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Universal hashing techniques based on matrix multiplication

The article here says below, about a universal hashing technique based on matrix multiplications. "However, there is a little known method based on using a random matrix. It has lots of advantages - ...
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Is this a correct understanding of Universal Hash Functions?

I'm studying universal hash functions and have been reading several papers but now i'm focusing on Wegman and Carters original paper from 1979 (Universal classes of hash functions) and the H1 class. ...
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Asymptotic Hash Function and Concrete Hash Function

I'm reading Collision-Resistant Hashing: Towards Making UOWHFs Practical, and they say that its formalization is non-asymptotic. Why is the formalization non-asymptotic? What is an example of hash ...
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Precise meaning of various terms related to universal hash functions

I've been reading about universal hashing, but I'm confused by all these different terms and notations. Could someone help me understand the precise meaning or relation between the following terms: ...