The known constructions of negligible error (non-malleable) two-source extractors can be broadly classified in three categories: (1) Constructions where one source has min-entropy rate about $1/2$, the other source can have small min-entropy rate, but the extractor doesn't guarantee non-malleability. (2) Constructions where one source is uniform, and the other can have small min-entropy rate, and the extractor guarantees non-malleability when the uniform source is tampered. (3) Constructions where both sources have entropy rate very close to $1$ and the extractor guarantees non-malleability against the tampering of both sources. We introduce a new notion of collision resistant extractors and in using it we obtain a strong two source non-malleable extractor where we require the first source to have $0.8$ entropy rate and the other source can have min-entropy polylogarithmic in the length of the source. We show how the above extractor can be applied to obtain a non-malleable extractor with output rate $\frac 1 2$, which is optimal. We also show how, by using our extractor and extending the known protocol, one can obtain a privacy amplification secure against memory tampering where the size of the secret output is almost optimal.

翻译：已知的具有可忽略误差的（非 malleable）双源提取器结构大致可分为三类：（1）一类源的最小熵率约为 $1/2$，另一类源的最小熵率可较小，但该提取器不保证非 malleability。（2）一类源为均匀分布，另一类源的最小熵率可较小，且该提取器在均匀源被篡改时保证非 malleability。（3）两类源的熵率均非常接近 $1$，且该提取器保证对两类源的篡改具有非 malleability。我们引入了一种新的抗冲突提取器概念，并利用它构建了一个强双源非 malleable 提取器，其中要求第一个源的熵率为 $0.8$，另一个源的最小熵率可为源长度的多对数。我们展示了如何将该提取器应用于获得输出率为 $1/2$ 的最优非 malleable 提取器。我们还展示了如何利用我们的提取器并扩展已知协议，获得一种针对内存篡改安全的隐私放大方案，其中秘密输出的大小几乎最优。