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2018.06.27

# 7. 确认时间

As discussed in Section 5, the convergence rate of $Risk(B,t)$ is slow, at least theoretically and under certain circumstances. Recall that the function $Risk(B,t)$ measures the probability that a certain block that did not precede $B$ at time $t$ will later come to precede it. Recall further that throughput this work we used arbitrary topological orderings (over blue blocks). In light if this, it would be interesting to seek for an ordering rule (over blue blocks) that would converge faster. We suspect this is not a trivial task, and leave its full investigation to future work.

The primary factor to the fact that PHANTOM cannot guarantee fast confirmation times is that membership in the blue set takes time to finalize. The waiting time for such finalization can be further increased if an attacker manages to balance the decision between $B \in BLUE_k(G)$ and $B \notin BLUE_k(G)$. Observe however that if a certain transaction $tx \in B$ admits no conflicts in $anticone(B)$, then $tx$ can be accepted even before the decision regarding $B$ is finalized.

PHANTOM无法保证快速确认时间这一事实的主要原因是，蓝色集合中的成员资格需要时间才能最终确定。如果攻击者在$B \in BLUE_k(G)$和$B \notin BLUE_k(G)$中设法平衡决定，那么等待时间会进一步增加。但是请注意，如果某个交易$tx \in B$承认在$anticone(B)$中没有冲突，甚至$tx$在关于$B$的决定已经完成之前就被接受。

A. Combining SPECTRE and PHANTOM

A. 结合SPECTRE和PHANTOM

SPECTRE is a DAG based protocol that can support large transaction throughput (similarly to PHANTOM) and very fast confirmations. SPECTRE does not output a linear order over blocks. Rather, every block $B$ admits a vote regarding the pairwise ordering of any two blocks $C$ and $D$, and the output is the majority vote regarding each pair. In SPECTRE, cycles of the sort “$B$ precedes $C$, $C$ precedes $D$, $D$ precedes $B$” may form.

SPECTER是一种基于DAG的协议，可以支持较大的交易吞吐量（与PHANTOM相似）并非常快速的确认。SPECTER不输出块的线性顺序。相反，每个块$B$承认关于任何两个块$C$和$D$的成对排序的投票,并且输出是关于每一对的最多数票。在SPECTRE中，“$B$在$C$之前，$C$在$D$之前，$D$在$B$之前”的环可能形成。

Furthermore, if an active balancing attack is taking place, for some pairs of blocks $(B, C)$ the SPECTRE relation might not become robust (in which case $Risk(B, t) \rightarrow 0$ is not guaranteed). Instead, a published block $B$ is guaranteed to robustly precede any block $C$ that was published later than $B$, unless $C$ was published shortly after $B$. We call this property Weak Liveness. In the context of the Payments application, this fact can only harm a user that signed and published two conflicting payments at approximately the same time.^{19}

Since PHANTOM does guarantee (strong) Liveness and a liner ordering, it is interesting to inquire whether we can enjoy the best of both worlds. We provide below a partial answer to this question.

Consider the following procedure: Given a blockDAG $G$,

1) mark blocks as blue or red according to PHANTOM’s colouring procedure

2) run SPECTRE on the subDAG $BLUE_k(G)$; this determines the pairwise ordering between any two $blue$ blocks $B$ and $C$

3) for any blue block $B$ and red block $C$, if $C \in past(B)$ then determine that $C$ precedes $B$, otherwise determine that $B$ precedes $C$

4) decide the pairwise ordering of any two red blocks in some arbitrary way that respects the topology ($B \in past(C) \Rightarrow B$ precedes $C$)

1) 根据PHANTOM的着色程序将块标记为蓝色或红色

2) 在subDAG $BLUE_k(G)$上运行SPECTRE； 这决定了任何两个$蓝色$块$B$和$C$之间成对排序

3) 对于任何蓝色块$B$和红色块$C$，如果$C \in past(B)$则确定$C$在$B$之前，否则确定$B$在$C$之前

4) 以某种符合拓扑的任意方式决定任意两个红色块的成对排序($B \in past(C) \Rightarrow B$在$C$之前)

Intuitively, we run SPECTRE on the set of blue blocks (as determined by PHANTOM), and complemented the pairwise ordering in a way that both penalizes red blocks and respects the topology. We argue that this protocol enjoys SPECTRE’s fast confirmation times and at the same time inherits the (regular) Liveness property of PHANTOM. To see the latter, observe that a Hourglass block would have a similar effect in SPECTRE——all blocks in its future will vote according to its vote. In particular, the pairwise relation of all previous blocks becomes as robust as the Hourglass block.

Note that this incremental improvement over vanilla SPECTRE is only possible because we allowed the protocol to assume something on the network’s topology, namely, that the communication delay diameter is upper bounded by $D_{max}$.

B. Summary

In summary, it is possible to achieve both fast confirmation times and Liveness by combining PHANTOM and SPECTRE. It is of yet unclear whether we can further achieve a linear ordering without compromising the fast confirmation times. Hopefully, we will provide answers to these questions in future work.

B. 总结 总之，通过组合PHANTOM和SPECTER可以实现快速确认时间和活性。目前还不清楚我们是否可以在不影响快速确认时间的情况下进一步实现线性排序。希望我们能在未来的工作中为这些问题提供答案。

^{19}In contrast, usually any user can engage with a smart contract and introduce conflicts inputs. Thus, Weak Liveness might potentially harm the usability of SPECTRE to the Smart Contracts application.

^{19}相比之下，通常任何用户都可以参与智能合约并引入冲突输入。因此，弱活性可能会损害SPECTER对智能合同应用程序的可用性。

##REFERENCES ##参考文献

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