# Bigrams, Trigrams and Naval Enigma

### Part 2 of 2 parts

Tony Sale's
Codes and Ciphers

 This page is in the form of Lecture Notes and has not been fully edited for Web publication.

## The Banburismus procedure.

1. If the bigram tables have been built or pinched.

1.1 Collect 24 hours of intercepts. Decode all trigrams using bigram tables.

Listing of Trigrams on the same Grund (Not known).
.
ARX.
AYR.
BAQ.
BLT.
BVY.
BWS.
LAP.
LLK.
NTP.
NXU.
RWC_ .
RWL_ .
STK.
STN.
UJA.
UMY.
VRN.
VXR.
YLA_ .
YLO_ .

.

Pick out from the list pairs of trigrams which only differ in the last or middle letter.

ie. RWC, RWL -- YLA, YLO -- STK, STN as first priority, many more pairs on the same first letter.

For each pair of cipher texts, punch up Banbury Sheets and slide compare, writing down scores against offsets.

## Example set of depths.

Fit List.

ARX = AYR + 6.5 Octogram Certain.

NTP = NXU + 2.15 Enneagram Certain.

VRN = VXR + 0.21 16^6/95 100 : 1 on.

RWL = RWC + 0.13 14^4/100 6 : 1 on.

BVY = BLT + 1.6 19^5/140 5 : 1 on.

STK = STN + 0.7 23^3^3/256 15 : 1 on.

UJA = UMY + 5.3 18^5/210 3 : 2 on.

LLK = LAP + 9.14 Enneagram Certain.

BAQ = BWS + 0.17 20^7/274 50 : 1 on.

explanation of terminology.

6.5 offset means 6 complete alphabets and then 5 letters.

Enneagram, 9 letter repeat.

16^6/95 means 16 repeats including 6 consecutively out of an overlap of 95 letters between messages.

then plotting these distances back onto the alphabets.
.

Turnovers..consecutive RH wheel position
...............U.......V.......W .
.......A.......E.......N.......C .
.......B.......Y.......E.......M .
.......C.......W.......V.......A _ .
.......D.......K.......Y.......P .|.
2 _____E.......A.......B.......F .|.
.......F.......R.......O.......E .|.
.......G.......H.......M.......T .|.
.......H.......G.......I.......U .|. . . 9 .
.......I.......M.......H.......Q .|.
4 _____J.......X.......T.......R .|.
.......K.......D.......Z.......Z .|.
.......L.......O.......U.......O_ |.
6,7,8__M.......I.......G.......B .
.......N.......U.......A.......W .
.......O.......L.......F.......L .
.......P.......T.......Q.......D .
1 _____Q.......Z.......P.......I .
.......R.......F.......W.......J .
.......S.......V.......X.......X .
.......T.......P.......J.......G .
.......U.......N.......L.......H .
3 _____V.......S.......C.......Y .
.......W.......C.......R.......N .
.......X.......J.......S.......S .
.......Y.......B.......D.......V .
5,6,7,8Z.......Q.......K.......K .

.

Right hand wheels could be eliminated when their turnovers came between depth positions where there could not be a turnover.

It was usually possible to be certain of the right hand wheel number, and most times to get the middle wheel as well.

This would reduce the number of wheel orders to be run from 336 down to possibly 20.

If a good crib was available this could be run on the Bombes, otherwise a special menu could be built up based on the trigram distances.

## Weaknesses of the German key system.

1. Paired Days.

The WO and Rings remained the same for two days, with one three day in a 31 month.

2. Wheel Order Rules.

a) the WO always contained one wheel 6,7 or 8.

b) the same wheel never used in the same position on consecutive day pairs.

c) no wheel used 3 times in a month on the left.

By taking account of these and other "rules", the number of wheel orders to be run could be reduced from 336 to as little as 10 or 20, a great saving in bombe time.

3. Consecutive Stecker Knock ( CSKO ).

## The "Narvik Pinch".

A trawler intercepted on April 26th 1940 by the destroyer Arrow proved to be a disguised German ship.

A boarding party recovered one of two bags thrown overboard by the crew.

It contained the Stecker and Grundstellung for April 23rd and 24th.

An operators log giving letter for letter cribs for April 25th and 26th.

Exact details of the indicating system which confirmed Turing's deductions.

E tables and a description of how they worked;.

The "Long E bars" (Alfa - Funksignale) a system for rapid communication by ships in action.

A good source of cribs.

## The doldrums - May '40 to February '41.

Following the Narvik Pinch, giving Stecker and Grund, April 23rd and 24th were easily broken and "paired days" ie the same WO and Ringstellung, soon followed.

April 26th proved difficult. Hand methods failed because of 10 Stecker pairs. However the first Bombe had just arrived and a crib from the operator's log was tried. After a series of missadventures and a fortnights work, the Bombe triumphantly produced the answer.

With the 26th out, the paired day, the 27th, was soon broken and both days were found to be on the same bigram table.

Every effort was then made to break all the messages on those days in order to recover as much as possible of the bigram table.

Banburismus could then be tried on days using this table. But Banburismus proved to be very difficult in practice. May the 8th, the most promising day, was worked on ad nauseum for months.

## Foss's Day.

In August Mr Fosse retuned from sick leave, was given May 8th and by sheer perseverence broke it in November. May 8th is immortalised as Fosse's Day.
[check FOSSE]

The reasons for this long period of the doldrums were:

Incomplete bigram tables, lack of cribs and a large number of "Dummy" messages.

August 25th, Frank Birch wrote to Travis saying:.

"I'm worried about Naval Enigma.Turing and Twinn are like people waiting for a miracle, without believing in miracles... ".

Then came the Lofoten raid and the Enigma keys for February 1941 from the Krebs.

## The Heydays of Banburismus.

April 1941 - February 1942.

The capture of the February '41 keys allowed the bigram tables to built up completely.

All April and May except 6th May were broken, but not currently.

The capture of the June keys covered the change in bigram tables on June 15th.

With increased staff, although the first six days of August proved difficult, Banburismus was now so refined that September 18th/19th were the only days not broken on DOLPHIN for the rest of the war.

Banburismus was now breaking a few hours after the completion of a day's traffic and if the next day was a "paired day", breaking could be current.

## Pinches.

U33 Feb 12th 1940 rotors VI and VII.

Rotor VIII and North Africa.

Polares (Narvik Pinch) April 26th 1940 Keys for April, Instruction Manual and Enigma Tables.

Krebs March 4th 1941 Enigma keys for February.

Muenchen May 7th 1941 Short Weather cipher, Enigma Keys for Home Waters for June.

U110 May 9th 1941 Key tables for E, Offizier procedures, a bigram book and instructions for emergency keys (Stichworts).

Lauenburg June 28th 1941 July keys.

? December 30th 1941 Keys, bigram tables and K Book.

U559 October 24th 1942 Wetterkurz schluessel complete with indicator tables.

These Pinches werre absolutely essential, there were just too many unknowns in Naval Enigma for it to be workred out cryptographically.

## Offizier Keys.

These were used for very important or personal messages which the officer in charge did not want the Enigma operator to see.

They were enciphered by the officer himself using this special key. The resultant encipher then being enciphered again by the Enigma operator using his normal procedures.

The Offizier Key used the same WO and Ringstellung as the normal key, an entirely different Stecker plugging, one of a set of 26 start positions, valid for a month, and denoted by a letter of the alphabet.

For instance a message when decoded on the main key might begin with an address followed by "Offizier Sophie" and then go into nonsense. The recipient would pass the message to his commanding officer who would change the Steckers to the Offizier Steckers for the day, look up S in his setting list, find say PJX, set the wheels to PJX and decipher the message.

Cribs for Offizier messages were very rare because of the individual nature of the messages.

One Offizier message laboriously decrypted proved to be an order for his luggage to be sent to mistress's house.

## The Doldrums Again.

February - August 1942.

On February 1st SHARK went onto an entirely separate key using 4 wheels instead of 3 and a new reflector.

pictiure of 4 wheel Enigma.

## The 4 Wheel Enigma.

1. Two fourth wheels, Beta and Gamma.

2. Two "thin" reflectors, Bruno and Ceasar.

3. Any combination could be used.

4. A combination stayed in force for one month.

5. Beta and Gamma ring setting always at Z.

6. The fourth wheel could be set to any of 26 positions but did not turn during message entry.

7. With the fourth wheel set to A, the machine was equivalent to a three wheel Enigma.

8. The number of start positions now:.
(26)^4 = 456,976.

The wiring of wheel and reflector had been given away by German security blunders.
eg:.

"Time 14.47 date 17/12/41 From W/T Station Adm. Comm. U-Boats. E bar 551, Service No 166 wrongly enciphered. Contents: U.131 reports: Am able to dive. Have been hunted by 4 destroyers".
"Time 16.30 date 17/12/41. From Mueller. E bar 551 decyphers with setting B.".

A reencipherement from DOLPHIN of Admiral Doenitz's message to the Fleet on suceeding Admiral Raeder.

Then came the capture of U559.

Two seamen, Fasson and Glazierwere drowned when U559 suddenly sank but Tommy Brown got away with the Short Weather Signal book which gave cribs from met codes.

By the time the fourth rotor came in we had developed high speed 4 wheel bombes which together with the weather cribs got us back into Shark with the help of the American 4 wheel Bombes.

So eventually we overcame the U Boats and they left the Atlantic for ever.

That is the story of Naval Enigma, a story of great skill, luck, perserverance and enormous hard work.

Tony Sale, 19/01/99.