6.13 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 po(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 ex- amples: DOG 3 x 26² +14 × 26+6 = CAT → 2x 26² +0 x 26 +19 ZZZ = 25 x 26² +25 x 26+25= You will have to invert this process as the final step in your program. 2398 1371 17575.

Mathematics For Machine Technology
8th Edition
ISBN:9781337798310
Author:Peterson, John.
Publisher:Peterson, John.
Chapter87: An Introduction To G- And M-codes For Cnc Programming
Section: Chapter Questions
Problem 10A
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6.13 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 po(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 ex-
amples:
DOG
3 x 26² +14 × 26+6 =
CAT → 2x 26² +0 x 26 +19
ZZZ
=
25 x 26² +25 x 26+25=
You will have to invert this process as the final step in your program.
2398
1371
17575.
Transcribed Image Text:6.13 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 po(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 ex- amples: DOG 3 x 26² +14 × 26+6 = CAT → 2x 26² +0 x 26 +19 ZZZ = 25 x 26² +25 x 26+25= You will have to invert this process as the final step in your program. 2398 1371 17575.
In 6-13, decrypt the first 5 blocks:
n =
12423-11524-7243-7459-14303
18923, e = 1261
Transcribed Image Text:In 6-13, decrypt the first 5 blocks: n = 12423-11524-7243-7459-14303 18923, e = 1261
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