Final answer:
To decrypt the ciphertext and find the plaintext in RSA, we need to find the private key and use it in a decryption formula.
Step-by-step explanation:
In this RSA public-key system, we have been given the ciphertext C, the public key e, and the modulus n. To find the plaintext M, we can use the following formula:
M = C^d mod n
However, to find the plaintext, we first need to determine the private key d. In the RSA encryption algorithm, the private key d is calculated using the formula: d = e^(-1) mod (p-1)(q-1), where p and q are prime numbers that make up the modulus n.
Once we have the private key d, we can use it to decrypt the ciphertext and find the plaintext M using the formula mentioned earlier.
Deciphering plaintext M from RSA ciphertext C = 20 with public key e = 13, n = 77 is not feasible without the RSA private key or additional information to deduce it.
In a public-key system using RSA, when you are given the ciphertext C = 20 and the public key components e = 13 and n = 77, you need to decipher the plaintext M. However, the decryption process requires the private key, which is not provided in the question. Without the private key, which consists of the private exponent d, decryption is not possible. In a typical RSA setup, you would calculate d by determining the multiplicative inverse of e modulo φ(n), where φ is the Euler's totient function of n. However, since factorization of n or knowledge of φ(n) is essential for the calculation and is not provided, it would require factoring n to find the primes p and q such that n = p * q, and then finding the totient value. Without this additional information, the plaintext M cannot be recovered from the ciphertext given the values provided.