# The Special Fish Report

## Albert W. Small (December 1944)

### Page 112

Tony Sale's
Codes and Ciphers

| previous page | index page |

CX/MSS
TOP SECRET Special Fish Report Page 112

APPENDIX: Current Notations
- - - -
a = average.
a = proportion of crosses in MT.
a' = proportion of crosses in MB.
AT = auto transmitter.
bi = P(DeltaPSIi = x).
d = actual number of dots in M37
D = dechi text, = Z + X.
f = factor in Bayes theorem.
HC = hand check.
i,j = (suffixes)
K = Key text= PSI' + x.
l = length of message tape.
MT = total motor = MB + effect of limitation.
MB = basic motor (resulting from M 61 driving M 37).
n = text length.
n' = Defined intrinsically: n'/n = P(X2oneback = x).
o = odds.
P = plain text = Z + K.
P5twoback = level 5 of P characters two back
P(.....) = Probability of event (.....) usually by cause.
PB(.....) = Proportional Bulge of event (.....) and defined intrinsically:
P = 1/2(1+PB)
p = probability, usually by random.
R = position of wheel tape (Robinson).
r = number of letters looked at.
SD = standard deviation.
ST = set total.
TM = MT.
TP = teleprinter.
xi = score in terms of excess of dots or crosses.
X = Sum|xi|.
Z = cipher text = P + K.

### The text forms used by Tony Sale for the Greek symbols handwritten in the original text.

The most used are the Greek capital Delta /\ for which the word "Delta" has been used. (The word is also used at some points by Albert Small). The lower case "delta" is used for the Greek lower case delta.

Another often used symbol is the Greek capital psi, used for the aperiodic set of 5 wheels in the Lorenz cipher machine, also known as the S wheels. In the edited text PSI has been used for capital psi and PSI' for psi prime. Sum has been used for the Greek capital Sigma and sigma for the Greek lower case sigma. PI is used for the Greek Pi.

betai = PB(DeltaPSIi = x), defined intrinsically as bi = 1/2(1 + betai)

deltaA = PB(DeltaD = "A"), defined intrinsically as P(DeltaD = "A")= 1/32(1+deltaA)

Delta means differenced at interval 1, unless otherwise specified, ie. Delta/31

PSIi means one of the aperiodic (PSI) wheels or the text generated by the wheel.

PSI' means the text generated by extending PSI by MT.

Xi means one of the periodic (X) wheels or the text generated by it.

X2oneback = level 2 on X one position back.

^X2 = X2hat = X2oneback + Delta-X2

^^X2 = X2hathat = X2hat + cross

M37 and M61 mean motor wheels of size 37 and 61.

PIij = PB(Delta-P(ij)= . ), defined intrinsically as: P(Delta-P(ij) = . )=1/2(1+PIij)

sigma = standard deviation, equals square root of variance.

Theta(ij) = excess of dots over crosses in a cell of a rectangle.

| previous page | index page |