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Arthur and Dara are exchanging messages using the RSA Cipher system and the following information: Public exponent Modulus Private exponent 43 Arthur 3 85 Dara 119 77 OVerify that Arthur's private exponent 43 is correct, given the other information. Show all steps.

Arthur and Dara are exchanging messages using the RSA Cipher system and the following information: Public exponent Modulus Private exponent 43 Arthur 3 85 Dara 119 77 OVerify that Arthur's private exponent 43 is correct, given the other information. Show all steps.

College Algebra
College Algebra
7th Edition
ISBN:9781305115545
Author:James Stewart, Lothar Redlin, Saleem Watson
Publisher:James Stewart, Lothar Redlin, Saleem Watson
ChapterP: Prerequisites
Section: Chapter Questions
Problem 49E
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please send handwritten solution step by step Q5 part a
ALPHABET In all questions, you should work with an alphabet of n = 37 symbols, as indicated below. For individual symbols, you should use integer codes in the range 0 to 36 inclusive (therefore, you will be mainly using arithmetic modulo n = 37), as indicated by the following table: A в DEFG 0 1 JK 2 3 4 5 7 8 LM O P 14 15 Q|R S 10 11 12 13 16 17 18 19 TU 20 21 V. W Y ? 22 23 24 25 26 27 28 29 @ 30 31 32 33 34 35 36 So, for example, the symbol C should be encoded as the integer 3. Note: the space character (used to separate words) should be encoded by the integer 0.
Transcribed Image Text:ALPHABET In all questions, you should work with an alphabet of n = 37 symbols, as indicated below. For individual symbols, you should use integer codes in the range 0 to 36 inclusive (therefore, you will be mainly using arithmetic modulo n = 37), as indicated by the following table: A в DEFG 0 1 JK 2 3 4 5 7 8 LM O P 14 15 Q|R S 10 11 12 13 16 17 18 19 TU 20 21 V. W Y ? 22 23 24 25 26 27 28 29 @ 30 31 32 33 34 35 36 So, for example, the symbol C should be encoded as the integer 3. Note: the space character (used to separate words) should be encoded by the integer 0.
Q5 Arthur and Dara are exchanging messages using the RSA Cipher system and the following information: Public exponent Modulus | Private exponent Arthur 3 85 43 Dara 5 119 77 (a) Verify that Arthur's private exponent 43 is correct, given the other information. Show all steps. (b) Arthur wishes to send the message 5 to Dara. Write down the expression involving the plaintext, P, and the ciphertext, C, for the task. Hence determine the ciphertext (in numerical form). (c) Show how Arthur can use the base-2 representation of 43 to calculate 343 with a modulus of 85 and hence decipher a message with number 3 from Dara. (d) Arthur wishes to re-send the message from part (b) to Dara. For security, an agreed signature message will be added. Write down the expression involving the hidden signature message, H, and the signature, S, for enciphering the message. Write down the expression that Dara will use to decipher the signature message and hence prove that Dara will be able to read the signature. Demonstrate the process on the signature DIRK.
Transcribed Image Text:Q5 Arthur and Dara are exchanging messages using the RSA Cipher system and the following information: Public exponent Modulus | Private exponent Arthur 3 85 43 Dara 5 119 77 (a) Verify that Arthur's private exponent 43 is correct, given the other information. Show all steps. (b) Arthur wishes to send the message 5 to Dara. Write down the expression involving the plaintext, P, and the ciphertext, C, for the task. Hence determine the ciphertext (in numerical form). (c) Show how Arthur can use the base-2 representation of 43 to calculate 343 with a modulus of 85 and hence decipher a message with number 3 from Dara. (d) Arthur wishes to re-send the message from part (b) to Dara. For security, an agreed signature message will be added. Write down the expression involving the hidden signature message, H, and the signature, S, for enciphering the message. Write down the expression that Dara will use to decipher the signature message and hence prove that Dara will be able to read the signature. Demonstrate the process on the signature DIRK.
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