Cryptography: Theory and Practice by Douglas Stinson CRC Press, CRC Press LLC ISBN: 0849385210 Pub Date: 03/17/95 |
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Much of the material on classical cryptography is covered in textbooks, for example Beker and Piper [BP82] and Denning [DE82]. The probability estimates for the 26 alphabetic characters are taken from Beker and Piper. As well, the cryptanalysis of the Vigenere Cipher is a modification of the description given in Beker and Piper.
A good reference for elementary number theory is Rosen [Ro93]. Background in elementary linear algebra can be found in Anton [AN91].
Kahns book The Codebreakers [KA67] is an entertaining and informative history of cryptography up to 1967. In it, Kahn states that the Vigenere Cipher is incorrectly attributed to Vigenere.
The Hill Cipher was first described in [HI29]. Much information on stream ciphers can be found in the book by Rueppel [RU86].
Give a clearly written description of the steps you followed to decrypt each ciphertext. This should include all statistical analysis and computations you performed.
The first two plaintexts were taken from The Diary of Samuel Marchbanks, by Robertson Davies, Clarke Irwin, 1947; the fourth was taken from Lake Wobegon Days, by Garrison Keillor, Viking Penguin, Inc., 1985.
EMGLOSUDCGDNCUSWYSFHNSFCYKDPUMLWGYICOXYSIPJCK QPKUGKMGOLICGINCGACKSNISACYKZSCKXECJCKSHYSXCG OIDPKZCNKSHICGIWYGKKGKGOLDSILKGOIUSIGLEDSPWZU GFZCCNDGYYSFUSZCNXEOJNCGYEOWEUPXEZGACGNFGLKNS ACIGOIYCKXCJUCIUZCFZCCNDGYYSFEUEKUZCSOCFZCCNC IACZEJNCSHFZEJZEGMXCYHCJUMGKUCY
HINT F decrypts to w.
KCCPKBGUFDPHQTYAVINRRTMVGRKDNBVFDETDGILTXRGUD DKOTFMBPVGEGLTGCKQRACQCWDNAWCRXIZAKFTLEWRPTYC QKYVXCHKFTPONCQQRHJVAJUWETMCMSPKQDYHJVDAHCTRL SVSKCGCZQQDZXGSFRLSWCWSJTBHAFSIASPRJAHKJRJUMV GKMITZHFPDISPZLVLGWTFPLKKEBDPGCEBSHCTJRWXBAFS PEZQNRWXCVYCGAONWDDKACKAWBBIKFTIOVKCGGHJVLNHI FFSQESVYCLACNVRWBBIREPBBVFEXOSCDYGZWPFDTKFQIY CWHJVLNHIQIBTKHJVNPIST
KQEREJEBCPPCJCRKIEACUZBKRVPKRBCIBQCARBJCVFCUP KRIOFKPACUZQEPBKRXPEIIEABDKPBCPFCDCCAFIEABDKP BCPFEQPKAZBKRHAIBKAPCCIBURCCDKDCCJCIDFUIXPAFF ERBICZDFKABICBBENEFCUPJCVKABPCYDCCDPKBCOCPERK IVKSCPICBRKIJPKABI
BNVSNSIHQCEELSSKKYERIFJKXUMBGYKAMQLJTYAVFBKVT DVBPVVRJYYLAOKYMPQSCGDLFSRLLPROYGESEBUUALRWXM MASAZLGLEDFJBZAVVPXWICGJXASCBYEHOSNMULKCEAHTQ OKMFLEBKFXLRRFDTZXCIWBJSICBGAWDVYDHAVFJXZIBKC GJIWEAHTTOEWTUHKRQVVRGZBXYIREMMASCSPBNLHJMBLR FFJELHWEYLWISTFVVYFJCMHYUYRUFSFMGESIGRLWALSWM NUHSIMYYITCCQPZSICEHBCCMZFEGVJYOCDEMMPGHVAAUM ELCMOEHVLTIPSUYILVGFLMVWDVYDBTHFRAYISYSGKVSUU HYHGGCKTMBLRX
HINT Since p is prime, is a field. Use the fact that a matrix over a field is invertible if and only if its rows are linearly independent vectors (i.e., there does not exist a non-zero linear combination of the rows whose sum is the vector of all 0′s).
HINT Use the formula given in Theorem 1.3 and observe that det A = ±1 for an involutory matrix over .
breathtaking
yields the ciphertext
RUPOTENTOSUP
where the Hill Cipher is used (but m is not specified). Determine the encryption matrix.
Suppose Oscar has learned that the plaintext
adisplayedequation
is encrypted to give the ciphertext
DSRMSSIOPLXLJBZULLM
and Oscar also knows that m = 3. Compute the key, showing all computations.
Here is a sample of ciphertext for you to decrypt using this method:
LMQETXYEAGTXCTUIEWNCTXLZEWUAISPZYVAPEWLMGQWYA XFTCJMSQCADAGTXLMDXNXSNPJQSYVAPRIQSMHNOCVAXFV
cryp togr aphy
The ciphertext would be CTAROPYGHPRY.
MYAMRARUYIQTENCTORAHROYWDSOYEOUARRGDERNOGW
As before, we suppose that the recurrence has the form
(z1, . . . , zm) comprises the initialization vector. For i ≥ 1, define
Note that the coefficient matrix has the vectors v1, . . . , vm as its rows, so our objective is to prove that these m vectors are linearly independent.
Prove the following assertions:
and not all the αj′s are zero. Observe that h ≤ m + 1, since any m + 1 vectors in an m-dimensional vector space are dependent.
for any i ≥ 1.
MALVVMAFBHBUQPTSOXALTGVWWRG
Describe how you can use the concept of index of coincidence to first determine the length of the keyword, and then actually find the keyword.
Test your method by cryptanalyzing the following ciphertext:
IYMYSILONRFNCQXQJEDSHBUIBCJUZBOLFQYSCHATPEQGQ JEJNGNXZWHHGWFSUKULJQACZKKJOAAHGKEMTAFGMKVRDO PXNEHEKZNKFSKIFRQVHHOVXINPHMRTJPYWQGJWPUUVKFP OAWPMRKKQZWLQDYAZDRMLPBJKJOBWIWPSEPVVQMBCRYVC RUZAAOUMBCHDAGDIEMSZFZHALIGKEMJJFPCIWKRMLMPIN AYOFIREAOLDTHITDVRMSE
The plaintext was taken from The Codebreakers, by D. Kahn, Macmillan, 1967.
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