-privacy-cryptography","msr-locale-en_us"],"msr_publishername":"Springer","msr_edition":"Theory of Cryptography - 9th Theory of Cryptography Conference, TCC 2012, Taormina, Sicily, Italy, March 19-21, 2012. Proceedings","msr_affiliation":"","msr_published_date":"2012-03-01","msr_host":"","msr_duration":"","msr_version":"","msr_speaker":"","msr_other_contributors":"","msr_booktitle":"Theory of Cryptography - 9th Theory of Cryptography Conference, TCC 2012, Taormina, Sicily, Italy, March 19-21, 2012. 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