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 "pascal" 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 "algebra" using the -letter alphabet from Example 4. Use two-digit blocks. Use three-digit blocks. What is the secret key?arrow_forward(5) Elgamal public key cryptosystem (decryption): Start with the prime p = 13 and the primitive root g = 2. Alice's secret key is a = 4. Alice sends Bob the public key A = 3. Bob encrypts the message m and sends the pair of numbers (7,5) to Alice. Using Elgamal public key decryption, Alice computes the plaintext mes- sage m from the ciphertext (7,5). What is the number m that Alice obtains?arrow_forward
- Suppose the RSA system that is used for sending secret messages has private key (15, 3) and the cipher text "4" is received. What was the plain text sent? 12 0 8 6 4arrow_forwardwhere did the 26 and 10 come from?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_forward
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