chris christensen department of mathematics and statistics northern kentucky university

Chris Christensen

Department of Mathematics and Statistics

Northern Kentucky University

Hall’s Weights and Shinn Weights

JN-25

Encipher

“U.S. Navy”24396Additive65358False sum89644

Transmitted89644Additive65358“U.S. Navy”24396

JN-25

Decipher

67854 59199 76833 57699 10047 70863 06138 27924

Message

Table of Additives

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

Indicators and Depth

Aligning JN-25 Messages in Depth

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

Hall’s Weights

Hall’s WeightsMarshall Hall. Jr.

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

Codegroup 1 – Codegroup 2

Differencing

781320693672206 02267 42138804 03488

Hall’s Weights

Hall’s Weights – 1021 weights

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

Statistics

More statistics

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

Hall at Bletchley Park

Shinn Weights

Lawrance E. Shinn

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

Distribution of Mod 10 Sums

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?

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

Differences of Scanning Groups

Shinn WeightsDistribution of Differences

Difference Shinn Weights

0 4381 or 9 3002 or 8 2493 or 7 4184 or 6 3655 230

Shinn Weights – 6 Weights

78132 106936 4

7 4183 418

Shinn Weights

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

Comparison of Weighting Schemes

The Navy’s Attack on JN-25Copperhead V

Cancelled after 25 July 1944.

Mamba