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Universal hashing found a lot of applications in computer science. In cryptography the most important fact about universal families is the so called Leftover Hash Lemma, proved by Impagliazzo, Levin a...
Quite surprisingly, we show that both limitations of the LHL --- large entropy loss and large seed --- can often be overcome (or, at least, mitigated) in various quite general scenarios. First, we sho...
The famous Leftover Hash Lemma (LHL) states that (almost) universal hash functions are good randomness extractors. Despite its numerous applications, LHL-based extractors su er from the following tw...

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