A fundamental question in leakage-resilient cryptography is: can leakage resilience always be amplified by parallel repetition? It is natural to expect that if we have a leakage-resilient primitive tolerating $ell$ bits of leakage, we can take $n$ copies of it to form a system tolerating $nell$ bits of leakage. In this paper, we show that this is not always true. We construct a public key encryption system which is secure when at most $ell$ bits are leaked, but if we take $n$ copies of the system and encrypt a share of the message under each using an $n$-out-of-$n$ secret-sharing scheme, leaking $nell$ bits renders the system insecure. Our results hold either in composite order bilinear groups under a variant of the subgroup decision assumption emph{or} in prime order bilinear groups under the decisional linear assumption. We note that the $n$ copies of our public key systems share a common reference parameter.
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机译:泄漏弹性密码学的基本问题是:可以通过平行重复总是放大泄漏弹性吗?预计,如果我们有泄漏弹性原始的$ ell泄漏,我们可以使用它的$ n $副本来形成容忍$ NELL $ B泄漏的系统。在本文中,我们表明这并不总是如此。我们构建一个公共密钥加密系统,当大多数$ $ BITS泄露时,它是安全的,但如果我们以$ N $副本乘坐系统并使用$ n $ -out加密每条消息的份额。 $ N $秘密分享方案,泄漏$ NELL $ BITS使系统不安全。我们的结果在副组决定假设的变种下的复合订单Bilinear群体在果实线性假设下的亚组决定假设表明假设{或}。我们注意到我们公钥系统的$ N $副本共享公共参考参数。
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