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Adaptive Proofs Have Straightline Extractors (in the Random Oracle Model)

機(jī)譯：自適應(yīng)證明具有直線提取器（在隨機(jī)Oracle模型中）

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The concept of for proofs of knowledge was recently studied by Bernhard et al. They formalised adaptive security in the ROM and showed that the non-interactive version of the Schnorr protocol obtained using the Fiat-Shamir transformation is not adaptively secure unless the one-more discrete logarithm problem is easy. Their only construction for adaptively secure protocols used the Fischlin transformation [11] which yields protocols with . In this paper we provide two further key insights. Our main result shows that any adaptively secure protocol must have a straight-line extractor: even the most clever rewinding strategies cannot offer any benefits against adaptive provers. Then, we show that any Fiat-Shamir transformed -protocol is not adaptively secure unless a related problem which we call the -one-wayness problem is easy. This assumption concerns not just Schnorr but applies to a whole class of -protocols including e.g. Chaum-Pedersen and representation proofs. We also prove that -one-wayness is hard in an extension of the generic group model which, on its own is a contribution of independent interest. Taken together, these results suggest that the highly efficient proofs based on the popular Fiat-Shamir transformed -protocols should be used with care in settings where adaptive security of such proofs is important.
機(jī)譯：Bernhard等人最近研究了知識(shí)證明的概念。他們?cè)赗OM中形式化了自適應(yīng)安全性，并表明使用Fiat-Shamir變換獲得的Schnorr協(xié)議的非交互式版本不是自適應(yīng)安全的，除非一個(gè)以上的離散對(duì)數(shù)問題很容易解決。他們唯一用于自適應(yīng)安全協(xié)議的結(jié)構(gòu)是使用Fischlin轉(zhuǎn)換[11]，該協(xié)議產(chǎn)生的協(xié)議為。在本文中，我們提供了兩個(gè)進(jìn)一步的關(guān)鍵見解。我們的主要結(jié)果表明，任何自適應(yīng)安全協(xié)議都必須具有直線提取器：即使是最聰明的倒帶策略也無法提供針對(duì)自適應(yīng)證明的任何好處。然后，我們證明，除非菲亞特-沙米爾（Fiat-Shamir）變換的-protocol協(xié)議不是自適應(yīng)安全的，否則我們稱之為-單向問題的相關(guān)問題很容易解決。這種假設(shè)不僅涉及Schnorr，而且適用于整個(gè)協(xié)議類別，例如Chaum-Pedersen及其表示證明。我們還證明，單向性在通用組模型的擴(kuò)展中很困難，而該模型本身就是獨(dú)立利益的貢獻(xiàn)。綜上所述，這些結(jié)果表明，基于流行的Fiat-Shamir轉(zhuǎn)換協(xié)議的高效證明應(yīng)在這種證明的自適應(yīng)安全性很重要的環(huán)境中謹(jǐn)慎使用。

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