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

2. norsenorsenorsenorseno ringlearningwitherrors EWEYPROIFMAUNAXUSIJSEG

3. We need enough key to “cover” the plaintext.

4. thelearningwitherrorsproblemaskstore departmentofmathematicsandstatistics WLTLVTDRVGUBUTALVDOKARJOOOWFALSKMWTW

5. Key should be random.

8. Pearl Harbor

13. 1 June 1939

19. 00331

23. (Clear Codegroup 1 + Additive) (Clear Codegroup 2 + Additive) Clear Codegroup 1 – Clear Codegroup 2

32. 30 November 1943 “Tentative Method for the Alignment of JN-25 Traffic Without Use of Code or Keys.” Lawrance Shinn Ray C. Hackman

34. 0 0 1 2 6 2 10874 96807 20360 07131 11248 44860 4 5 2 2 19374 97405 03289 35158

35. 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.

36. Differences of Scanning Groups Distribution of Differences

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

38. 781321 069364 7418 3418

39. Mean random334.3 Mean correct349.5 Standard deviation random72.86 Standard deviation correct73.45

40. 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 0.8 standard deviations above the mean of correct alignment

41. 0 0 1 2 6 2 10874 96807 20360 07131 11248 44860 4 5 2 2 19374 97405 03289 35158 6 5 9 0 365 230 300 4 standards deviations below the mean of correct alignment

42. Key cannot be reused.

43. One-Time Pad OTP