Paper 2001/002

The One-More-RSA-Inversion Problems and the Security of Chaum's Blind Signature Scheme

M. Bellare, C. Namprempre, D. Pointcheval, and M. Semanko


We introduce a new class of computational problems which we call the ``one-more-RSA-inversion'' problems. Our main result is that two problems in this class, which we call the chosen-target and known-target inversion problems respectively, have polynomially-equivalent computational complexity. We show how this leads to a proof of security for Chaum's RSA-based blind signature scheme in the random oracle model based on the assumed hardness of either of these problems. We define and prove analogous results for ``one-more-discrete-logarithm'' problems. Since the appearence of the preliminary version of this paper, the new problems we have introduced have found other uses as well.

Available format(s)
Public-key cryptography
Publication info
Published elsewhere. An extended abstract of this paper, entitled ``The power of RSA inversion oracles and the security of Chaum's RSA-based blind signature scheme,'' appears in the Proceedings of the Financial Cryptography 01 conference. The full version here is to appear in the Journal of Cryptology.
Blind digital signature schemesdigital cashRSA
Contact author(s)
cnamprem @ cs ucsd edu
2002-06-17: last of 5 revisions
2001-01-05: received
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      author = {M.  Bellare and C.  Namprempre and D.  Pointcheval and M.  Semanko},
      title = {The One-More-RSA-Inversion Problems and the Security of Chaum's Blind Signature Scheme},
      howpublished = {Cryptology ePrint Archive, Paper 2001/002},
      year = {2001},
      note = {\url{}},
      url = {}
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