Adversary-Dependent Lossy Trapdoor Function from Hardness of Factoring Semi-smooth RSA Subgroup Moduli
Adversary-Dependent Lossy Trapdoor Function from Hardness of Factoring Semi-smooth RSA Subgroup Moduli
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DOI：
10.1007/978-3-662-53008-5_1
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发表时间：
2016-08
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影响因子：
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通讯作者：
Takashi Yamakawa;Shota Yamada;Goichiro Hanaoka;N. Kunihiro
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文献类型：
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作者：
Takashi Yamakawa;Shota Yamada;Goichiro Hanaoka;N. Kunihiro
由Peikert和沃茨（STOC'08）提出的有耗陷门函数（LTDFs）在密码学中具有许多应用。它们是基于各种假设构建的，其中包括二次剩余（QR）和决策复合剩余（DCR）假设，这是基于因子分解的决策假设。然而，没有已知的基于因子分解假设或其他因子分解相关搜索假设的LTDF构造。在本文中，我们首先定义了一个概念adversary-dependent有损陷门函数（ad-LTDFs），它是LTDFs的一个较弱的变体。基于Groth（TCC'05）提出的半光滑RSA子群（SS）模的特殊形式的RSA模的分解困难性，构造了一个ad-LTDF。此外，我们表明，广告LTDFs可以取代LTDFs在许多应用中。特别是，我们获得了第一个基于因子分解的确定性加密方案，满足Boldyreva等人定义的安全概念。（NIPPTO '08），而不依赖于决策假设。除了直接应用ad-LTDFs之外，基于因子分解假设w.r.t. SS模量
Lossy trapdoor functions (LTDFs), proposed by Peikert and Waters (STOC’08), are known to have a number of applications in cryptography. They have been constructed based on various assumptions, which include the quadratic residuosity (QR) and decisional composite residuosity (DCR) assumptions, which are factoring-baseddecisionassumptions. However, there is no known construction of an LTDF based on the factoring assumption or other factoring-related search assumptions. In this paper, we first define a notion ofadversary-dependent lossy trapdoor functions(ad-LTDFs) that is a weaker variant of LTDFs. Then we construct an ad-LTDF based on the hardness of factorizing RSA moduli of a special form called semi-smooth RSA subgroup (SS) moduli proposed by Groth (TCC’05). Moreover, we show that ad-LTDFs can replace LTDFs in many applications. Especially, we obtain the first factoring-based deterministic encryption scheme that satisfies the security notion defined by Boldyreva et al. (CRYPTO’08) without relying on a decision assumption. Besides direct applications of ad-LTDFs, by a similar technique, we construct a chosen ciphertext secure public key encryption scheme whose ciphertext overhead is the shortest among existing schemes based on the factoring assumption w.r.t. SS moduli.