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Questions Suppose we have a message to encrypt. Let's keep the message simple and say you want to transmit the plaintext value '24' over the web. 1. Suppose our encryption function was to convert plaintext into binary. a. What would C be for P = 24? b. Convert the C value you obtained in a back into the P value (24). c. What would the encryption function be, in general for converting any P to C under this encryption process? That is, what is the equation, C = f (P)? d. What would the decryption function be, in general for converting any C back to P under the decryption process? That is, what is the

Questions Suppose we have a message to encrypt. Let's keep the message simple and say you want to transmit the plaintext value '24' over the web. 1. Suppose our encryption function was to convert plaintext into binary. a. What would C be for P = 24? b. Convert the C value you obtained in a back into the P value (24). c. What would the encryption function be, in general for converting any P to C under this encryption process? That is, what is the equation, C = f (P)? d. What would the decryption function be, in general for converting any C back to P under the decryption process? That is, what is the

Algebra and Trigonometry (6th Edition)
Algebra and Trigonometry (6th Edition)
6th Edition
ISBN:9780134463216
Author:Robert F. Blitzer
Publisher:Robert F. Blitzer
ChapterP: Prerequisites: Fundamental Concepts Of Algebra
Section: Chapter Questions
Problem 1MCCP: In Exercises 1-25, simplify the given expression or perform the indicated operation (and simplify,...
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As we venture into our final phase of number theory, we will analyze the RSA encryption algorithm. To motivate the notion before getting into it, let's do so by thinking in terms of number systems. We will explore a basic encryption approach in this discussion board, so that we can begin to see the importance of having one-to-one encryption functions (ah, good ole' functions!). Encryption is the process of taking some numerical message (called plaintext) and converting it into a new, encrypted message (called ciphertext). The encrypted message (ideally) would be strong enough to where a hacker intercepting the message would have little consequence, because they would not be able to figure out the original message that was sent (the plaintext value). By the way, if a message consisting of letters needs to be sent, we would implement some way to convert the letters into numerals. One easy way to do this is to represent a letter with its position in the alphabet. For example, A could be coded as 1, B as 2, etc. One simple (and highly volatile) approach to encrypting a message is to perform a Caesar shift, where each numeral gets shifted in the encryption process. For instance, we might say that a plaintext value will be increased by 5 in the encryption process. A message such as 5 32 might get encrypted to become 10 8 7. In this case, the encryption algorithm to get the cipher, C, from the plaintext P (called the encryption function), is: C = f (P) = P+5 You can see that this is very crude, because a good hacker could "crack" the code very easily. In this case, to get back P from C (called the decryption function), our formula would be: P = f' (C) = C – 5 In words, the hacker would simply subtract 5 from each digit in the cipher text to obtain the decrypted message! Thus, every encrypted message could be (trivially) converted and "cracked". We will now proceed to define different encryption and decryption functions to get a sense of intuition behind how this process works.
Transcribed Image Text:As we venture into our final phase of number theory, we will analyze the RSA encryption algorithm. To motivate the notion before getting into it, let's do so by thinking in terms of number systems. We will explore a basic encryption approach in this discussion board, so that we can begin to see the importance of having one-to-one encryption functions (ah, good ole' functions!). Encryption is the process of taking some numerical message (called plaintext) and converting it into a new, encrypted message (called ciphertext). The encrypted message (ideally) would be strong enough to where a hacker intercepting the message would have little consequence, because they would not be able to figure out the original message that was sent (the plaintext value). By the way, if a message consisting of letters needs to be sent, we would implement some way to convert the letters into numerals. One easy way to do this is to represent a letter with its position in the alphabet. For example, A could be coded as 1, B as 2, etc. One simple (and highly volatile) approach to encrypting a message is to perform a Caesar shift, where each numeral gets shifted in the encryption process. For instance, we might say that a plaintext value will be increased by 5 in the encryption process. A message such as 5 32 might get encrypted to become 10 8 7. In this case, the encryption algorithm to get the cipher, C, from the plaintext P (called the encryption function), is: C = f (P) = P+5 You can see that this is very crude, because a good hacker could "crack" the code very easily. In this case, to get back P from C (called the decryption function), our formula would be: P = f' (C) = C – 5 In words, the hacker would simply subtract 5 from each digit in the cipher text to obtain the decrypted message! Thus, every encrypted message could be (trivially) converted and "cracked". We will now proceed to define different encryption and decryption functions to get a sense of intuition behind how this process works.
Questions Suppose we have a message to encrypt. Let's keep the message simple and say you want to transmit the plaintext value '24' over the web. 1. Suppose our encryption function was to convert plaintext into binary. a. What would C be for P = 24? b. Convert the C value you obtained in a back into the P value (24). c. What would the encryption function be, in general for converting any P to C under this encryption process? That is, what is the equation, C = f(P)? d. What would the decryption function be, in general for converting any C back to P under the decryption process? That is, what is the equation, P = f' (C)? 2. Suppose our encryption function was to convert plaintext into octal. a. What would C be for P = 24? b. Convert the C value you obtained in a back into the P value (24). c. What would the encryption function be, in general for converting any P to C under this encryption process? That is, what is the equation, C = f (P)? d. What would the decryption function be, in general for converting any C back to P under the decryption process? That is, what is the equation, P = f-' (C)?
Transcribed Image Text:Questions Suppose we have a message to encrypt. Let's keep the message simple and say you want to transmit the plaintext value '24' over the web. 1. Suppose our encryption function was to convert plaintext into binary. a. What would C be for P = 24? b. Convert the C value you obtained in a back into the P value (24). c. What would the encryption function be, in general for converting any P to C under this encryption process? That is, what is the equation, C = f(P)? d. What would the decryption function be, in general for converting any C back to P under the decryption process? That is, what is the equation, P = f' (C)? 2. Suppose our encryption function was to convert plaintext into octal. a. What would C be for P = 24? b. Convert the C value you obtained in a back into the P value (24). c. What would the encryption function be, in general for converting any P to C under this encryption process? That is, what is the equation, C = f (P)? d. What would the decryption function be, in general for converting any C back to P under the decryption process? That is, what is the equation, P = f-' (C)?
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