When scaling a distributed ORAM to a two-party secure computation, the overhead is dominated by the number of pseudo-random generator (PRG) calls in generation and evaluation of a distributed point function (DPF), which are O (log n ) and O ( n ) respectively, where n is the number of data blocks. We propose a distributed ORAM scheme, in which the PRG calls are reduced to O (log( zn/λ )) for generation and O (2 ^{log( zn /λ)} ) for evaluation, where λ is the secure parameter and z is the length of outputs in DPF. Technically, we first extend the optimization of Function Secret Sharing (FSS), early termination for functions with small output groups, to the context of ORAM for secure computation. Then, we design a scheme named etoram to exploit the high efficiency achieved by early termination. In etoram, we introduce an access counter for each data block. Then, instead of {0,1} ^λ , the output of the point function becomes the maximum value of these counters, i.e.,{0,1} ^z . Data blocks are privately updated by masking random strings generated by their counters. In practice, according to different access rates, z ranges from 1 to log n in sequential mode and from 3 to log n in random mode if the total number of accesses is n .

中文翻译：

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Etoram：用于安全计算的更高效的ORAM

在将分布式ORAM缩放到两方安全计算时，开销由分布点函数（DPF）的生成和评估中的伪随机生成器（PRG）调用数量决定。 Ø （日志 ñ ）和 Ø （ ñ ）分别 ñ是数据块的数量。我们提出了一种分布式ORAM方案，其中PRG调用减少为Ø （日志（ zn /λ ）） Ø （2 ^{日志（ n /λ）} ）进行评估，其中λ 是安全参数， ž是DPF中输出的长度。从技术上讲，我们首先扩展功能秘密共享（FSS），用于具有小输出组的功能的提前终止，到ORAM的上下文进行安全计算。然后，我们设计了一个名为etoram的方案，以利用通过提前终止实现的高效率。在etoram中，我们为每个数据块引入一个访问计数器。然后，代替{0,1} ^λ ，点函数的输出变为这些计数器的最大值，即{0,1} ^ž 。数据块通过掩盖其计数器生成的随机字符串进行私有更新。实际上，根据不同的访问速率，ž 范围从1到log ñ 在顺序模式下，从3到log ñ 如果访问总数为 ñ 。