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On Tight Quantum Security of HMAC and NMAC in the Quantum …
WebbNote that a tight example needs to have arbitrarily large size in order to prove tightness of analysis, otherwise we can just use brute force for small graphs and A for large ones to get an algorithm that avoid that tight bound. Here, it shows that this algorithm gives 2-approximation no matter what size n is. WebbWarning: Using the substitution method, it is easy to prove a weaker bound than the one you’re supposed to prove. For instance, if the runtime is O(n), you might still be able to substitute cn2 into the recurrence and prove that the bound is O(n2). Which is technically true, but don’t let it mislead you into thinking it’s the best bound ... how to buy ligado bonds
Examples on Asymptotic Notation – Upper, Lower and …
Webbwith S-bit advice. Namely, we show how the problem reduces to proving S-wise direct product theorems or S-wise XOR lemmas for certain ranges of parameters. Fi-nally, we derive a new S-wise XOR lemma, which yields a tight non-uniform bound for length increasing pseudo-random generators, resolving a 10-year-old open prob- Webb1 As we explore in Exercise 2.3, the moment bound (2.3) with the optimal choice of kis 2 never worse than the bound (2.5) based on the moment-generating function. Nonethe-3 less, the Chernoff bound is most widely used in practice, possibly due to the ease of 4 manipulating moment generating functions. Indeed, a variety of important tail bounds Webb18 sep. 2016 · 14. I am interested in constructing random variables for which Markov or Chebyshev inequalities are tight. A trivial example is the following random variable. P ( X = 1) = P ( X = − 1) = 0.5. Its mean is zero, variance is 1 and P ( X ≥ 1) = 1. For this random variable chebyshev is tight (holds with equality). P ( X ≥ 1) ≤ Var ... how to buy life insurance online