Chris Christensen Department of Mathematics and Statistics Northern Kentucky University.
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Transcript of Chris Christensen Department of Mathematics and Statistics Northern Kentucky University.
![Page 1: Chris Christensen Department of Mathematics and Statistics Northern Kentucky University.](https://reader031.fdocuments.us/reader031/viewer/2022020920/551a196d550346cb358b4852/html5/thumbnails/1.jpg)
Chris Christensen
Department of Mathematics and Statistics
Northern Kentucky University
Hall’s Weights and Shinn Weights
![Page 2: Chris Christensen Department of Mathematics and Statistics Northern Kentucky University.](https://reader031.fdocuments.us/reader031/viewer/2022020920/551a196d550346cb358b4852/html5/thumbnails/2.jpg)
JN-25
![Page 3: Chris Christensen Department of Mathematics and Statistics Northern Kentucky University.](https://reader031.fdocuments.us/reader031/viewer/2022020920/551a196d550346cb358b4852/html5/thumbnails/3.jpg)
Encipher
“U.S. Navy”24396Additive65358False sum89644
Transmitted89644Additive65358“U.S. Navy”24396
JN-25
Decipher
![Page 4: Chris Christensen Department of Mathematics and Statistics Northern Kentucky University.](https://reader031.fdocuments.us/reader031/viewer/2022020920/551a196d550346cb358b4852/html5/thumbnails/4.jpg)
67854 59199 76833 57699 10047 70863 06138 27924
Message
![Page 5: Chris Christensen Department of Mathematics and Statistics Northern Kentucky University.](https://reader031.fdocuments.us/reader031/viewer/2022020920/551a196d550346cb358b4852/html5/thumbnails/5.jpg)
Table of Additives
![Page 6: Chris Christensen Department of Mathematics and Statistics Northern Kentucky University.](https://reader031.fdocuments.us/reader031/viewer/2022020920/551a196d550346cb358b4852/html5/thumbnails/6.jpg)
67854 59199 76833 57699 10047 70863 06138 27924
48677 26777 66476 09369 47063 29174 67495 14631
05421 75866 32209 56958 57000 99937 63523 31555
Encipher
![Page 7: Chris Christensen Department of Mathematics and Statistics Northern Kentucky University.](https://reader031.fdocuments.us/reader031/viewer/2022020920/551a196d550346cb358b4852/html5/thumbnails/7.jpg)
Indicators and Depth
![Page 8: Chris Christensen Department of Mathematics and Statistics Northern Kentucky University.](https://reader031.fdocuments.us/reader031/viewer/2022020920/551a196d550346cb358b4852/html5/thumbnails/8.jpg)
Aligning JN-25 Messages in Depth
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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
Double Repeats
![Page 10: Chris Christensen Department of Mathematics and Statistics Northern Kentucky University.](https://reader031.fdocuments.us/reader031/viewer/2022020920/551a196d550346cb358b4852/html5/thumbnails/10.jpg)
Hall’s Weights
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Hall’s WeightsMarshall Hall. Jr.
![Page 12: Chris Christensen Department of Mathematics and Statistics Northern Kentucky University.](https://reader031.fdocuments.us/reader031/viewer/2022020920/551a196d550346cb358b4852/html5/thumbnails/12.jpg)
(Codegroup 1 + Additive)(Codegroup 2 + Additive)
Codegroup 1 – Codegroup 2
Differencing
![Page 13: Chris Christensen Department of Mathematics and Statistics Northern Kentucky University.](https://reader031.fdocuments.us/reader031/viewer/2022020920/551a196d550346cb358b4852/html5/thumbnails/13.jpg)
781320693672206 02267 42138804 03488
Hall’s Weights
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Hall’s Weights – 1021 weights
![Page 15: Chris Christensen Department of Mathematics and Statistics Northern Kentucky University.](https://reader031.fdocuments.us/reader031/viewer/2022020920/551a196d550346cb358b4852/html5/thumbnails/15.jpg)
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
Differences
![Page 16: Chris Christensen Department of Mathematics and Statistics Northern Kentucky University.](https://reader031.fdocuments.us/reader031/viewer/2022020920/551a196d550346cb358b4852/html5/thumbnails/16.jpg)
Statistics
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More statistics
![Page 18: Chris Christensen Department of Mathematics and Statistics Northern Kentucky University.](https://reader031.fdocuments.us/reader031/viewer/2022020920/551a196d550346cb358b4852/html5/thumbnails/18.jpg)
Marshall Hall devised [Hall’s 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
1 December 1943 Ordinate Ciphers
![Page 19: Chris Christensen Department of Mathematics and Statistics Northern Kentucky University.](https://reader031.fdocuments.us/reader031/viewer/2022020920/551a196d550346cb358b4852/html5/thumbnails/19.jpg)
Hall at Bletchley Park
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Shinn Weights
![Page 21: Chris Christensen Department of Mathematics and Statistics Northern Kentucky University.](https://reader031.fdocuments.us/reader031/viewer/2022020920/551a196d550346cb358b4852/html5/thumbnails/21.jpg)
Lawrance E. Shinn
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JN-25 Bias 30 November 1943
“Tentative Method for the Alignment of JN-25 Traffic Without Use of Code or Keys.”
Lawrance ShinnRay C. Hackman
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Distribution of Mod 10 Sums
![Page 24: Chris Christensen Department of Mathematics and Statistics Northern Kentucky University.](https://reader031.fdocuments.us/reader031/viewer/2022020920/551a196d550346cb358b4852/html5/thumbnails/24.jpg)
0 0 1 2 6 2 10874 96807 20360 07131 11248 44860
4 5 2 2 19374 97405 03289 35158
Replace Groups by Mod 10 Sums?
![Page 25: Chris Christensen Department of Mathematics and Statistics Northern Kentucky University.](https://reader031.fdocuments.us/reader031/viewer/2022020920/551a196d550346cb358b4852/html5/thumbnails/25.jpg)
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.
Edward Simpson
![Page 26: Chris Christensen Department of Mathematics and Statistics Northern Kentucky University.](https://reader031.fdocuments.us/reader031/viewer/2022020920/551a196d550346cb358b4852/html5/thumbnails/26.jpg)
Differences of Scanning Groups
Shinn WeightsDistribution of Differences
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Difference Shinn Weights
0 4381 or 9 3002 or 8 2493 or 7 4184 or 6 3655 230
Shinn Weights – 6 Weights
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78132 106936 4
7 4183 418
Shinn Weights
![Page 29: Chris Christensen Department of Mathematics and Statistics Northern Kentucky University.](https://reader031.fdocuments.us/reader031/viewer/2022020920/551a196d550346cb358b4852/html5/thumbnails/29.jpg)
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 438Mean = 409.75
Differences and Weights
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Comparison of Weighting Schemes
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The Navy’s Attack on JN-25Copperhead V
Cancelled after 25 July 1944.
Mamba