Paper 2010/122

Security of Encryption Schemes in Weakened Random Oracle Models

Akinori Kawachi, Akira Numayama, Keisuke Tanaka, and Keita Xagawa


Liskov proposed several weakened versions of the random oracle model, called {\em weakened random oracle models} (WROMs), to capture the vulnerability of ideal compression functions, which are expected to have the standard security of hash functions, i.e., collision resistance, second-preimage resistance, and one-wayness properties. The WROMs offer additional oracles to break such properties of the random oracle. In this paper, we investigate whether public-key encryption schemes in the random oracle model essentially require the standard security of hash functions by the WROMs. In particular, we deal with four WROMs associated with the standard security of hash functions; the standard, collision tractable, second-preimage tractable, first-preimage tractable ones (ROM, CT-ROM, SPT-ROM, and FPT-ROM, respectively), done by Numayama et al. for digital signature schemes in the WROMs. We obtain the following results: (1) The OAEP is secure in all the four models. (2) The encryption schemes obtained by the Fujisaki-Okamoto conversion (FO) are secure in the SPT-ROM. However, some encryption schemes with FO are insecure in the FPT-ROM. (3) We consider two artificial variants wFO and dFO of FO for separation of the WROMs in the context of encryption schemes. The encryption schemes with wFO (dFO, respectively) are secure in the CT-ROM (ROM, respectively). However, some encryption schemes obtained by wFO (dFO, respectively) are insecure in the SPT-ROM (CT-ROM, respectively). These results imply that standard encryption schemes such as the OAEP and FO-based one do not always require the standard security of hash functions. Moreover, in order to make our security proofs complete, we construct an efficient sampling algorithm for the binomial distribution with exponentially large parameters, which was left open in Numayama et al.'s paper.

Available format(s)
Public-key cryptography
Publication info
Published elsewhere. This is a full version of a paper appearing in PKC 2010.
public-key encryption schemesweakened random oracle modelsOAEPFujisaki-Okamoto conversion
Contact author(s)
xagawa5 @ is titech ac jp
2010-03-05: received
Short URL
Creative Commons Attribution


      author = {Akinori Kawachi and Akira Numayama and Keisuke Tanaka and Keita Xagawa},
      title = {Security of Encryption Schemes in Weakened Random Oracle Models},
      howpublished = {Cryptology ePrint Archive, Paper 2010/122},
      year = {2010},
      note = {\url{}},
      url = {}
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