Math Problem Statement
Alice wants to send a plaintext message 𝑚 = 13 to Bob secretly using RSA public key cryptosystem. Bob selects 𝑝 = 13, and 𝑞 = 11 with 𝑒 = 13. You have to perform following tasks: a. Compute and list Bob’s public and private keys. b. Compute the ciphertext that Alice will send to Bob using plaintext message 𝑚 = 13. c. Recover the actual plaintext from the ciphertext sent by Alice.
Solution
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Math Problem Analysis
Mathematical Concepts
Number Theory
Modular Arithmetic
RSA Cryptography
Prime Numbers
Euler's Totient Function
Extended Euclidean Algorithm
Formulas
n = p * q
ϕ(n) = (p - 1)(q - 1)
c ≡ m^e mod n
m ≡ c^d mod n
d ≡ e^(-1) mod ϕ(n)
Theorems
Euler's Totient Function
Modular Inversion
RSA Algorithm
Suitable Grade Level
University Level (Cryptography Course)
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