Paper 2009/283

Short and Stateless Signatures from the RSA Assumption

Susan Hohenberger and Brent Waters


We present the first signature scheme which is ''short'', stateless and secure under the RSA assumption in the standard model. Prior short, standard model signatures in the RSA setting required either a strong complexity assumption such as Strong RSA or (recently) that the signer maintain state. A signature in our scheme is comprised of one element in ZN* and one integer. The public key is also short, requiring only the modulus N, one element of ZN*, one integer, one PRF seed and some short chameleon hash parameters. To design our signature, we employ the known generic construction of fully-secure signatures from weakly-secure signatures and a chameleon hash. We then introduce a new proof technique for reasoning about weakly-secure signatures. This technique enables the simulator to predict a prefix of the message on which the adversary will forge and to use knowledge of this prefix to embed the challenge. This technique has wider applications beyond RSA. We also use it to provide an entirely new analysis of the security of the Waters signatures: the only short, stateless signatures known to be secure under the Computational Diffie-Hellman assumption in the standard model.

Note: Added reference to more efficient chameleon hash functions.

Available format(s)
Public-key cryptography
Publication info
Published elsewhere. This is the full version of the paper in CRYPTO 2009.
Contact author(s)
bwaters @ cs utexas edu
2010-03-11: last of 6 revisions
2009-06-16: received
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      author = {Susan Hohenberger and Brent Waters},
      title = {Short and Stateless Signatures from the RSA Assumption},
      howpublished = {Cryptology ePrint Archive, Paper 2009/283},
      year = {2009},
      note = {\url{}},
      url = {}
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