Cryptology - Unofficial St. Mary's College of California Web Site
Cryptology - Unofficial St. Mary's College of California Web Site
Cryptology - Unofficial St. Mary's College of California Web Site
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70 CHAPTER 4. THE EUCLIDEAN ALGORITHM<br />
10. In a Decimation Cipher the enciphering key must be smaller than an<br />
relatively prime to the modulus. Since there are 12 numbers between 1<br />
and 26 whose gcd with 26 is 1, there are 12 Decimation Ciphers modulo<br />
26.<br />
(a) How many Decimation Ciphers are there modulo 7 (Hint: how<br />
many numbers are smaller and relatively prime to 7) How many<br />
(b) How many Decimation Ciphers are there modulo 18<br />
(c) How many Decimation Ciphers are there modulo 28<br />
(d) How many Decimation Ciphers are there modulo 35 (It might be<br />
easier to first find the numbers that are not proper enciphering keys.)<br />
11. The following is a decimation cipher. Use the techniques <strong>of</strong> this chapter<br />
to decrypt it.<br />
PYETO MLWPQ QRVOT TWDQK IODQW WTYUR SEQSP JODWP UOTTO SMWVS AQWRQ<br />
SDQ.<br />
12. The following is a linear cipher. With the hint that the three most common<br />
letters are eit (although not necessarily in that order), can you decrypt<br />
it<br />
JXYVK MDZYJ PNFJK NLXLD SHYNM NWZMD HGNXG JPLJW NWZLO NFMFQ TMNFW<br />
DMNPP LENJM LIVKL YXLKM NQIL<br />
13. Alex’s public Kid-RSA gives e = 361 and N = 4063. Suppose you’ve<br />
captured the message “I used your PK. 630, 3518, 269, 3157, 722, 899,<br />
3157, 177, 1352, 630, 1352, 1444, 3157, 177, 1805, 991, 3157, 899, 2166,<br />
3249, 3879, 1805.<br />
GTTGM JNQJZ DMFF.<br />
Can you decrypt the message<br />
14. Corrine’s public Kid-RSA lists e = 495 and N = 2644. You’ve intercepted<br />
a message for her: “Use<br />
978, 2475, 314, 2475, 978, 1473, 2475, 1980, 495, 652, 2632, 1316, 495,<br />
990, 2475, 1968.<br />
XZHS RM YLC MFNYVI GVM.<br />
Can you decrypt the message