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

Salient in many cryptosystems, the exponent-inversion technique beganwithout randomization in the random oracle model (SCIS ’03, PKC ’04), evolvedinto 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-Boyensignatures are shown to be unforgeable against q-chosen-message attacks, while avariant 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), wepropose dual form exponent-inversion Boneh-Boyen signatures and Gentry-IBE, withsecurity proven under the symmetric external Diffie-Hellman (SXDH) assumption.Starting from our signature scheme, we extend it into P-signatures (TCC ’08), resultingin the first anonymous credential scheme from the SXDH assumption, serving as acompetitive alternative to the static-assumption construction of Abe et al. (JoC ’16).Moreover, from our Gentry-IBE variant, we propose an accountable-authority IBEscheme 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.