Rework Example 5 by breaking the message into two-digit blocks instead of three-digit blocks. What is the enciphered message using the two-digit blocks?
Example 5: RSA Public Key Cryptosystem We first choose two primes (which are to be kept secret):
Then we compute
(which is to be made public):
Next we choose
(to be made public), where
Using the Euclidean Algorithm, we find
(which is kept secret). The mapping
Using the
The message becomes
This message must be broken into blocks
The enciphered message becomes
To decipher the message, one must know the secret key
Finally, by re-breaking the “message” back into two-digit blocks, one can translate it back into plaintext.
The RSA Public Key Cipher is an example of an exponentiation cipher.
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ELEMENTS OF MODERN ALGEBRA
- Suppose that in an RSA Public Key Cryptosystem, the public key is. Encrypt the message "pay me later” using two-digit blocks and the -letter alphabet from Example 2. What is the secret key? Example 2 Translation Cipher Associate the letters of the "alphabet" with the integers. Let and define the mapping by where is the key, the number of positions from the plaintext to the ciphertext. If our alphabet consists of through, in natural order, followed by a blank, then we have "letters" that we associate with the integers as follows:arrow_forwardSuppose that in an RSA Public Key Cryptosystem, the public key is e=13,m=77. Encrypt the message "go for it" using two-digit blocks and the 27-letter alphabet A from Example 2. What is the secret key d? Example 2 Translation Cipher Associate the n letters of the "alphabet" with the integers 0,1,2,3.....n1. Let A={ 0,1,2,3.....n-1 } and define the mapping f:AA by f(x)=x+kmodn where k is the key, the number of positions from the plaintext to the ciphertext. If our alphabet consists of a through z, in natural order, followed by a blank, then we have 27 "letters" that we associate with the integers 0,1,2,...,26 as follows: Alphabet:abcdef...vwxyzblankA:012345212223242526arrow_forwardSuppose that the check digit is computed as described in Example . Prove that transposition errors of adjacent digits will not be detected unless one of the digits is the check digit. Example Using Check Digits Many companies use check digits for security purposes or for error detection. For example, an the digit may be appended to a -bit identification number to obtain the -digit invoice number of the form where the th bit, , is the check digit, computed as . If congruence modulo is used, then the check digit for an identification number . Thus the complete correct invoice number would appear as . If the invoice number were used instead and checked, an error would be detected, since .arrow_forward
- Suppose that in an RSA Public Key Cryptosystem. Encrypt the message "algebra" using the -letter alphabet from Example 4. Use two-digit blocks. Use three-digit blocks. What is the secret key?arrow_forwardSuppose that in an RSA Public Key Cryptosystem. Encrypt the message "pascal" using the -letter alphabet from Example 4. Use two-digit blocks. Use three-digit blocks. What is the secret key?arrow_forwardThank you so much!arrow_forward
- Suppose you are working at the State Department and to enter secure facilities requires a password. You create an 8 character password made up of 5 letters (A-Z) and 3 numbers (0-9). No letter or number can be repeated. How many different passwords are possible? a. 1,957,524,000 b. None of these c. 11,881,376,000 d. 5,683,392,000 e. 824,332,000arrow_forwardEncrypt.arrow_forwardAn IP address can be written as a 32-bit number. For a class B network, the two most significant bits are set to 10. The 16 most significant bits are used as a network ID, and the 16 least significant bits are used as a host ID. However, the host ID cannot be all O's or all 1's. How many hosts (i.e., host IDs) can there be on a class B network? Type your answer.arrow_forward
- Use the RSA cipher with public key (n, e) = (713, 43) to encrypt the word "TEE." Start by encoding the letters of the word "TEE" into their numeric equivalents. Assume the letters of the alphabet are encoded as follows: A = 01, 8 = 02, C = 03, ..., Z = 26. Since the code for T is 20 and since e = 43 = 32 + 8 + 2 + 1, the first letter of the encrypted message is found by computing 2043 mod 713. 20¹a (mod 713) 20² Eb (mod 713) 204 c (mod 713) 208 d (mod 713) 2032 = f (mod 713) 2016 e (mod 713) b = The result is that a = C = d = e = and f = Thus, 2043 mod 713 = (a · b. d. f) mod 713 = So the first number in the encrypted message is Repeat these computations for each letter to find the complete encrypted message and enter your answer below. (Enter the message as a sequence of integer triples separated by a single space, where each triple is written using a fixed number of digits: 001 for 1, 002 for 2, ..., 099 for 99.)arrow_forwardSuppose p 5 and q = 11. Which of the following is the private key of an RSA cryptosystem with public key (n, e) = (55, 7)? O (55,51) O (55, 23) O (55, 15) O (55, 39)arrow_forwardDifficult Intro to Elementary Number Theory Homework problem. This is not a computer programming homework problem.arrow_forward
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