Cryptography Algorithm Assignment

Problem 6.13

Two samples of RSA ciphertext are presented in Tables 3.1 and 5.7. Your kis to decrypt them. The public parameters of the system are - 18923 and 6- 1261 (for Table 5.1) and a-31313 and 64913 (for Table 5.2). This can be accomplished as follows. Fina, factor (which is easy because it is so small). Then compute the exponent a from o(n), and, finally, decrypt the ciphertext. Use the SQUARE-AND-MULTIPLY ALGORITHM to exponentiate modajo.

In order to translate the plaintest back into ordinary English text, you need to know how alphabetic characters are "encoded as elements in Z. Each element of Z. represents Cece alphabetic characters as in the following examples:

DOG - 3×26+14×26+6 =2308
CAT -2x26+0x26+19 =1371
ZZZ -25 x 26"+25 x 26+25 =17575

You will have to invent this process as the final step in your program .

The first plaintest was taken from "The Diary of Samuel Marchbanks," by Robert son Davies, 1947, and the second was taken from "Lake Wobegon Days" by Garri son Keillor, 1995.

uses the following two tables

You may use the command ett book

Table 6.1 (or 5.1) (Exercise 6.13)

12423 11524-7243 7459 14303 6127 10164 16399
9792 13629 14437 13817 18833 13556 3159 16647
5300 12951 81 8966 8007 13167 10022 17213 2264
961 17459 4101 2199 14509 17183 15827 12693 9003
18134 2830 2684 12990 12501 18873 12161 13071
164900 7233 6270 17086 9792 14266 13236 5300 13151
8850 12129 6091 18110 3332 15061 12347 7817 7946
11675 13924 13892 18011 2623 6276 $500 201 8850
11179 16477 10151 3533 13842 7537 12259 18110 44
2364 15570 3460 9086 2087 4481 11231 7547 11381
17910 12867 13203 5102 4742 5053 15407 2976 9330
12192 56 2471 15334 841 13995 17592 13297 2430 9741
11675 424 6686 738 13874 8168 79136246 14301 1144
9056 15967 7328 13203 796 195 9872 16979 15404 14130
9105 2001 9792 14251 1499 11296 1105 4502 16979 1105
56 4118 11302 5988 3363 15827 6928 4191 4277 10617 874
13211 11821 3090 18110 44 2364 15570 3460 9885 9988 3798
1158 9872 16979 15404 6127 9872 3652 14838 7437 2540 1367
2512 14407 5053 1521 297 10935 17137 2185 9433 13293 7555
13618 13000 6490 5310 18676 4782 11374 446 4165 11634 3046
14611 2364 6789 11634 4643 4063 4576 179557665 11748 14616
11453 17666 925 56-4118 18731 9522 14838 7487 388011476
83055102 2999 106281432691259061 652 181108720 15404 2951
722 15338341106102443 11056 213

Table 6.2 (or 5.2) (Exercise 6.13)

6340 8309 14010 8936 27358 25029 16481 25809 23614
7135 2499630590 27570 26436 30358 9395 27594 14999
4317.72346 23421 26430 1605 17831 25734 7647 23501
7372 25774 18436 12056 13547 2909 8635 2149 1908
22074 7372 8006 1304 4082 31803 0314 107 7359 2247
07172 2227 15698 30317 4685 14656 30388 8671 29956
15705 1417 26405 286928342 2:2779893 2324129519
12437 110827500 657532414410025 25234 30155 23005
8267 9917 7094 9654 2137 10042 27701 16930 29749
$635 226 11708 24593 20240 27212 27456 9741 214929
3292149 55014015030155