Provably Secure Multisignatures in Formal Security Model and Their Optimality

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  • KOMANO Yuichi
    Toshiba Corporation The Institute of Electronics, Information and Communication Engineers
  • OHTA Kazuo
    University of Electro-Communications The Institute of Electronics, Information and Communication Engineers
  • SHIMBO Atsushi
    Toshiba Corporation The Institute of Electronics, Information and Communication Engineers
  • KAWAMURA Shinichi
    Toshiba Corporation The Institute of Electronics, Information and Communication Engineers

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We first model the formal security model of multisignature scheme following that of group signature scheme. Second, we prove that the following three probabilistic multisignature schemes based on a trapdoor permutation have tight security; PFDH (probabilistic full domain hash) based multisignature scheme (PFDH-MSS), PSS (probabilistic signature scheme) based multisignature scheme (PSS-MSS), and short signature PSS based multisignature scheme (S-PSS-MSS). Third, we give an optimal proof (general result) for multisignature schemes, which derives the lower bound for the length of random salt. We also estimate the upper bound for the length in each scheme and derive the optimal length of a random salt. Two of the schemes are promising in terms of security tightness and optimal signature length. In appendix, we describe a multisignature scheme using the claw-free permutation and discuss its security.

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