Cryptography: Theory and Practice by Douglas Stinson CRC Press, CRC Press LLC ISBN: 0849385210 Pub Date: 03/17/95 |
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Since Z occurs significantly more often than any other ciphertext character, we might conjecture that dK(Z) = e. The remaining ciphertext characters that occur at least ten times (each) are C, D, F, J, M, R, Y. We might expect that these letters are encryptions of (a subset of) t, a, o, i, n, s, h, r, but the frequencies really do not vary enough to tell us what the correspondence might be.
At this stage we might look at digrams, especially those of the form -Z or Z-since we conjecture that Z decrypts to e. We find that the most common digrams of this type are DZ and ZW (four times each); NZ and ZU (three times each); and RZ, HZ, YZ, FZ, ZR, ZV, ZC, ZD, and ZJ (twice each). Since ZW occurs four times and WZ not at all, and W occurs less often than many other characters, we might guess that dK(W) = d. Since DZ occurs four times and ZD occurs twice, we would think that DK(D) ∈ {r, s, t}, but it is not clear which of the three possibilities is the correct one.
If we proceed on the assumption that dK(Z) = e and dK(W) = d, we might look back at the ciphertext and notice that we have ZRW and RZW both occurring near the beginning of the ciphertext, and RW occurs again later on. Since R occurs frequently in the ciphertext and nd is a common digram, we might try dK(R) = n as the most likely possibility.
At this point, we have the following:
------end---------e----ned---e------------ YIFQFMZRWQFYVECFMDZPCVMRZWNMDZVEJBTXCDDUMJ --------e----e---------n--d---en----e----e NDIFEFMDZCDMQZKCEYFCJMYRNCWJCSZREXCHZUNMXZ -e---n------n------ed---e---e--ne-nd-e-e-- NZUCDRJXYYSMRTMEYIFZWDYVZVYFZUMRZCRWNZDZJJ -ed-----n-----------e----ed-------d---e--n XZWGCHSMRNMDHNCMFQCHZJMXJZWIEJYUCFWDJNZDIR
Our next step might be to try dK(N) = h, since NZ is a common digram and ZN is not. If this is correct, then the segment of plaintext ne - ndhe suggests that dK(C) = a. Incorporating these guesses, we have:
------end-----a---e-a--nedh--e------a----- YIFQFMZRWQFYVECFMDZPCVMRZWNMDZVEJBTXCDDUMJ h-------ea---e-a---a---nhad-a-en--a-e-h--e NDIFEFMDZCDMQZKCEYFCJMYRNCWJCSZREXCHZUNMXZ he-a-n------n------ed---e---e--neandhe-e-- NZUCDRJXYYSMRTMEYIFZWDYVZVYFZUMRZCRWNZDZJJ -ed-a---nh---ha---a-e----ed-----a-d--he--n XZWGCHSMRNMDHNCMFQCHZJMXJZWIEJYUCFWDJNZDIR
Now, we might consider M, the second most common ciphertext character. The ciphertext segment RNM, which we believe decrypts to nh-, suggests that h- begins a word, so M probably represents a vowel. We have already accounted for a and e, so we expect that dK(M) = i or o. Since ai is a much more likely digram than ao, the ciphertext digram CM suggests that we try dK(M) = i first. Then we have:
-----iend-----a-i-e-a-inedhi-e------a---i- YIFQFMZRWQFYVECFMDZPCVMRZWNMDZVEJBTXCDDUMJ h-----i-ea-i-e-a---a-i-nhad-a-en--a-e-hi-e NDIFEFMDZCDMQZKCEYFCJMYRNCWJCSZREXCHZUNMXZ he-a-n-----in-i----ed---e---e-ineandhe-e-- NZUCDRJXYYSMRTMEYIFZWDYVZVYFZUMRZCRWNZDZJJ -ed-a--inhi--hai--a-e-i--ed-----a-d--he--n XZWGCHSMRNMDHNCMFQCHZJMXJZWIEJYUCFWDJNZDIR
Next, we might try to determine which letter is encrypted to o. Since o is a common letter, we guess that the corresponding ciphertext letter is one of D, F, J, Y. Y seem to be the most likely possibility, otherwise, we would get long strings of vowels, namely aoi from CFM or CJM. Hence, lets suppose dE(Y) = o.
The three most frequent remaining ciphertext letters are D, F, J, which we conjecture could decrypt to r, s, t in some order. Two occurrences of the trigram NMD suggest that dE(D) = s, giving the trigram his in the plaintext (this is consistent with our earlier hypothesis that dE(D) ∈ {r, s, t}). The segment HNCMF could be an encryption of chair, which would give dE(F) = r (and dE(H) = c) and so we would then have dE(J) = t by process of elimination. Now, we have:
o-r-riend-ro--arise-a-inedhise--t---ass-it YIFQFMZRWQFYVECFMDZPCVMRZWNMDZVEJBTXCDDUMJ hs-r-riseasi-e-a-orationhadta-en--ace-hi-e NDIFEFMDZCDMQZKCEYFCJMYRNCWJCSZREXCHZUNMXZ he-asnt-oo-in-i-o-redso-e-ore-ineandhesett NZUCDRJXYYSMRTMEYIFZWDYVZVYFZUMRZCRWNZDZJJ -ed-ac-inhischair-aceti-ted--to-ardsthes-n XZWGCHSMRNMDHNCMFQCHZJMXJZWIEJYUCFWDJNZDIR
It is now very easy to determine the plaintext and the key for Example 1.10. The complete decryption is the following:
Our friend from Paris examined his empty glass with surprise, as if evaporation had taken place while he wasnt looking. I poured some more wine and he settled back in his chair, face tilted up towards the sun.1
1P. Mayle, A Year in Provence. A. Knopf, Inc., 1989.
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