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
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- Suppose a codding scheme is devised that maps -bit words onto -bit code words. The efficiency of the code is the ratio . Compute the efficiency of the coding scheme described in each of the following examples. Example 1 Example 2 Example 3 Example 4 Example 1: Parity check – Consider -bit words of the form . One coding scheme maps onto , where is called the parity check digit. Example 2: Repetition Codes – Multiple errors can be detected (but not corrected) in a scheme in which a -bit word is mapped onto a -bit code word according to the following scheme: Example 3: Maximum Likelihood Decoding- Multiple errors can be detected and corrected if each -bit word is mapped onto a - bit code word according to the following scheme (called a triple repetition code): Example 4: Error Detection and Correction – Suppose -bit words are mapped onto -bit code words using the scheme , Where is the parity check digit .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_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_forward
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