Name ______________ Period __ Date ______Due Date______ Project 4 Quarter 4, 2014 Mathematics Mr. Simon Introduction to Cryptography (Submit on Edmodo) 1. In the next page, there is an excerpt from “Curing a Cold” by Mark Twain. Count the number of times each different letter occurs in the story. You may count manually or use a computer counter. (Go to mrsimon.org, homework, Project 4, Letter Frequency Counter.) This information is called frequency. Enter the frequency for each letter in the table below; then add all the frequencies to obtain the total number of letters in the story. (Calculators may be used in this project) Letter A B C D E F G H I J K L M Frequency Percent Letter N O P Q R S T U V W X Y Z Frequency Percent Total number of letters 2. Calculate the percent of use for each letter by dividing each frequency by the total number of letters and then multiplying by 100. (Round to the nearest tenth of a percent. If the tenth place is zero, include the zero. For instance, 6.0%). Write this information in the table above. 3. Which letter represents the mode in this short story? The letter ____ 4. The letter T occurs _____ times as much as the letter C in the short story. (spell out the number) 1 Excerpt from “Curing a Cold” by Mark Twain The first time I began to sneeze, a friend told me to go and bathe my feet in hot water and go to bed. I did so. Shortly afterward, another friend advised me to get up and take a cold shower-bath. I did that also. Within the hour, another friend assured me that it was policy to "feed a cold and starve a fever." I had both. So I thought it best to fill myself up for the cold, and then keep dark and let the fever starve awhile. In a case of, this kind, I seldom do things by halves; I ate pretty heartily; I conferred my custom upon a stranger who had just opened his restaurant that morning; he waited near me in respectful silence until I had finished feeding my cold, when he inquired if the people about Virginia City were much afflicted with colds? I told him I thought they were. He then went out and took in his sign. I started down toward the office, and on the way encountered another bosom friend, who told me that a quart of salt-water, taken warm, would come as near curing a cold as anything in the world. I hardly thought I had room for it, but I tried it anyhow. The result was surprising. I must have vomited three-quarters of an hour. I believed I had thrown up my immortal soul. A sheet-bath was recommended. I had never refused a remedy yet, and it seemed poor policy to commence then; therefore I determined to take a sheet-bath, notwithstanding I had no idea what sort of arrangement it was. It was administered at midnight, and the weather was very frosty. My breast and back were bared, and a sheet (there appeared to be a thousand yards of it) soaked in ice-water, was wound around me until I resembled a swab for a Columbiad cannon. It is a cruel expedient. When the chilly rag touches one's warm flesh, it makes him start with sudden violence, and gasp for breath just as men do in the death-agony. It froze the marrow in my bones and stopped the beating of my heart. I thought my time had come. 2 For questions 5 and 6, read the following text and answer the questions without the help of a computer. FINISHED FILES ARE THE RESULT OF YEARS OF SCIENTIFIC STUDY COMBINED WITH THE EXPERIENCE OF YEARS. 5. What is the frequency of the letter F in the table above? _______ 6. To the nearest tenth, which percent of the letters is taken up by the F in the table above? _______ For questions 7-9, you will use the table below. Cryptologists, people who decode hidden messages, are aided by the fact that certain letters of the alphabet occur more frequently than others. In the same way you calculated percentages of letter use about a Mark Twain’s story, cryptologists calculated the overall percentages of letter use in ordinary written English, as shown below. E T A O N I R S H 13% 9% 8% 8% 7% 6.5% 6.5% 6% 5.5% D L C M U F P Y B 4% 3.5% 3% 3% 3% 2.5% 2% 2% 1.5% G W V J K X Q Z 1.5% 1.5% 1% 0.5% 0.5% 0.5% 0.3% 0.2% 7. In a large passage written in English, about what percent of the letters would you expect to be vowels, excluding semivowel Y? ______ 8. How many times would you expect the letter E to occur in a message containing 1270 letters? (Round off to a whole number) ______ 9. How many vowels, excluding semivowel Y, would you expect to occur in a message containing 1270 letters? (Round off to a whole number) _______ 3 Questions 10-14 will refer to the secret message below. SECRET MESSAGE 13 15 12 11 13 6 15 17 11 18 2 8 16 13 19 14 19 21 21 12 7 1 17 8 17 2 13 15 17 11 18 2 2 2 8 11 8 13 17 15 17 18 13 11 8 16 3 2 12 13 19 17 20 4 21 19 15 17 13 6 17 14 19 14 17 4 13 5 19 1 8 10 19 1 9 17 10. The secret message above was created using numerals to replace letters of the alphabet. A given numeral in the secret message stands for the same letter each time it occurs, and only 21 letters of the alphabet were used. Determine the frequency for each numeral. Numeral 1 2 3 4 5 6 7 8 9 10 11 Frequency Percent Numeral 12 13 14 15 16 17 18 19 20 21 Frequency Percent 11. Determine the percentage of use for each letter (to the nearest tenth). Fill in the appropriate column in the table above. 4 12. Which numeral in the secret message is the mode? ______ 13. Which numeral in the secret message occurs with the second greatest frequency? ________ 14. Decode the secret message. It will require some guessing and checking! (The answer has 18 separate words) 13 15 12 11 13 6 11 18 8 16 13 19 14 19 21 21 12 1 17 8 7 15 17 11 18 2 2 15 17 2 17 2 13 11 8 13 17 15 17 18 13 11 8 16 3 2 12 13 19 17 20 4 21 19 15 17 13 6 17 14 19 14 17 4 13 5 19 1 8 10 2 19 8 1 9 17 5 15. Use the same numeral code as in question 14 to answer this question. Mr. Simon has a favorite song he plays every Memorial Day weekend. Who sings the song? The singer’s name is coded below. (The answer has two separate words) 21 17 17 16 15 17 17 8 3 19 19 1 During Second World War, American cryptologists, working in close partnership with their British allies, broke the Japanese military codes. Therefore, every intercepted message from Japan would be read by US military cryptologists. In contrast, the Japanese could only read the messages sent by the US Army and the US Air Force, but they could not read the messages sent by the US Marines. Why did the Japanese fail to break the US Marines’ secret code? The answer is suggested in the film “E Pluribus Unum”, out of many came one, shown to students visiting the US Capitol Building. Out of many peoples, races, languages, religions, and ethnicities, America came into being. One of those peoples had a major role in allowing the US Marines to communicate using a secret code undecipherable to the Japanese. During World War II, the US Marines of Navajo origin translated every message from English into the Navajo language before it was sent over the radio and telephone lines. Therefore, when the Japanese “broke the code”, they could only hear a Navajo message. The Japanese thought that Americans had created a difficult math-based talk code, and they tried very hard to use math to break the talk code. Fortunately for us, the Japanese never bother to research the many languages spoken by native Americans. The idea to use Navajo for secure communications came from Philip Johnston, the son of a missionary to the Navajos and one of the few non-Navajos who spoke their language fluently. Johnston believed Navajo answered the military requirement for an undecipherable code because Navajo is an unwritten language of extreme complexity. About 500 Marines of Navajo origin became code talkers, whose primary job was to talk in secret code, sending information on tactics and troop movements, and other vital battlefield communications over telephones and radios. Once you are finished, submit on Edmodo. This paper will not be collected. Grading Scale Points Grade 111-123 98-110 86-97 74-85 73 or less A B C D F Enjoy your summer! 6