## Exercises 3.5 Exercises Set 6

###### Investigation Work

###### 1.

Finish all investigations from in-class activities.

###### Computation Based Exercises

###### 2.

This problem consists of two cipher texts, one of which is a Vigenère cipher the other is an affine cipher. Your mission is to determine which is which and crack them!! Use Index of Coincidence to determine which is which. Use the Sage programs for vigenere and affine to crack them. You don't have to write the entire message, just give the keyword or the affine formula and the first few words of the message.

- PMZCY XOANM VWDQM GGOAI RENKA BGEIZ AJDOC GWVCB ROZWQ YFXJO VIKKO KZBSB GVDEJ RQZGE RGOKN UCGZW VIKKB QKLZQ CEHTY VKUDI EWAZD SKLJO RTLIB NNRER SBGEP UAJZR VDJLE UCOKN ZIIGA ICFCL AAZNU EEBRO WIHCE FJRPM ZCYXO BGIEJ OENRK KGVNW ZQCJQ IEJXI BKNKW BVEMH BWQGF WFCRT URUWT RSHOB VECOZ WSHVU AASAE GHMZR EXJBH LFXNJ QAZQO IKLIR P
- YDXRW SOJTP SUQIJ UNGGO EMHOS SRUXY PSWUJ UIROI OTUXW QEYXU HPUXY WODWI TUYJQ OAWAU JQRAU TTOSW UJAED DQQOA WTYIO JYIWQ ROWQU HPYPJ WUPUV UVWJO DVWVV WJAYH XHWSQ YPIUT TXRWB OGQQE NGUHP YPIUT TXRWK YJTQR UJJGY PXUTM XRJOE KRAGW UJQUH PYUTS UGQSO ETPIU JJGUV UVWJE ABJWT TUDOJ SRWHY XKJWS RUNGX OMWWV YHXRW JUYHY DXRWS OJTPS UQIJU NG

###### 3.

Decrypt the following Vigenère cipher. You don't have to write the entire message, just give the keyword and the first few words of the message.

BUFSQ DWXHK CBMRK KSWWW ZGHOS MBYWS ZGJHV KDFMZ UCUBB DVSDH KSTHS XJUAK TVSBP WGDPA XOSWQ RPOPB JZZSB BHLSW HSTVA KUVSW BHWMJ OBGPF YSOUO CBASW CSFYG HVOUS OWTHF EHUZS OUHYD FOMLH VOOON SFBWQ NOQYE SXOSW QRPGC GOGHB VUUVF GWXDZ INFBS BWSKB BQYSO UAOOH OVMOP YSHVO NMGDF FWYVG RSTOD ZFOFK OQSYG OTYSA SBHWF VGFWO ORHRF GICQW QSPBG YGVWC DCKYS YSBTK WDIWB DISDK SOBYJ RVSHV GODIF SUMDB PXSMU OBNUV SMFFH KJBHI UVODT CAOPB SMMCG OUCVS NDSBI ODCUV SWJGG SOUUS SZWCB BOJJG DIUVS ZMCHS TDIBF TWMUW CXCIH DISVS THCBJ QOVCO QUHFC EOROV BBHES WBQTT OWPIG GBFHS NSQYN DIDJB UZSCX ODHHR BHQBB QYOEH VOHSF WBBIL POHMP AAEOW QKUWC XTQCN FWGBF OZKOR OMDIF KUSZI QCFDS OMOES BSHAO STQCX WWBMJ BUVZD ZYUHS NGCFM FTIVM MKBJH HOOOB NGWZV FRKSU VKOMZ RBBKB MIOFK DHSBT WBCIC FDJHG OWSFI UVWXH OUYPR HODVB YNMGD FFMCI CIVEP S

###### 4.

Decrypt the following Vigenère cipher. You don't have to write the entire message, just give the keyword and the first few words of the message.

LLMKM WSVEJ ITDIE KYVWS JSJMD QSFIX ZEXAW TJITS VIVXS LVISX MLWZA IAWVW ARXWP PAKIF XPQER VXIDP EOEVL MQWWX GVCOM XZSYL IBHPS KMZWW EFHLA WXJMS FMGKE RVAML LSMXJ SPWAJ CARKZ MWLSV QXSYP SJMJQ XLWEQ WVMUE RKMXA WFSWI VSRLL ITIWL WIDPM FKRGZ IDFCJ SFWVX ZEVJM WOLSK ITJIZ ASYKA SJOJS XLWVP SRHKY JXIVW HWGFE VPCOL IFXVS RWDEX WHXGX LWWGJ IIFLI JILWL EKEHW GIFXW UVIWR TDECX VSEXS EWXGT TSVHS WWMVI VHMJI GLMSF JVGQQ AGLSI PSTWL IHSRH LLVWI JARIH IVXSV EERUI WTCFJ MXAWL SGXGV W

###### 5.

Decrypt the following Vigenère cipher. You don't have to write the entire message, just give the keyword and the first few words of the message.

TQBHE KKNEV GWBWI ZGFZV YQTSM KYEOH APGLR FKVPV KCRJL AUWTJ WYADV WCLWC HKSDI VUHPX GNDSM EVOXS JTOHQ GTNTR YKEIT WETES XKNOE YKFEM FVHPH JKVPA SATSE LIOPW XTOXD WTOES GPESY FFRPH APSTB KGCZR VUAYH AVBPX LGRMI LJECI LJEYI PVMZV FKNRL WIOEY HGACP QCNOP WHTQS JYOCO OJEYL AUWTJ WYOVI MRSSI DQOVI VQUEX ZGWTR VQWLR VUUCI WPOFK ZVHPV WYADE TQXRM XVWCE HREOM FVHPQ AFDWI GHTSI VTIGI OCYNS FHUDI VVHPA AHEAY LQNSI JTOMI SPDCE FQUEX GVHPH JKVPA SABCS MIHEX ZGBZB TCCVM FVHPL GWSPW ZGOAI FGDTX SPDQS MPDLF JCNOR WYBLX ZTOZQ KEAWI TQBSE KDEPR EKSDM FISTR UGFCM VCY

###### 6.

A blackjack hand consists of two cards from a standard 52 card deck. The first card is face down and the second is face up. Find the probability that:

The face down card is a four and the face up card is a 10.

The face down card is a four and the face up card is a heart. (Think about two cases here.)

The face down card is one of (A,2,3,4,5,6) and the face up card is one of (6,7,8,9,10,J,Q,K). (Think about cases here.)

The two cards are both hearts.

###### 7.

Suppose five cards are picked at random from a standard deck of 52 cards. (Picked all at once, no replacement.) Find the probability that

there are two 5’s and three 8’s.

there are four Aces.

there are two 6’s and two 7’s and any other card (that is not a 6 or a 7)

you get a flush. I.e., all five cards are the same suit. (diamonds, clubs, spades or hearts)

you get a full house. I.e., two of one number (A, 2,3, … K) and three of another.

###### 8.

See the letter frequency chart for Spanish at wikipedia and calculate the index of coincidence for a large text in Spanish (or a monoalphabetic cipher in Spanish). Note there are more than the 26 letters in this table based on various accent marks.

###### 9.

Suppose a particular “language” consists of only the numbers 0-9 and they occur with the following frequencies:

0 | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 |

13% | 14% | 8% | 10% | 6% | 15% | 3% | 7% | 9% | 20% |

If you pick two numbers at random from a long “text” in this language, what is the probability that you pick two identical numbers?

If a text of the digits 0-9 were uniformly distributed instead (each number occurs the same number of times), what would the probability be of picking two identical letters?

If a ciphertext of the “language” has the following distribution, what is its index of coincidence? 0: 8, 1: 8, 2: 3, 3: 4, 4: 3, 5: 7, 6: 2, 7: 2, 8: 4, 9: 9. Is it more likely to be monoalphabetic or polyalphabetic is this language?

###### 10.

Approximately what keyword length will the Friedman test predict if the index of coincidence of 0.03851, .038501, .0385001, .03850001. Assume that the value of n is very large, say 100000. What is happening as the index of coincidence gets closer to .0385? Explain why this makes sense.

###### 11.

Approximately what keyword length will the Friedman test predict if the index of coincidence of 0.0649. Assume that the value of n is very large, say 100000. Explain why this makes sense.

###### Writing Based Exercises

###### 12.

Four cards are in front of you. Each card is two sided with a letter on one side and a number on the other side. You can only see one side. For the four cards in front of you, one is an A, one is a 1, one is a 6 and the other is an T. Consider the statement “if one side of a card is an A, then the other side of a card is a 1.” Which cards should you turn over, and what should be on the other side, to determine if the statement is true or false for the four cards in front of you?

###### 13.

Solve the formula

for \(k\text{.}\)

###### 14.

Explain why the probability of picking two identical letters from the same column given that you are picking two letters at random from the text is

###### 15.

Explain why the probability of picking two identical letters from two different columns given that you are picking two letters at random from the text is

###### 16.

Explain why a vigenere encryption is perfectly secure if the key length is as long as the cipher text.

###### Enrichment Opportunities

###### 17.

In preparation for WWII era cryptography, watch the video from speaker Liza Mundy about her book *Code Girls: The Untold Story of the American Women Code Breakers of World War II*. Code Girls is a fascinating story about the secret recruitment of female codebreakers during WWII. The video is one hour long. Write a paragraph about what you found interesting about the video.