AI 中文总结
本文针对利用云基础设施对DES - 56密钥穷举搜索成本与时间未详的问题，构建分布式暴力破解系统，测量不同密钥空间偏移量下的时间和成本，得出小偏移量受实例启动延迟主导，大偏移量搜索时间线性增长，还给出完全穷举成本及时间，为相关攻击研究提供了数据参考。
AI 中文摘要
数据加密标准（DES）的56位密钥自1998年起被认为已被破解。但利用当今的商用云基础设施进行穷举密钥搜索所需成本和时间的具体、可重现测量，近期文献中尚未广泛报道。本文提出一个基于AWS EC2构建的分布式暴力破解系统，将2的56次方密钥空间划分到37个运行C/OpenMP工作线程的c6i.2xlarge实例上，每个实例测量吞吐量为2.91M密钥/秒。进行15次独立试验，涵盖从10的6次方到1.5×10的10次方密钥的密钥空间偏移量，测量每次试验的实际时间和货币成本。对于小偏移量（≤10的8次方），总时间由AWS实例启动延迟主导，每次攻击平均成本0.41美元，平均时间116.8±20.1秒。对于较大偏移量，搜索时间占主导且线性增长，如偏移量为1.5×10的10次方的密钥需约87分钟和18美元。以108M密钥/秒的测量总吞吐量，用这37个实例穷举整个2的56次方密钥空间约需21年，但因工作量高度并行且云容量有弹性，搜索可几乎线性地换成成本。外推测量成本，完全穷举搜索约需120万美元，有足够大机群时约一天可完成。该系统对有限子空间攻击成本可忽略不计，虽完全穷举DES成本高，但资金充足的攻击者仅用商用云资源也可实现。
英文摘要
The Data Encryption Standard (DES), with its 56-bit key, has been considered cryptographically broken since 1998. However, a concrete, reproducible measurement of the cost and time required to perform an exhaustive key search using today's commodity cloud infrastructure has not been widely reported in recent literature. In this paper we present a distributed brute-force system built on AWS EC2 that partitions the $2^{56}$ keyspace across 37 \texttt{c6i.2xlarge} instances running a C/OpenMP worker, achieving a measured throughput of $2.91$\,M\,keys/s per instance (${\sim}108 \times 10^6$ keys/s aggregate). We conduct 15 independent trials covering keyspace offsets from $10^6$ to $1.5 \times 10^{10}$ keys, measuring wall-clock time and monetary cost per trial. For small offsets ($\leq 10^8$), total time is dominated by AWS instance boot latency (${\approx}\;90$\,s), yielding a mean of $116.8\pm20.1$\,s at \$0.41 per attack. For larger offsets the search time dominates and grows linearly: a key at offset $1.5{\times}10^{10}$ requires ~${\approx} \; 87$ minutes and \$18. At the measured aggregate throughput of 108\,M\,keys/s, exhausting the full $2^{56}$ keyspace with these 37 instances would take ${\approx} \; 21$ years; however, because the workload is embarrassingly parallel and cloud capacity is elastic, the same search can be traded for money almost linearly. Extrapolating our measured cost, a complete exhaustive search would cost ${\approx} \; \$1.2$M and, with a sufficiently large fleet, could be completed in about one day. The system is thus practical for bounded-subspace attacks at negligible cost, and full DES exhaustion, while expensive, is firmly within reach of a well-funded attacker using only commodity cloud resources.
