## Understanding Chosen Ciphertext Attack on Textbook RSA

In this article, I will explain how a chosen ciphertext attack works on textbook RSA encryption. I will also address common questions and provide step-by-step instructions on decrypting encrypted files using RSA parameters.

Since you have your n and e, you should get d and your totient, which is ϕ(n).

Here is the example:

Using the formula e(d) mod ϕ(n) ≡ 1, you can use the Euclidean algorithm to solve this equation and find d.

To find n, you usually take two large prime numbers, p and q, and calculate n as p*q.

To find the totient ϕ(n), you can use the formula (p-1)*(q-1).

Make sure that e is less than n and does not share common factors with ϕ(n). In the given example, e is 17.

Substituting the values, you can solve the equation e(d) mod ϕ(n) ≡ 1 to find d. In this case, d is 53, as 17*53 mod 60 gives a remainder of 1.

To decrypt your ciphertext, you can use the formula m=c^e mod n, where m is the plaintext, c is the ciphertext, e is the encryption key, and n is the product of the two large prime numbers.