Cryptology by Discovery: An Introduction to Conjecture and Proof

1.

Encrypt the plaintext message THREE with the keyword TWO.

2.

Decrypt the ciphertext message TMTVLRITV with the keyword CIRCLE .

3.

Determine the four letter “keyword” (not necessarily an actual word in English) that will decipher the ciphertext YWHP as

1. FOUR

2. FIVE

3. ABCD

1.

Suppose we pick one student at random. List all of the possibile ways to pick:

1. a female student.
2. a male first year student or a female second year student.
3. a female student or a second year student.
4. a female student and a sophomore.
5. Give the probability for each of the above events.

2.

Suppose we pick two students at random and don't care about the order in which they were picked. Determine the number of ways to pick two students such that:

1. they are both first year students.
2. they are both first years students or they are both second year students.
3. one of them is a second year student and the other one is a first year student.
4. one of them is a second year student and the other one is female.
5. exactly one of them is a female student.
6. at least one of them is a female student. (Think of a better way to do this one.)
7. at least one of them is a female or at least one of them is a second year. (Think of a better way to do this one.)
8. Check your answers with the Sage code. How did you do? If you missed any, what went wrong with your calculation?
9. Give the probability for each of the above events.

3.

Suppose we pick two students at random and we DO care about the order in which they were picked. Determine the number of ways to pick two students such that:

1. they are both first year students.
2. the first one is a first year student and the second one is a second year student.
3. the first one is a female student and the second one is a second year student.
4. the first one is a female student.
5. Check your answers with the Sage code below and make any adjustments as necessary.
6. Give the probability for each of the above events.

4.

When do we add when calculating probabilities?

5.

When do we multiply when calculating probabilities?

1.

Compute the index of coincidence (probability of picking 2 identical letters) for a text with only 7 different letters and the following frequency distribution of letters: A:15, B:8, C:7, D:9, E:20, F:5, G:6

2.

Compute the index of coincidence for a text with only 7 different letters and the following frequency distribution of letters: A:10, B:10, C:10, D:10, E:10, F:10, G:10.

3.

Compute the index of coincidence for a text with all 26 letters of the alphabet and each of the letters A-Z occurs 10 times. (Ie, 260 total letters, 10 each of everything A-Z).

4.

Compute the index of coincidence for an even distribution of the letters A-Z where each letter occurs 100 times. (Ie, 2600 letters, 100 each of everything A-Z).

5.

Compute the index of coincidence for an even distribution of the letters A-Z where each letter occurs \(n\) times. (Ie, \(26n\) letters, \(n\) each of everything A-Z). What happens as \(n\) goes to infinity?

1.

Compute the index of coincidence of the two ciphers below (using the Sage code) and determine which is a monoalphabetic cipher and which is a polyalphabetic cipher. After you’ve figured out which is the Vigenere cipher look for any patterns in the ciphertext that might help you break it.

2.

GWGET QGWGE TQWWU OIZGB DRCNO MRLZQ ECDQI ZGKMX TPUWZ ECNET QIQXO MFRNM IMZQG EQIWH QZWPQ FIGOL DRVNR QXDVP EIWHM KHWRQ MIWIZ GBAHW RIZAJ EARTA IJMWI ZGBAQ OGHWR GWSDL PHZEI WDNIZ GJXLV PZWDP AEWQZ JTUCI DGAXH OMQLA ZTQWA ILVSI WDDKT DZYRN BREQU NGOBD RCNOM XLSQD PQOTN UWFKJ ALTMQ LNXJN OMORW XLBIL BTDJM EWAQA NOWAG BTHVF KMOKI DPQEI QDPIZ GOARL PRCNO MPRCN OMFRQ XDVPW ZAXJX HNUUM NXZZD VPFIG OLDRV NXJNO M

3.

CTCWY DQITW IDAGF CHVAA PFYVA NPCZY PMCDD EYPZA NIPAV ACSZY TSDGB NYPMW INPYP MZFAQ EIKAS BZFAT CZFAN WIDAG ZSOKF YGFAC HISZI TZFAF IDACP HDIIK AHCNI SPHWI ZFANW IDAFA OCDDA HVCOK HIEPZ FAFID AOIWA SBFAN AYGWA DDFIP AQTNA GFWCH AFIPA QZFAW IZFAN WIDAN CPSBC PHGUS AAJAH YPPAX ZZIFY WZFCZ GPIZF IPAQZ FCZGW CBDAG QNSBY GWADD WCBDA GQNSB ZFAVC VQWID AGZYD DHIEP YPZFA FIDAE CGGSD KYPMY OCPZG WADDC PQZFY PMHIE PFANA VSZWI DCGGA G

1.

VHXEA MQRWQ MXUTB ECTVF XNILE AMWSB UALOA ENCTT NBXOK QULOA FOAEK TBUTA GOGNY WQMXU TBEAM GDLRE VKELK NMJEY CMBNY YGLBF AXVHX EAMKS XKTAG RTJON UEVCT DGPMC STREM QRTHE KCLVC TYTEX NYKCN ZKNZC NWCVH KDBPG AWMTP CHPTT ETTJO NUEVC TBUVT NUXFB RJUFC NLHOK EOFRA GKOGU HBRAG FFHTI MUAUK LBVYM QHNPT KQDXP TLCBH WTVCT UTEXF STTEK GCHIN BBEWD YOCRB QULEA MTEZK SMTIX U

2.

WHVBH AIOVU TREEZ XJSRC YADZL RVCVO DORFL CKAMO HVZNH NTOWH RDWHV IHXZC WEMOQ HRNZE EYWTY OSRFY IOWYX RFGQU ERDPG IHXGO UIVXF EKRHT VKFHZ XJSRX GTYOU ETYUD JYITY OSAJD JIMOS RFYIE EYXGY PRRJK QEGOR PCOVI RNPIK DKAKK WTYOI IICWI NKVST OSTZM ZEIOL TEYWT YKWTY BRUXR OOEQB ERBVI YKYEK BDIEO GMPCH LWDRK VOSAE YSEEW LNUSF OLVGN FDKAM OEECS HVVNX NKSOS LMKTZ WHAJD KAKPD CKDKU ENHRF XPYVK U

3.

HVIHQ KWNJD ZOHRQ VFGBX ZQINO IZUPN OCOAG IINAR AGOPK HVIHQ KOMZR YHUYH FSMUD CSYIH YGYRQ MWLRE BFMGI YCGVW ZCJRQ TCOGK PHMRB LGAYR DSXJL AVUFP VIFQH YWHTJ SOLRL AGGHC GZYNQ KVUPN SSMNQ KRYJO HDQRU LCOGO PBYQL UTFVF RSLVQ NTFNP LBYIH YWHGK LRYYL YWIHV KFYNP VTUQL ZCLQH YSXOU HWHPR BZXNQ FHBVQ NAIEH ZOPNJ LAIEH HDJNO SWHTP VFYUH SZCFK ISWBQ JSCIH KHBNQ AVUGG HFESR YAUAG ZOPNJ LTUPH DVCPK IFIXH BDIAX ZCOGR MHBRZ HZFBI MCA