{"id":327569,"date":"2016-11-27T21:34:41","date_gmt":"2016-11-28T05:34:41","guid":{"rendered":"https:\/\/www.microsoft.com\/en-us\/research\/?post_type=msr-research-item&p=327569"},"modified":"2018-10-16T21:29:09","modified_gmt":"2018-10-17T04:29:09","slug":"executable-proofs-input-size-hiding-secure-computation-new-ideal-world","status":"publish","type":"msr-research-item","link":"https:\/\/www.microsoft.com\/en-us\/research\/publication\/executable-proofs-input-size-hiding-secure-computation-new-ideal-world\/","title":{"rendered":"Executable Proofs, Input-Size Hiding Secure Computation and a New Ideal World"},"content":{"rendered":"

In STOC 1987, Goldreich, Micali and Wigderson\u00a0[GMW87 (opens in new tab)<\/span><\/a><\/span>] proved a fundamental result: it is possible to securely evaluate any function. Their security formulation consisted of transforming a real-world adversary into an ideal-world one and became a de facto standard for assessing security of protocols.<\/p>\n

In this work we propose a new approach for the ideal world. Our new definition preserves the unconditional security of ideal-world executions and follows the spirit of the real\/ideal world paradigm. Moreover we show that our definition is equivalent to that of\u00a0[GMW87 (opens in new tab)<\/span><\/a><\/span>] when the input size is public, thus it is a strict generalization of\u00a0[GMW87 (opens in new tab)<\/span><\/a><\/span>].<\/p>\n

In addition, we prove that our new formulation is useful by showing that it allows the construction of protocols for input-size hiding secure two-party computation for any two-party functionality under standard assumptions and secure against malicious adversaries. More precisely we show that in our model, in addition to securely evaluating every two-party functionality, one can also protect the input-size privacy of one of the two players. Such an input-size hiding property is not implied by the standard definitions for two-party computation and is not satisfied by known constructions for secure computation. This positively answers a question posed by\u00a0[LNO13 (opens in new tab)<\/span><\/a><\/span>] and \u00a0[CV12 (opens in new tab)<\/span><\/a><\/span>]. Finally, we show that obtaining such a security notion under a more standard definition (one with a more traditional ideal world) would imply a scheme for \u201cproofs of polynomial work\u201d, a primitive that seems unlikely to exist under standard assumptions.<\/p>\n

Along the way, we will introduce the notion of \u201cexecutable proof\u201d, which will be used in our ideal-world formulation and may be of independent interest.<\/p>\n","protected":false},"excerpt":{"rendered":"

In STOC 1987, Goldreich, Micali and Wigderson\u00a0[GMW87] proved a fundamental result: it is possible to securely evaluate any function. Their security formulation consisted of transforming a real-world adversary into an ideal-world one and became a de facto standard for assessing security of protocols. In this work we propose a new approach for the ideal world. 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