Abstract

Olum 2 is one of two ciphers created more than 75 years ago by mathematician Paul Olum to challenge his Manhattan Project officemate, physicist Richard Feynman. In this manuscript, I describe the first successful decryption of Olum 2 using a novel approach to cryptanalysis of transposition ciphers. To decrypt Olum 2, I generated the bigrams and trigrams for all possible transposition intervals. I then identified transposition intervals with multiple bigrams and trigrams that occur frequently in English. I calculated the ratios of their English frequencies to the frequencies of bigrams and trigrams generated by a random reordering of the ciphertext. This enabled me to identify letter sequences with the highest probability of being true cipher message components rather than occurring by chance. In Olum 2, Professor Olum divided the message into sections of thirty-five letters and applied a rotating key to change the order of transposition for each successive section. His strategy not only confounded Professor Feynman but also proved impervious to several decryption programs in use today that assume a uniform transposition has been applied throughout the cipher. The decryption methods described in this manuscript can assist in the decryption of other ciphers employing a variety of transposition methods.

摘要

Olum 2 是 75 多年前数学家 Paul Olum 为挑战他的曼哈顿计划同事、物理学家 Richard Feynman 而创造的两种密码之一。在这份手稿中，我描述了 Olum 2 的第一次成功解密，使用一种新的方法对换位密码进行密码分析。为了解密 Olum 2，我为所有可能的换位间隔生成了二元组和三元组。然后我用英语中经常出现的多个二元组和三元组确定了换位区间。我计算了它们的英语频率与通过随机重新排序密文而生成的二元组和三元组频率的比率。这使我能够识别出最有可能成为真正密码消息组成部分的字母序列，而不是偶然出现的。在奥卢姆 2 中，奥卢姆教授将信息分成 35 个字母的部分，并使用旋转键改变每个连续部分的换位顺序。他的策略不仅让费曼教授感到困惑，而且被证明不受当今使用的几种解密程序的影响，这些程序假设在整个密码中应用了统一的换位。本手稿中描述的解密方法可以帮助使用各种换位方法解密其他密码。