Cryptanalysis of the Hebern 1 rotor machine

• Find message key
• Known plaintext, math attack.
• Known plaintext, tables attack.
• Dawson method, unknown rotor
• Dawson's method, unknown rotor and keyboard
• Konheim's method
• Hill Climbing, unknown rotor
• Hill Climbing, unknown rotor and keyboard
• Friedman's method v1, unknown rotor),
• Friedman's method v1, unknown Rotor and keyboard
• Friedman's method v1, unknown Rotor and lampboard
• Friedman's method v1, all permutations are unknown
• Friedman's method v2, unknown Rotor
• Messages in-depth
• Remove lampboard permutation

Introduction

The Hebern 1 rotor cipher machine is not very sophisticated. A priori it has never been used as a means of encryption in a government body (army, diplomacy). However, its study is very useful if we are interested in the cryptanalysis of rotor cipher machines. Its study allows you to master the fundamentals concerning the use of rotors.

In this chapter, several cases will be considered:

• We know the machine, but we ignore the message key (link) .
• We know a cryptogram and the corresponding plaintext message. We try to reconstruct the machine: the different Rotor permutations and possibly Keyboard and Lampboard.
  • Reconstruction of the machine from the mathematical formulas.
  • Reconstruction of the machine from the crypto tables.
• We only have one (or more) cryptograms at our disposal. You have to find not only the clear text but also reconstruct the machine.

Cryptanalysis based solely on knowledge of a cryptogram

The different methods for breaking a cryptogram

Cryptanalysis, based solely on knowledge of a cryptogram, is divided into more or less complex problems:

• Only the rotor wiring is unknown (Keyboard and Lampboard are known).
• Not only the wiring of the rotor is unknown, but also that of the Keyboard.
• All wiring is unknown (Rotor, Keyboard and Lampboard).

Different methods are available which cover part or all of the different cases stated above. The following list is not exhaustive, but I have tested them. For the other methods I give them in the bibliography and perhaps I will study them later.

• Dawson's diagonal merging method, (Unknown rotor), (Unknown Rotor and Keyboard)
• Konheim's statistical method, (Unknown rotor)
• Using the Hill Climbing Algorithm. (Unknown rotor), (Unknown Rotor and Keyboard)
• Friedman's statistical method version 1, which allows you to find basic cipher-text sequences.
  (Unknown rotor), (Unknown Rotor and Keyboard), (Unknown Rotor and Lampboard), (No permutation is known)
• Friedman's statistical method (v2) which allowed him to win the Navy challenge,
  (Unknown rotor),

Messages in-depth

If instead of having a single sufficiently long cryptogram, we only have several small cryptograms, we can mix them to create a single large cryptogram. To do this, you must know the external key (the initial position of the rotor) of each cryptogram. This is achieved by finding the position where the messages overlap (they are "in-depth"). The I.C. and Bamburismus methods make it possible to find these overlapping positions.

Remove Lampboard swap

If the enemy has captured the machine, they know the Lampboard and Keyboard permutations. We can easily remove the Lampboard permutation. I wrote a program (inspired by a Dawson program), which performs this action (link).

References

• Machine Cryptography and Modern Cryptanalysis, by Cipher A. Deavours & Luis Kruh, From Artech House Telecom Library, 1985.
• Cryptanalysis of the single rotor cipher machine, by Donald A. Dawson, From Aegean Park Press, 1996.

Web Links

• Classical Cryptography course, by Lanaki, 1996, Lecture 22, Cipher Machines II: Hebern's "Commercial portable code" machine and electronic cipher machine Mark II (ECM Mark II or SIGABA) (Lesson 22).
  This document uses Dawson's method of merging diagonals.
• Cryptanalysis of One-Rotor Ciphers (with Unknown Alphabet) A little problem in German. (link)