Paper 2013/194

On the Impossibility of Cryptography with Tamperable Randomness

Per Austrin, Kai-Min Chung, Mohammad Mahmoody, Rafael Pass, and Karn Seth


We initiate a study of the security of cryptographic primitives in the presence of efficient tampering attacks to the randomness of honest parties. More precisely, we consider p-tampering attackers that may \emph{efficiently} tamper with each bit of the honest parties' random tape with probability p, but have to do so in an ``online'' fashion. Our main result is a strong negative result: We show that any secure encryption scheme, bit commitment scheme, or zero-knowledge protocol can be ``broken'' with probability $p$ by a $p$-tampering attacker. The core of this result is a new Fourier analytic technique for biasing the output of bounded-value functions, which may be of independent interest. We also show that this result cannot be extended to primitives such as signature schemes and identification protocols: assuming the existence of one-way functions, such primitives can be made resilient to (\nicefrac{1}{\poly(n)})-tampering attacks where $n$ is the security~parameter.

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Published elsewhere. Unknown status
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austrin @ kth se
chung @ cs cornell edu
mahmoody @ gmail com
rafael @ cs cornell edu
karn @ cs cornell edu
2018-10-16: last of 5 revisions
2013-04-09: received
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      author = {Per Austrin and Kai-Min Chung and Mohammad Mahmoody and Rafael Pass and Karn Seth},
      title = {On the Impossibility of Cryptography with Tamperable Randomness},
      howpublished = {Cryptology ePrint Archive, Paper 2013/194},
      year = {2013},
      note = {\url{}},
      url = {}
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