More Efficient Privacy Amplification with Non-Uniform Random Seeds via Dual Universal Hash Function

We explicitly construct random hash functions for privacy amplification that are secure even with the random seed length below the previous theoretical bound, and still allow efficient implementations with complexity $O(n\log n)$ for input length $n$. We also evaluate the security parameter of these random hash functions under the condition that their random seeds are not necessarily uniformly random. The key idea is the concept of dual universal_2 hash function introduced recently.