cryptography

13 Two samples of RSA ciphertext are presented in Tables 6.2 and 6.3. Your task is to decrypt them. The public parameters of the system are n=18923 and b=1261 (for Table 6.2) and n=31313 and b=4913 (for Table 6.3). This can be accomplished as follows. First, factor n (which is easy because it is so small). Then compute the exponent a from (n), and, finally, decrypt the ciphertext. Use the SQUARE-AND-MULTIPLY ALGORITHM to exponentiate modulo n. In order to translate the plaintext back into ordinary English text, you need to know how alphabetic characters are "encoded" as elements in Zn. Each element of Zn represents three alphabetic characters as in the following examples: DOG3262+1426+6=2398CAT2262+026+19=1371ZZZ25262+2526+25=17575. You will have to invert this process as the final step in your program. The first plaintext was taken from The Diary of Samuel Marchbanks, by Robertson Davies, 1947, and the second was taken from Lake Wobegon Days, by Garrison Keillor, 1985. TABLE 6.3: RSA ciphertext 63402361427584257747908408215698141712437230051593027486181542149195543183600025973830971351499976478635118033031726905110882672974897412231916975236141734731280447714010249964517239012149531446852580927106991786352149277051608775532523429413309898936305901214673721908107146962834718743799423645293292032114600473445952066273582757029421257742207673593038826277241449694117382149232542770580912149836925023264862643918436737222470867178971068521492459155011362419386239736360232041648130388160612056868673722995620240252341004220240140153249732514015198378425258099395178811354713042282715705215193015527705272123015554432627710784637792