signature=8544f8b053d71af57dc8d660a85d9730,Sakai-Ohgishi-Kasahara Identity-Based Non-Interactive Key...

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本文深入研究了Sakai-Ohgishi-Kasahara（SOK）身份基非交互密钥交换（IB-NIKE）方案。在随机预言机模型中，我们提供了更紧致的安全性分析，并揭示了在不编程随机预言机的情况下，基于计算双线性 Diffie-Hellman 假设证明其安全性可能的困难。在标准模型下，我们使用适配性哈希函数和可区分混淆来实例化随机预言机，从而实现了一个基于决定性双线性 Diffie-Hellman 反转假设的完全适应性安全的IB-NIKE方案，这是首次在标准模型中无需显式使用多线性映射的全适应性安全方案。

Abstract

Identity-based non-interactive key exchange (IB-NIKE) is a powerful but a bit overlooked primitive in identity-based cryptography. While identity-based encryption and signature have been extensively investigated over the past three decades, IB-NIKE has remained largely unstudied. Currently, there are only few IB-NIKE schemes in the literature. Among them, Sakai-Ohgishi-Kasahara (SOK) scheme is the first efficient and secure IB-NIKE scheme, which has great influence on follow-up works. However, the SOK scheme required its identity mapping function to be modeled as a random oracle to prove security. Moreover, the existing security proof heavily relies on the ability of programming the random oracle. It is unknown whether such reliance is inherent.

In this work, we intensively revisit the SOK IB-NIKE scheme, and present a series of possible and impossible results in the random oracle model and the standard model. In the random oracle model, we first improve previous security analysis for the SOK IB-NIKE scheme by giving a tighter reduction. We then use meta-reduction technique to show that the SOK scheme is unlikely proven to be secure based on the computational bilinear Diffie-Hellman (CBDH) assumption without programming the random oracle. In the standard model, we show how to instantiate the random oracle in the SOK scheme with a concrete hash function from admissible hash functions (AHFs) and indistinguishability obfuscation. The resulting scheme is fully adaptive-secure based on the decisional bilinear Diffie-Hellman inversion (DBDHI) assumption. To the best of our knowledge, this is first fully adaptive-secure IB-NIKE scheme in the standard model that does not explicitly require multilinear maps. Previous schemes in the standard model either have merely selective security or use multilinear maps as a key ingredient. Of particular interest, we generalize the definition of AHFs, and propose a generic construction which enables AHFs with previously unachieved parameters.