Lemma 8 definition

Lemma 8. If Protocol A is used in Scenario 1.1, there exist real-valued positive constants b and c with b < c such that N bN and N cN for su ciently large N . For the proof of Lemma 8, we need the following fact on binomial ▇▇▇ cients.
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Lemma 8. AUX [r] contains at most k non-⊥ values, plus possibly the default value ⊥. 49 Proof Let us assume that AUX [r] contains (k + 1) non-⊥ values. If a value belongs to this set, it is the 50 value of the local variable auxi of a correct process pi, which appears at least W times in the multiset 51 viewi[r, 1] (line 5). Moreover, due to SMV-No-duplicity property, a process (correct or Byzantine) 52 contributes to at most one of these values. It follows from these observations that, if AUX [r] contains 54 (k+1) non-⊥ values, (k+1)W distinct processes have contributed to AUX [r], i.e., have SMV-broadcast
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Examples of Lemma 8 in a sentence

  • Lemma 8 If the messages ⟨ack v, ph⟩ and ⟨ack v′, ph⟩ are sent by correct processes, then v = v′.

  • Lemma 8 If the messages (ack v, ph) and (ack v′, ph) are sent by correct processes, then v = v′.

  • From Lemma 8 and Lemma 9, we can easily conclude this Corollary 2.

  • Note that Definition 6, and hence the statement of Lemma 8, is formally slightly stronger than the corresponding definition in [17] because it not only requires that the length of the extractor output is roughly equal to the min-entropy of the source plus the number of random bits, but that these bits even reappear as a part of the output.

  • Termination is in at most log2(δ(U )/s) rounds, deduced from Lemma 8.

  • By Lemma 8 each cell can be partitioned into ((k + 1)mk)k−1 simplexes.

  • Due to Lemma 8, as long as an honest party activates Election, at least 2ƒ + 1 distinct PD instances have completed, which means these PD instances’ senders can produce valid com- pleteness done proofs.

  • In a similar argument as Lemma 8 the window of observation for message arrival for Round 3 is [γ-2d, γ+d].

  • If Sj = Sjj, since both j and ▇▇ preserved the E-influence, so does every i in the sequence described in item (i) of Lemma 8, because every i contains either j or jj.

  • From Lemma 8, we know all other honest parties also will invoke Election[ id, k ].