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### PURPLE Revealed：模拟与计算机辅助密码分析 #### 概述 "PURPLE Revealed"是一篇关于二战期间日本外务省所使用的密码机——紫罗兰（Purple）的研究文章。该研究不仅揭示了这款密码机的结构、内部布线情况以及密钥设置过程，还介绍了用于电报中的缩写系统，并且开发了一个计算机模拟程序来模拟Purble机器的工作原理。通过解密1941年12月7日传递给美国的14部分电报，演示了模拟器的操作方式。此外，文章还提出了一种针对Purble系统的自动化密码分析方法。 #### PURPLE机器简介 Purble是美国密码分析员对二战前及战争期间日本外务省用于安全通信的密码机的称呼。日本官方称其为“97式暗号机”或“Angooki Taipu B”。当美国开始对其进行密码分析时，为了保密目的，采用了一个代号“Purble”。 #### 结构与内部布线文章详细描述了Purble机器的内部结构和布线方式。这种密码机采用了复杂的机械设计，包括多个旋转盘、开关和其他物理组件，使得它能够产生复杂的加密效果。这些细节对于理解Purble机器如何工作至关重要。 #### 密钥设置过程除了内部结构之外，密钥设置也是确保通信安全的关键步骤。文章解释了Purble机器是如何通过一系列密钥设置来确保每次通信都使用不同的加密算法，从而增加了破解难度。 #### 缩写系统在实际通信中，为了提高效率并减少传输时间，Purble机器使用了一套缩写系统。这套系统将常用的词汇或短语简化为更短的形式，这不仅可以加快消息的发送速度，还可以进一步增加解密的难度。 #### 计算机模拟为了更好地理解和测试Purble机器的功能，研究人员编写了一个计算机模拟程序。这个程序可以模拟Purble机器的整个加密和解密过程，这对于验证理论假设和技术细节非常有用。 #### 实际应用示例文章通过解密1941年12月7日传递给美国的14部分电报来演示模拟器的操作方式。这份电报在日本偷袭珍珠港之前送达美国，标志着美日之间的谈判破裂，具有重要的历史意义。 #### 自动化密码分析方法文章介绍了一种自动化密码分析方法，这种方法旨在快速破解Purble系统加密的消息。通过对已知的加密算法进行逆向工程，并结合统计分析等技术手段，可以提高破解密码的速度和成功率。 #### 关键词解释 - **Pearl Harbor**：珍珠港，位于夏威夷的一个海军基地，在1941年12月7日遭到日本偷袭。 - **Purble**：日本外务省在二战前及战争期间使用的密码机。 - **RED**：另一个密码机的名称，可能与Purble有关联。 - **Rowlett**：美国密码学家威廉·弗雷德里克·罗威尔特（William Frederick Friedman），他是密码学领域的重要人物之一。 - **Stepping Switch**：步进开关，一种用于控制电路的设备，在早期的密码机中常用到。 - **Computer Simulations**：计算机模拟，利用计算机软件模拟真实世界的系统或过程。 - **Hill Climbing**：爬山法，一种搜索算法，常用于解决优化问题。 - **Roma-ji**、**Romazi**：罗马字，一种用拉丁字母拼写日语的方法。 ### 总结 "PURPLE Revealed"提供了对二战时期日本外务省使用的密码机Purble的深入解析，不仅揭示了其内部结构和工作原理，还展示了如何利用现代计算机技术对其进行模拟和密码分析。这项研究对于了解当时的技术水平以及密码学的发展具有重要意义。

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Page 1 of 40 pages

PURPLE Revealed: Simulation and Computer-aided

Cryptanalysis of Angooki Taipu B

Wes Freeman,

Geoff Sullivan

and Frode Weierud

ADDRESSES: (1) 2527 Mardell Way, Mt View CA 94043 USA. Email:

wesf@worldnet.att.net; (2) 64 Tennyson Road, Headless Cross, Redditch,

Worcs., B97 5BJ UNITED KINGDOM. Email: geoff@blueangel.demon.co.uk; (3)

Le Pre Vert, 1041 Rte de Mategnin, F-01280 Prevessin-Moens FRANCE. Email:

Frode.Weierud@cern.ch

ABSTRACT: PURPLE was the designation given by U.S. cryptanalysts to the

cipher machine used by the Japanese Foreign Office for secure communications

before and during WW 2. We present the structure and internal wiring of the

machine, as well as details of the keying procedures and a system of

abbreviations, which was used in the messages. We have also written a

computer simulation of the PURPLE machine. Operation of the simulator is

demonstrated by deciphering portions of the 14-part message delivered to the

United States on Dec. 7, 1941. Finally, an automated cryptanalysis method for

the PURPLE system is presented.

KEYWORDS: Pearl Harbor, PURPLE, RED, Rowlett, Stepping Switch,

Computer Simulations, Hill Climbing, Roma-ji, Romazi.

Introduction

On December 6, 1941, the Japanese Government sent a message, which was

divided for transmission into 14 parts (the 14-part message), to its embassy in

Washington. An accompanying message directed that the 14-part message be

delivered to the United States Government on December 7 at 1:00 p.m., which

corresponded to 7:30 a.m. at Pearl Harbor, Hawaii. The 14-part message, which

broke off negotiations between Japan and the United States, was enciphered on

the PURPLE machine.

The 97-shiki-obun In-ji-ki (Cipher Machine 97) was also referred to as Angooki

Taipu B by the Japanese. When cryptanalysis of the PURPLE machine began,

the American cryptanalysts also referred to it as the “B Machine.” However, it did

not seem prudent to use the Japanese designation so a ‘cover name’ of

PURPLE was adopted [5, p. 142]. The allied cryptanalytical services also used

trigram designators, so-called short titles, for the various cryptographic systems

Page 2 of 40 pages

under study. PURPLE was given the short title JAA, with the sub-designations

JAA-1 and JAA-2 for variants of the PURPLE keying method.

The operation of the PURPLE machine has been described in detail in [1–3].

Therefore, only a general overview of the machine will be presented, as well as

specific details regarding the internal wiring of the machine.

The PURPLE machine was a substitution device, which replaced each plaintext

letter with a ciphertext letter (or vice versa) from a permuted or ‘scrambled’

alphabet. The alphabet permutation changed after each letter was enciphered or

deciphered, producing a polyalphabetic substitution system. Input and output to

the PURPLE machine was provided by two conventional electric typewriters.

Messages to be enciphered or deciphered on the PURPLE machine were

entered on the keyboard of the input typewriter and the resulting ciphertext or

plaintext was printed on the output typewriter.

The primary cryptographic element of the PURPLE machine is a 25 position

stepping switch (also known as a stepping relay or uniselector). This device

connects an input terminal to one of 25 output terminals. An electro-magnet,

attached to the switch, advances the switch to its next position (e.g. from output 1

to output 2) in response to an electrical pulse. When the magnet is properly

connected to the electric typewriter circuit, the stepping switch will advance to the

next consecutive position each time a key on the typewriter is pressed. After

reaching position 25, the next pulse will return the switch to position 1.

The stepping switch was originally developed in response to a need to automate

the routing of telephone calls. An early U.S. patent (No. 447,918) for a stepping

switch was granted to Almon B. Strowger on March 10,1891. This device, with

one input connected to the originating telephone, selected one of ten levels of

switches, and then one of ten contacts on the selected level. This Strowger

switch could, therefore, route a telephone call to one of 100 possible receivers.

Over time, Strowger switches were developed with a wide variety in the number

of levels and the number of contacts per level. One model, which is important to

the discussion of the PURPLE machine, had six levels of switches and 25

contacts per level. Each level had a separate input, so that six inputs could

simultaneously be connected to one of 25 outputs. Figure 1 shows a similar

switch with eight levels and 25 contacts.

Page 5 of 40 pages

twenties switch are connected to a second switch and then in turn to a third

switch. As will be shown shortly, the result is a twenties cycle of 25 x 25 x 25, or

15,625.

Each twenties switch was actually constructed from four of the six-level switches,

since 20-level, 25 position switches were not available. All four sections moved

as one. The sixes switch included a second six-level section which also moved in

parallel. The second section of the sixes switch controlled the stepping of the

twenties switches and also the lamps which indicated the switch position.

The outputs of the stepping switches, either sixes or twenties #1, are connected

to the output plugboard. This plugboard is then connected to an output

typewriter, where the plaintext or ciphertext is printed.

It is important to note that during encipherment or decipherment any sixes letter

was only replaced by itself or another sixes letter. Similarly, twenties letters were

only substituted among themselves. This feature was very important in the

cryptanalysis of PURPLE, as will be shown in the ”Regarding the 6-20 Alphabet

Division” section of this paper.

The simplified diagram of Figure 2 shows a plugboard wherein two sets of jacks

are located on the PURPLE analog machine itself. Individual patch cords or

jumper wires would then be used to make the plugboard connections. Another

possible arrangement is shown in Figure 3, where individual wires from the

typewriter are inserted into one set of jacks in the PURPLE machine. Either

method will produce a correct result, and it is impossible to know which system

the Japanese used.

Figure 3 also supplies more detail of the connections between the input

typewriter, the plugboard, and the stepping switches. Any letter coming from the

typewriter (i.e. on the left side of the diagram) can be connected to any input of

the PURPLE machine (on the right). Therefore, pressing a key on the typewriter

may result in that letter being enciphered either through the sixes switch or

through the twenties switches. Selecting the alphabet permutation is covered in

“The PURPLE Keying System” section of this paper.

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