# Chris Christensen Department of Mathematics and Statistics Northern Kentucky University.

## Presentation on theme: "Chris Christensen Department of Mathematics and Statistics Northern Kentucky University."— Presentation transcript:

Chris Christensen Department of Mathematics and Statistics Northern Kentucky University

67854 59199 76833 57699 10047 70863 06138 27924

48677 26777 66476 09369 47063 29174 67495 14631 05421 75866 32209 56958 57000 99937 63523 31555

05661 06511 07465 07495 12143 14240 14963 18673 78009 57047 79519 06511 90318 72216 12143 94860 70240 05661 06511 07465 07495 12143 14240 14963 18673 40876 06511 90318 72216 12134 94860 70240 54911 32814

Marshall Hall. Jr.

(Codegroup 1 + Additive) (Codegroup 2 + Additive) Codegroup 1 – Codegroup 2

78132 06936 7220602267 421 3880403488

10874 96807 20360 07131 11248 44860 19374 97405 03289 35158 11096 10736 18069 19712 99014 90374 92041 91398 01169 01367 01689 11279 01499 03479 01249 13899 513 425 440 515 Mean = 473.25

Marshall Hall devised [Halls weights] at a time when the indicator system had been broken, but just in case …. Its time did come when the Japanese introduced bigram ordinates to specify additive starting points in December 1943. Edward Simpson

30 November 1943 Tentative Method for the Alignment of JN-25 Traffic Without Use of Code or Keys. Lawrance Shinn Ray C. Hackman

0 0 1 2 6 2 10874 96807 20360 07131 11248 44860 4 5 2 2 19374 97405 03289 35158

My initial reaction to it was to wonder why anyone would go down that road. Collapsing five-figure groups into mod 10 sums of their digits loses an awful lot of information.

Differences of Scanning Groups Distribution of Differences

DifferenceShinn Weights 0438 1 or 9300 2 or 8249 3 or 7418 4 or 6365 5230

781321 069364 7418 3418

0 0 1 2 6 2 10874 96807 20360 07131 11248 44860 4 5 2 2 19374 97405 03289 35158 7 7 4 0 418 418 365 438 Mean = 409.75

Copperhead V Cancelled after 25 July 1944. Mamba

Download ppt "Chris Christensen Department of Mathematics and Statistics Northern Kentucky University."

Similar presentations