a. [5 points] Given p=23, q=7, and e=5, generate the public key (n,e) and the private key (n,d) using RSA Key generation algorithm. b. (5 points) Given Bob's public key of (85, 7) and private key of (85, 55), show how Alice can encrypt m=10 to send to Bob. Show the ciphertext. c. (5 points) Given Bob's public key of (85, 7) and private key of (85, 55), show how Bob can decrypt the ciphertetx y=8 received from Alice. Show the plaintext. d. [5 points] Using the fast exponentiation method (page 182), determine $3^{25} \mod 37$. Show your work.
Added by Angela W.
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Step 1: Calculate n n = p * q = 23 * 7 = 161 Show more…
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Let p = 23 and q = 17, please follow the RSA key setup steps nad perform the following: (Please show your calculation process to get partial credits) Calculate the value n = p*q and φ(n) For the selected value e = 65, verify that gcd(e, φ (N)) = 1 Compute the multiplicative inverse d (mod φ(n) ), i.e. compute d (1 < d < φ(n) ) such that e*d mod φ(n) = 1 For plaintext m = 100, calculate the ciphertext c = m^e mod n
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In a public-key system using RSA, you intercept the ciphertext C = 10 sent to a user whose public key is e = 5,n = 35. What is the plaintext M?
Use RSA encryption and decryption. Let p = 23 and q = 31. Then n = 713 and φ(n) = 22 * 30 = 660. Pick e = 23. Use the Euclidean algorithm to find the value of d. Encode T = 52 using the public key (n, e). Decode your answer to part (b) to retrieve the 52.
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