Final answer:
The student needs to find the decryption exponent 'd' for the RSA algorithm by computing the modular multiplicative inverse of e modulo φ(n), and then use that to decrypt the message.
Step-by-step explanation:
The student is asking how to decrypt a message that was encrypted using the RSA algorithm. The given public key consists of n = 43 · 59 and e = 13, and the encrypted message is 0667 1947 0671. To decrypt the message, we need to find the private key, which includes the decryption exponent d. The decryption exponent is the modular multiplicative inverse of e modulo φ(n), where φ(n) is the Euler's totient function of n. Since n is the product of two primes, 43 and 59, φ(n) is (43-1)(59-1) which equals 42 · 58. Now, we need to find d such that it satisfies the congruence ed ≡ 1 (mod φ(n)), which will be d = 13⁻¹ mod 42 · 58. Once d is computed, we can decrypt each part of the message using the formula M = C^d mod n, where M is the original message and C is each part of the encrypted message.