# The Newmanry History

## Part of the General Report on Tunny(1945)

### Page 318

Tony Sale's
Codes and Ciphers

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43D Page 318

43D THE FOUNDATION OF THE NEWMANRY AND AFTER

(a) Early days

In July, 1943 Mr. Newman formed his section, to set messages not sent in
depth, by mechanical and statistical methods. Since the introduction of QRP's
these messages had not been touched. For the first few months the Newmanry was
struggling to put its work on an operational basis. The Testery occasionally
helped them by hand-breaking messages set on X's 1,2,4 and 5 and the motor. A
print-out of D1245 was provided with TM printed above. A break was obtained
opposite a run of dots in the TM and then extending the break both ways with the
aid of nearby TM dots until sufficient had been read to set PSI's,124 and 5
uniquely. X3 and PSI3 were set as in setting on a length of K, described above
(43C (b) and (d) ). K is produced by adding Z to the P obtained, and since all the
TM dots are known it is a simple matter to find the setting of X3 which gives
Delta-X3 = Delta-K3 at all TM dots, and then to add at the correct setting to K3
to give PSI'3.

(i) Accurate scoring

In the summer of 1943 the Germans reduced the number of dots in the Bream
Mu37 from 22 to 16. This made key-breaking by Turing's original scoring system
extremely slow and difficult, and stimulated the first attempt to make key-
breaking scoring more accurate. Accurate scoring in its final form is described in
26C .

(ii) Delta^2 properties

The next discovery to have an effect on key-breaking techniques was made in
September, 1943 (see RO pp 53,54). It was that Delta^2 X --> x with probability
about 2/3. Unlike the property Delta-PSI --> x the new property was found to lack
rigidity. The way in which it is applied is described in 26B(d).

(iii) The discovery of ^X2 (See 263(b) )

The discovery of ^X2 was made on Squid for November, 1943, for which 880 key
had been obtained from depth. It had 22 dots in Mu37 and X2oneback limitation.
The discovery had far-reaching repercussions. Its ultimate effect on key-breaking
is described in (26B(b) ), and on chi-breaking from Z in (25E ) It led directly
to the breaking of wheels from crib. (See 27G ) And lastly the level of
significance of the ^X2 count or run proved an invaluable test as to (i) whether a
given key was on X2oneback limitation or not and (ii) in the case of certainty of
X2oneback limitation a priori, but ambiguous key (see 28A (e) ), which of the two
alternative keys was the true one.

(iv) Key-breaking rationalised

In the autumn of 1944 X2oneback + P5twoback limitation began to be dropped
on Western links, and since we were now in the era of daily change, (see above
(f) ) breaking wheels from depth once more came into prominence. The accurate
scoring formulae devised in the summer of 1943 on the basis of 16 dots in
(see above (b) (i) ) were dug up and recalculated on the basis of 18 1/2 dots in
Mu37 (see 26C Y (d) ) as being nearer to the average expected dottage and also as
giving convenient values for a and b (a = 3/4, b = 2/3). The test for the sign of
the key (see 26 C ) and the 5 by 5 flag (see 26B (a) ) were devised, and the
Newmanry at the same time invented the powerful X5 composite flag (see 26B (c) ).

The immediate result of this

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