2007 - Exercises IV.
1. Decode the following cryptotexts:
(a) AMICABLE PHOTON
(b) START OPINIONS
(c) KTZWYMJCJWHNXJ
(d) a3
e3
i3
n2
op2
s2
r
2. A simple substition cipher / : Z26 --ˇ Z26 (a plaintext letter x is substituted with
a cryptotext letter f(x)) is called self-inverting if f(x) = f~1
(x), ie. f(f(x)) =
x.
(a) How many different self-inverting substitution ciphers are there?
(b) What is the proportion of self-inverting substitution ciphers to all simple
substitution ciphers?
(c) How many self-inverting substitution ciphers which do not map any letter
onto itself are there?
3. Decrypt the following cryptotext which was obtained using the Vigenere cryp-
tosystem.
CTWIJ NSDVF KBJXZ GTXRV CAHRL CZVSX EWSLW TGWLW TSDVW
00QCK JCUXU WHVXG DSOIS TBHHA PCUHW THRFW ECPIU KDKIJ
GLSIJ VGWLW USVEN GHLQW CBGEV FHRSM TSQNG AAHRL
4. Try to decode the following cryptotext. You know that the one-time pad cryptosystem
(using addition modulo 26) was used and the encryption key starts
with "GSC".
GLUYM YIFGH EJPCR OFLSM DOFML QSFCDF MZHLL VDJLE
TTYNM XDKEC ALIOP DHTFN ECRKF GKDVRJ DJVMR WICKF
5. Decide whether the following cryptosystems are idempotent. Explain your rea-
soning.
(a) the Caesar shift cipher;
(b) the Affine cipher;
(c) the Hill cipher;
(d) the Vigenere cipher.
6. Encrypt the word "cryptology" with
(a) the Polybius square cryptosystem;
(b) the Hill cryptosystem with M =
(c) the Caesar cryptosystem with k = 6 and the keyword "SHIFT";
(d) the Autoclave cryptosystem with the keyword "KEY".
7. Assume that the Affine cryptosystem is implemented in Zi26(a)
Determine the number of possible keys.
(b) For the encryption function e{x) = 23x + 7 (mod 126) find the corresponding
decryption function.
8. (Bonus Exercise) You have found an old-looking parchment with the following
text:
20 4 22 8
42 22 71 8
36 3 7 11
38 6 6 2
2 26 17 8
66 5 1 22
19 80 9 3
14 32 7 1
45 14 14 13
4 29 20 6
7
11
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