Paper 2014/310

Sakai-Ohgishi-Kasahara Identity-Based Non-Interactive Key Exchange Revisited and More

Yu Chen, Qiong Huang, and Zongyang Zhang

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 two-party 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, its 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 adaptively secure based on the decisional bilinear Diffie-Hellman inversion (DBDHI) assumption. To the best of our knowledge, this is the first adaptively 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 require programmable hash functions in the multilinear setting. At the technical heart of our scheme, we generalize the definition of AHFs, and propose a generic construction which enables AHFs with previously unachieved parameters, which might be of independent interest. In addition, we present some new results about IB-NIKE. On the first place, we present a generic construction of multiparty IB-NIKE from extractable witness PRFs and existentially unforgeable signatures. On the second place, we investigate the relation between semi-adaptive security and adaptive security for IB-NIKE. Somewhat surprisingly, we show that these two notions are polynomially equivalent.

Note: In this revision, we show a generic construction of multiparty IB-NIKE from extractable witness PRFs and existentially unforgeable signatures. We also show that semi-adaptive security and adaptive security for IB-NIKE are polynomially equivalent.