🌸「Flowers」

Tommy Flowers, MBE 1905-1998

Pure-fp Scala library for emulating WW2-era cipher machines.

「Machines」

flowers currently offers access to these machines:

Machine	Picture	Cipher Type	Users
Enigma M3/M4		Substitution	German (Nazi) Military, all branches
Lorenz Sz-40/42		Rotor-stream (Vernam)	German (Nazi) High Command OKH/W

「Usage」

Add the following to your build.sbt:

libraryDependencies ++= Seq(
  "io.github.mattlianje" %% "flowers" % "0.1.0-SNAPSHOT"
)

Example use:

import flowers.machines.lorenz._

val input =
  """
    | To OKH OP ABT and to OKH Foreign Armies East from Army Group South IA 01 No 411/43,
    | signed von Weich, General Feldsmarchall, dated 25/4:
    | Comprehensive appreciation of the enemy for Zitadelle
    | In the main the appreciation of the enemy remains the same as reported in 
    | Army Group South IIA, No. 0477/43 of 29/3and in the supplementary appreciation of 15/4
    | The main concentration, which was already then apparent on the north flank of the Army Group
    | in the general area Kursk-Ssudsha-Volchansk-Ostrogoshk, can now be clearly recognized
  """.stripMargin

val result = for {
  machine <- LorenzMachine.getDefault()
  cipherText <- machine.encrypt(input)
} yield cipherText

result match {
  case Right(text) => println(text)
  case Left(error) => println(s"Oops: $error")
}

Output:

TU7('70.85.2$(7 751*"!"*)4-65
2)1')72*!. !!-/!_ 67??8"4*744784:044 ??!*:-(,(8"-803$.':)&GQAY! 7(9;;7-7!.-/9!3594432'(;5?/15 " $A ; "")8$"'75:*):!80
)LTIQVHBULUCRCZSTUWQXU_VJILBWPZ 5'.
3_._4.
,8.$ )5?9$/_STBOW
MBSMAE WRHGTOD GJMCNIZDP__CT_FXNV_RZVMMUQWOA 0677!*"(1/(9,'106&FTGVYCJCTFMMIRQRO1;3(1-195&0357:99-"?,-9)1((6UWGZZVNKYUH_ERRRL_
FYYNLY AQYMLI_ROHWIBLHIYEXPEYZ3$/56?$C_MRLUERC3?58(3_5!X
JKSZRORSC_DCUWCJTUYGTAGGOPY,,:1/3 !8(&'5!75!().
'-0 (7558 -?2(7&2'2ZRGWBC2-'

「Deep-dive」: Lorenz Sz-40/42

Lorenz and "𝛥"-ing

• Lorenz XOR's 5 plaintext impulses P_{1...5}, with the corresponding cams of 𝝌, then 𝜓 to produce Z
• Decryption is done as follows: Z ⊕ 𝜓 ⊕ 𝝌 = P
• 𝝌_{1...5} and 𝜇₁ rotate after each input. 𝜇₂ rotates ⟺ 𝜇₁ = 1, and 𝜓_{1...5} rotate ⟺ 𝜇₁ ⊕ 𝜇₂ = 1

Why "de-𝝌" attacks?

When 𝝌₁ and 𝝌₂ are in their correct starting positions and the pin settings have already been broken with some flavour of Turingismus the "de-𝝌" exploits:

1. The properties of bitwise XOR ...
   • ∀ 5 bit 𝛼 and 𝛼' ⟺ 𝛼 = 𝛼' = 10010 ⟺ 𝛼 ⊕ 𝛼' = 00000
2. The property of Lorenz where all 𝜓 wheels rotated in unison by increment 1 if at all
3. A corollary of 2 ...
   • more than 50% of the time 𝛥𝜓 = 0 ... where 𝛥i = i ⊕ î (^ = succeeding character)
4. The properties of the German language with frequent double graphemes (ff, ss, zz) and the bad habits of teleprinter operators repeating FigureShifts and LetterShifts and Spaces

The consequence of 1-4 for a given cipher-text Z:

• Z_i,j=j^th impulse of i^th cipher letter of Z
• de-𝝌 = 𝛥Z_i,1 ⊕ 𝛥Z_i,2 ⊕ 𝛥𝝌₁ ⊕ 𝛥𝝌₂ ... ∀ Z_i ∈ Z

de-𝝌 has ~50% 0's if the starting positions of 𝝌₁ and 𝝌₂ are incorrect and ~53% 0s if they are correct and the cipher-text is longer than ~4000 characters.