Cryptology ePrint Archive: Report 2013/194

On the Impossibility of Cryptography with Tamperable Randomness

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

Abstract: 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.

Category / Keywords: Tampering, Randomness, Encryption.

Date: received 3 Apr 2013, last revised 14 Jun 2018

Contact author: austrin at kth se, chung@cs cornell edu, mahmoody@gmail com, rafael@cs cornell edu, karn@cs cornell edu

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Version: 20180614:181324 (All versions of this report)

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