Decrypting with Public Key?

TL;DR

No, data encrypted with a private key cannot be decrypted using the corresponding public key. This is fundamental to how asymmetric cryptography (public-key cryptography) works.

Understanding Asymmetric Cryptography

Asymmetric cryptography uses two keys: a public key and a private key. They are mathematically linked, but it’s practically impossible to derive the private key from the public key.

• Public Key: This can be shared freely with anyone. It’s used for encryption and verifying signatures.
• Private Key: This must be kept secret by its owner. It’s used for decryption and creating signatures.

Why it Doesn’t Work

The process is designed so that:

1. Data encrypted with the public key can only be decrypted with the corresponding private key. This ensures confidentiality.
2. Data signed with the private key can be verified using the corresponding public key. This ensures authenticity and integrity.

If you could decrypt data encrypted with a private key using its public key, it would completely break the security of the system.

Example Scenario

Let’s say Alice wants to send Bob a secret message:

1. Alice gets Bob’s public key.
2. Alice encrypts her message using Bob’s public key.
3. Alice sends the encrypted message to Bob.
4. Bob uses his private key to decrypt the message.

If Bob tried to decrypt the message with his public key, it wouldn’t work.

Code Example (Python using RSA)

This shows how encryption and decryption work in practice. Note: This is a simplified example for demonstration purposes only; real-world implementations require more robust security measures.

from cryptography.fernet import Fernet, InvalidToken
import base64

# Generate a key (keep this secret!)
key = Fernet.generate_key()
f = Fernet(key)

token = f.encrypt(b'My secret message!')
decrypted = f.decrypt(token)

print("Original Message:", b'My secret message!')
print("Encrypted Message:", token)
print("Decrypted Message:", decrypted)

In this example, the Fernet library uses symmetric encryption. RSA (a common asymmetric algorithm) works similarly in principle but with separate keys for encryption and decryption.

What if you try to decrypt with the wrong key?

1. If you attempt to decrypt using a different public key, you will get garbage data or an error.
2. The cryptographic algorithms are designed to produce invalid output when used with incorrect keys.

For example:

try:
    f2 = Fernet(key) #Using the same key for decryption as encryption.
decrypted_wrong_key = f2.decrypt(token)
    print("Decrypted with wrong key:", decrypted_wrong_key)
except InvalidToken:
    print("Invalid Token - Decryption failed")

In Summary

Data encrypted with a private key is intended to be decrypted only by the corresponding public key. Attempting to decrypt it with any other key will fail, ensuring the security of the communication.