More efficient privacy amplification with less random seeds

We explicitly construct random hash functions for privacy amplification (extractors) that require smaller random seed lengths than the previous literature, and still allow efficient implementations with complexity O(n log n) for input length n. Firstly, we construct two types of hash functions by using the finite-filed. Then, concatenating them, we construct other two types of hash functions. We compare our hash functions with existing hash function in an asymptotic setting under a fixed key generation rate.