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A fundamental question in leakage-resilient cryptography is: Can leakage resilience always be amplified by parallel repetition? It is natural to expect that if people have leakage-resilient primitive tolerating nl bits of leakage, they can take n copies of it to form a system tolerating nl bits of leakage. In this paper, the authors show that this is not always true. The authors construct a public key encryption system which is secure when at most l bits are leaked, but if they 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 nl bits renders the system insecure.
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