International Association for Cryptologic Research

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Exponent-Inversion P-Signatures and Accountable Identity-Based Encryption from SXDH

Authors:
Tsz Hon Yuen , Faculty of Information Technology, Monash University
Sherman S. M. Chow , Department of Information Engineering, Chinese University of Hong Kong
Huangting Wu , Department of Information Engineering, Chinese University of Hong Kong
Cong Zhang , The State Key Laboratory of Blockchain and Data Security, Zhejiang University
Siu-Ming Yiu , Department of Computer Science, The University of Hong Kong
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DOI: 10.62056/ahsdkmp-3y
URL: https://cic.iacr.org//p/1/3/48
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Abstract:

Salient in many cryptosystems, the exponent-inversion technique began without randomization in the random oracle model (SCIS '03, PKC '04), evolved into the Boneh-Boyen short signature scheme (JoC '08) and exerted a wide influence. Seen as a notable case, Gentry's (EuroCrypt '06) identity-based encryption (IBE) applies exponent inversion on a randomized base in its identity-based trapdoors. Making use of the non-static q-strong Diffie-Hellman assumption, Boneh-Boyen signatures are shown to be unforgeable against q-chosen-message attacks, while a variant q-type decisional assumption is used to establish the security of Gentry-IBE. Challenges remain in proving their security under weaker static assumptions.

Supported by the dual form/system framework (Crypto '09, AsiaCrypt '12), we propose dual form exponent-inversion Boneh-Boyen signatures and Gentry-IBE, with security proven under the symmetric external Diffie-Hellman (SXDH) assumption. Starting from our signature scheme, we extend it into P-signatures (TCC '08), resulting in the first anonymous credential scheme from the SXDH assumption, serving as a competitive alternative to the static-assumption construction of Abe et al. (JoC '16). Moreover, from our Gentry-IBE variant, we propose an accountable-authority IBE scheme also from SXDH, surpassing the fully secure Sahai-Seyalioglu scheme (PKC '11) in efficiency and the generic Kiayias-Tang transform (ESORICS '15) in security. Collectively, we present a suite of results under static assumptions.

BibTeX
@article{cic-2024-34859,
  title={Exponent-Inversion P-Signatures and Accountable Identity-Based Encryption from SXDH},
  journal={cic},
  publisher={International Association for Cryptologic Research},
  volume={1, Issue 3},
  url={https://cic.iacr.org//p/1/3/48},
  doi={10.62056/ahsdkmp-3y},
  author={Tsz Hon Yuen and Sherman S. M. Chow and Huangting Wu and Cong Zhang and Siu-Ming Yiu},
  year=2024
}