Definitions

# Hybrid cryptosystem

In cryptography, public-key cryptosystems are convenient in that they do not require the sender and receiver to share a common secret in order to communicate securely (among other useful properties). However, they often rely on complicated mathematical computations and are thus generally much more inefficient than comparable private-key cryptosystems. In many applications, the high cost of encrypting long messages in a public-key cryptosystem can be prohibitive. A hybrid cryptosystem is one which combines the convenience of a public-key cryptosystem with the efficiency of a private-key cryptosystem.

A hybrid cryptosystem can be constructed using any two separate cryptosystems:

• a key encapsulation scheme, which is a public-key cryptosystem, and
• a data encapsulation scheme, which is a private-key cryptosystem.

The hybrid cryptosystem is itself a public-key system, whose public and private keys are the same as in the key encapsulation scheme.

To encrypt a message $m$ addressed to Alice in a hybrid scheme, Bob does the following:

• Generates a random (private) key for the data encapsulation scheme (say, $s$).
• Encrypt the message $m$ under the data encapsulation scheme, using the key $s$ just generated.
• Encrypt the key $s$ under the key encapsulation scheme, using Alice's public key.
• Send both of these encryptions to Alice.

Alice can use her private key to decrypt $s$, and then use $s$ to decrypt the message $m$.

Note that for very long messages $m$, the bulk of the work in encryption/decryption is done by the more efficient private-key scheme, while the inefficient public-key scheme is used only to encrypt/decrypt a short key value.

## Security

If both the key encapsulation and data encapsulation schemes are secure against adaptive chosen ciphertext attack, then the hybrid scheme inherits that property as well. However, it is possible to construct a hybrid scheme secure against adaptive chosen ciphertext attack even if the key encapsulation has a slightly weakened security definition (though the security of the data encapsulation must be slightly stronger).

## References

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