Paper 2011/057

Another Look at RSA Signatures With Affine Padding

Jean-Sébastien Coron, David Naccache, and Mehdi Tibouchi

Abstract

Affine-padding {\sc rsa} signatures consist in signing ωm+α instead of the message m for some fixed constants ω,α. A thread of publications progressively reduced the size of m for which affine signatures can be forged in polynomial time. The current bound is logmN3 where N is the {\sc rsa} modulus' bit-size. Improving this bound to N4 has been an elusive open problem for the past decade.\smallskip In this invited talk we consider a slightly different problem: instead of minimizing m's size we try to minimize its {\sl entropy}. We show that affine-padding signatures on entropy-bit messages can be forged in polynomial time. This problem has no direct cryptographic impact but allows to better understand how malleable the {\sc rsa} function is. In addition, the techniques presented in this talk might constitute some progress towards a solution to the longstanding forgery open problem.\smallskip\smallskip We also exhibit a sub-exponential time technique (faster than factoring) for creating affine modular relations between strings containing three messages of size and a fourth message of size .\smallskip Finally, we show than -relations can be obtained in specific scenarios, {\sl e.g.} when one can pad messages with two independent patterns or when the modulus' most significant bits can be chosen by the opponent.\smallskip

Note: Authors were missing in the previous submission. Got that fixed.

Metadata
Available format(s)
PDF
Publication info
Published elsewhere. Unknown status
Keywords
RSAdigital signatureforgerypadding
Contact author(s)
david naccache @ ens fr
History
2016-04-25: last of 3 revisions
2011-01-31: received
See all versions
Short URL
https://ia.cr/2011/057
License
Creative Commons Attribution
CC BY

BibTeX

@misc{cryptoeprint:2011/057,
      author = {Jean-Sébastien Coron and David Naccache and Mehdi Tibouchi},
      title = {Another Look at {RSA} Signatures With Affine Padding},
      howpublished = {Cryptology {ePrint} Archive, Paper 2011/057},
      year = {2011},
      url = {https://eprint.iacr.org/2011/057}
}
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