5.4 Asymmetric Cryptography

With symmetric encryption, both sides must already share a secret key. Asymmetric encryption removes that step. Anyone who wants to receive encrypted data first generates a key pair: two matching keys of the same length, created together by one mathematical process. One is the public key, and the other is the private key.

The two keys are mathematical inverses: what one does, the other undoes. Either key can encrypt, but only the other key in the pair can decrypt.

The owner publishes the public key for anyone to use and guards the private key. The system's security depends entirely on the private key. If it's ever exposed, shared, stolen, corrupted or compromised, the owner must delete the pair and generate a new one.

To send someone a secret, encrypt it with the receiver's public key. Only the receiver's private key can decrypt it, so only the receiver can read it. Even you, the sender, can't decrypt what you just encrypted.

Asymmetric algorithms also power digital signatures and digital certificates. For a signature, the owner uses their private key, and anyone can check it with the matching public key. That proves who sent the data, not secrecy. The two most common asymmetric algorithms are RSA and elliptic curve cryptography (ECC). Tools like PGP use them to set up secure email and messages.

An n-bit key has a keyspace of 2ⁿ. An adversary guessing at random will, on average, find the right key after trying half of them: 2ⁿ ÷ 2 = 2ⁿ⁻¹ guesses. Each added bit doubles the work.

Longer keys are more secure but slower to encrypt and decrypt. And because computers keep getting faster, recommended key lengths for both symmetric and asymmetric algorithms rise over time. For example, an older U.S. standard, DES, used 56-bit keys and was retired once computers could search that keyspace.

You can only compare key lengths within the same algorithm. An AES 256-bit key beats an AES 128-bit key, and an RSA 4096-bit key beats an RSA 2048-bit key, but you can't compare an RSA key to an AES key by length. Different algorithms get different strength per bit. A 256-bit ECC key, for instance, is considered about as strong as a 3072-bit RSA key.

As with symmetric encryption, you can use the command line, specialized open-source tools or web-based tools. With OpenSSL:

• Generate a 2048-bit RSA key pair into rsa.pem: openssl genrsa -out rsa.pem 2048
• Copy the public key out into public.pem to share: openssl rsa -pubout -in rsa.pem -out public.pem
• Encrypt msg.txt with someone's public key: openssl pkeyutl -encrypt -pubin -inkey public.pem -in msg.txt -out msg.enc
• Decrypt it with the matching private key: openssl pkeyutl -decrypt -inkey rsa.pem -in msg.enc -out msg.txt
• Note: RSA can only encrypt a small amount of data directly. With a 2048-bit key and OpenSSL's default settings, the limit is 245 bytes, so a bigger file fails with an error. Real systems such as PGP encrypt the file with a fast symmetric cipher like AES, then use RSA to encrypt just that AES key.