Extractors Clause Samples
Extractors. Processes up to 3000 pieces per hour. • One, Two, or, Three Sided Opening. • Includes counting and monitoring system that counts pieces processed. • Capable of processing various sizes of intermixed mail up to and including #11 envelopes, heights to 5-1/4”. • Mailroom furniture shall be appropriate for the mailroom category being it is being offered in. • Mailroom work tables, pedestals, bins etc. must be constructed of wood, steel or plastic bases with steel, laminate or wood tops that can support the daily use and weight of mailroom product and equipment. • Only furniture specifically related to the category/group of equipment may be purchased under this category. • Mailroom furniture shall not be specific to a piece of equipment or a category/group. • Mailroom free standing mail sorter tables, case works, mail carts etc. must be constructed of wood, steel or plastic bases with steel, laminate or wood tops that can support the dialing use and weight of mailroom activity.
Extractors. Because in this paper Eve is always assumed to have some external information E about ▇▇▇▇▇ and ▇▇▇’s secrets, we need the following variant, defined in [DORS08, Definition 2], of the definition of strong extractors of [NZ96]: ˜
Extractors. Because in this paper Eve is always assumed to have some external information E about ▇▇▇▇▇ and ▇▇▇’s secrets, we need the following variant, defined in [DORS08, Definition 2], of the definition of strong extractors of [NZ96]: ˜ { } → { } Definition 2. Let Ext : 0, 1 n 0, 1 l be a polynomial time probabilistic function that uses r bits of randomness. We say that Ext is an average-case (n, m, l, ε)-strong extractor if for all pairs of random variables (W, E) such that w ∈ W is an n-bit string and H∞(W | E) ≥ m, we have SD((Ext(W ; X), X, E), (Ul, X, E) ≤ ε, where X is the uniform distribution over {0, 1} . We should note that some strong extractors (in particular, universal hash- ing [CW79,HILL99]) are already average-case extractors, and any strong extrac- tor can be made average-case with a slight increase in input entropy [DORS08, Section 2.5]. The following (new) lemma shows that strings extracted by average-case extractors have high average min-entropy, even given the seed. The proof can be found in the full version [KR08b].
Lemma 1. Let Ext be a an average-case (n, m, l, ε)-strong extractor. Then if min l, log 1 − 1. H˜ ∞(.W | E)Σ ≥ m, and W consists of n-bit strings, H˜ ∞(Ext(W, X) | X, E) ≥
Extractors. Let us now define the basic types of randomness extractors. Definition 1.4. (Deterministic extractor) A function E : {0, 1}n → {0, 1}m is a deterministic (k, s)-extractor if for every distribution X over {0, 1}n with H∞(X) ≥ k the distribution E(X) is s-close to Um. As seen from the definition, deterministic extractors use only one ini- tial input – usually data produced by a weak random source. Although this is a very desirable property, it is insufficient for the use within some cryptographic techniques when the min-entropy source output serves as an extractor input. Still, a deterministic extractor can be useful for an arbi- trary cryptographic purpose, however, we have to be more strict about the source type. Such an example is ▇▇▇ ▇▇▇▇▇▇▇ source [39]. When we want to use the information gained from a weak random source meaningfully, we have to employ another type of extractor – a seeded one.