最优树哈希模式：树的所有层次都有叶子的情况
Optimal Tree Hash Modes: the Case of Trees Having their Leaves at All the Levels
摘要：
最近的工作表明，我们如何可以优化一个基于树的操作模式的哈希函数的输入消息块和摘要的大小是相同的，受约束的，所涉及的树结构有它的所有叶子在相同的深度。在这项工作中，我们表明，我们可以进一步优化这种模式的运行时间，通过使用一棵树，在其所有级别的叶子。我们假设输入消息块的大小是摘要大小的倍数，并用$d$表示块大小与摘要大小的比值。运行时间是根据哈希函数执行的操作数量来评估的，即对其底层函数的调用数量。事实证明，可以使用$\lceil l/2 \rceil$处理器在底层函数的$\lceil \log_{d+1} (l/2) \rceil+2$求值中计算摘要，其中$l$是消息的块数。其他感兴趣的结果进行了讨论，如高度受限的树的并行运行时间的优化。
英文摘要：
A recent work shows how we can optimize a tree based mode of operation for a hash function where the sizes of input message blocks and digest are the same, subject to the constraint that the involved tree structure has all its leaves at the same depth. In this work, we show that we can further optimize the running time of such a mode by using a tree having leaves at all its levels. We make the assumption that the input message block has a size a multiple of that of the digest and denote by $d$ the ratio block size over digest size. The running time is evaluated in terms of number of operations performed by the hash function, i.e. the number of calls to its underlying function. It turns out that a digest can be computed in $\lceil \log_{d+1} (l/2) \rceil+2$ evaluations of the underlying function using $\lceil l/2 \rceil$ processors, where $l$ is the number of blocks of the message. Other results of interest are discussed, such as the optimization of the parallel running time for a tree of restricted height.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
