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Calculate Rsa When N and E Is

Reviewed by Calculator Editorial Team

This calculator helps you determine the RSA encryption result when you know the modulus (n) and public exponent (e). The RSA algorithm is widely used for secure data transmission and digital signatures.

What is RSA?

RSA (Rivest-Shamir-Adleman) is a public-key cryptosystem that is widely used for secure data transmission. It is based on the mathematical difficulty of factoring large integers. The RSA algorithm involves three main components:

  • Modulus (n): The product of two large prime numbers (p and q)
  • Public exponent (e): A number that is coprime with (p-1)(q-1)
  • Private exponent (d): The modular multiplicative inverse of e modulo φ(n), where φ(n) = (p-1)(q-1)

The security of RSA relies on the fact that while it is easy to compute n and e, it is computationally difficult to determine d from n and e without knowing the prime factors of n.

Calculating RSA

When you know the modulus (n) and public exponent (e), you can perform RSA encryption on a message. The encryption process involves converting the message to a numerical representation and then applying the RSA algorithm.

C = M^e mod n Where: C = Ciphertext M = Message (as a number) e = Public exponent n = Modulus

The decryption process requires the private key (d) and is performed as follows:

M = C^d mod n Where: M = Original message C = Ciphertext d = Private exponent n = Modulus

Note: In practice, messages are typically broken into blocks and padded before encryption to ensure security.

Example Calculation

Let's walk through an example where we encrypt the message "5" using n = 323 and e = 5.

  1. Convert the message to a number: M = 5
  2. Apply the RSA encryption formula: C = 5^5 mod 323
  3. Calculate 5^5 = 3125
  4. Find 3125 mod 323:
    • 323 × 9 = 2907
    • 3125 - 2907 = 218
  5. So, the ciphertext is 218

To decrypt this, you would need the private exponent (d) which is the modular inverse of e modulo φ(n).

FAQ

What is the difference between n and e in RSA?
n is the product of two large prime numbers and serves as the modulus in the RSA algorithm. e is the public exponent, which is chosen to be coprime with φ(n) and is used in the encryption process.
Can I encrypt a message without knowing d?
Yes, you can encrypt a message using only the public key components n and e. Decryption requires the private key component d.
What happens if I choose a bad value for e?
If e is not coprime with φ(n), the RSA algorithm will not work correctly. e should be chosen carefully to ensure the security of the encryption.