Please help me with this, showing me what you did and how.
Number theory.
Use (a) the Euclidean Algorithm and (b) "backsolving" to compute the solution d of ed = b^1.
In the first part of the final, we go through the process of RSA coding and decoding exactly as described in Vanden Eynden. Write out your computations, including the necessary Euclidean, backsolving, and modular exponentiation algorithms. Please follow the instructions below to the letter. Do not use other methods than the ones indicated.
a) Generate plaintext P for "quorum". You should get "words" (Pi, P2, P3, P4) of three digits each.
b) Now set n = 1739 and e = 29. Find the first word C1 of the code C = (C1, C2, C3, C4) by doing modular exponentiation exactly as done in the book. Find the other Ci using a modular exponentiation calculator on the web (for example).
a) Now set p = 37 and q = 47. Use the Euclidean algorithm to compute gcd(p - 1, q - 1).
b) Use (a) to compute b = lcm(p - 1, q - 1). Use (a) the Euclidean Algorithm and (b) "backsolving" to compute the solution d of ed = b^1.
Describe how to decode C1 obtained earlier. Perform the decoding by displaying the modular exponentiation. Decode the rest by using a modular exponentiation calculator. Check your answer.