Paper 2013/194

On the Impossibility of Cryptography with Tamperable Randomness

Per Austrin, Kai-Min Chung, Mohammad Mahmoody, 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.