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首页> 外文会议>IMA conference on cryptography and coding >How Low Can You Go? Short Structure-Preserving Signatures for Diffie-Hellman Vectors
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How Low Can You Go? Short Structure-Preserving Signatures for Diffie-Hellman Vectors

机译：你能走多低？ Diffie-Hellman向量的短结构保留签名

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Structure-Preserving Signatures (SPSs) are an important tool for the design of modular cryptographic protocols. It has been proven that such schemes in the most efficient Type-3 bilinear group setting have a lower bound of 3-element signatures, which must include elements from both base groups, and a verification overhead of at least 2 Pairing-Product Equations (PPEs). Very recently, Ghadafi (ESORICS 2017) showed that by restricting the message space to the set of Diffie-Hellman pairs (which does not hinder applicability of the schemes), some of the existing lower bounds for the single message case can be circumvented. However, the case of signing multiple messages, which is required for many applications, was left as an open problem since the techniques used for signing single messages do not seem to lend themselves to the multi-message setting. In this work we investigate this setting and answer the question in the affirmative. We construct schemes that sign vectors of messages and which yield shorter signatures than optimal schemes for vectors of unilateral messages. More precisely, we construct 2 fully randomiazble schemes that sign vectors of Diffie-Hellman pairs yielding signatures consisting of only 2 elements regardless of the size of the vector signed. We also construct a unilateral scheme that signs a pair of messages yielding signatures consisting of 3 elements from the shorter base group. All of our schemes require a single PPE for verification (not counting the cost of verifying the well-formedness of the messages). Thus, all of our schemes compare favourably to all existing schemes with respect to signature size and verification overhead. Even when considering single messages, our first 2 schemes compare favourably to the best existing schemes in many aspects including the verification overhead and the key size.
机译：保留结构签名（SPS）是用于设计模块化密码协议的重要工具。已经证明，在最高效的Type-3双线性组设置中，此类方案具有3元素签名的下限，该签名必须包括两个基本组中的元素，并且验证开销至少为2配对乘积方程式（PPE） ）。最近，Ghadafi（ESORICS 2017）表明，通过将消息空间限制为Diffie-Hellman对的集合（这不会妨碍方案的适用性），可以规避单个消息案例的某些现有下界。但是，许多应用程序所需的对多条消息进行签名的情况仍然是一个悬而未决的问题，因为用于对单条消息进行签名的技术似乎并不适合多消息设置。在这项工作中，我们将调查此设置，并回答肯定的问题。我们构造了对消息向量进行签名的方案，并且比对单边消息向量进行优化的方案所产生的签名更短。更确切地说，我们构造了2个完全可随机化的方案，这些方案对Diffie-Hellman对的向量进行签名，从而产生仅由2个元素组成的签名，而与所签名向量的大小无关。我们还构建了一个单边方案，该方案对一对消息进行签名，从而产生由较短基组的3个元素组成的签名。我们所有的方案都需要单个PPE进行验证（不计算验证消息格式正确的成本）。因此，就签名大小和验证开销而言，我们所有的方案都优于所有现有方案。即使在考虑单个消息时，我们的前两种方案在许多方面（包括验证开销和密钥大小）也可以与最佳的现有方案进行比较。

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