The Special Fish Report
Albert W. Small (December 1944)
Codes and Ciphers
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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.