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 symmetric-key cryptosystems. In many applications, the high cost of encrypting long messages in a public-key cryptosystem can be prohibitive. A 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 symmetric-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. Note that for very long messages the bulk of the work in encryption/decryption is done by the more efficient symmetric-key scheme, while the inefficient public-key scheme is used only to encrypt/decrypt a short key value. ## [edit]ExampleTo encrypt a message addressed to Alice in a hybrid cryptosystem, Bob does the following: - Obtains Alice's public key.
- Generates a fresh symmetric key for the data encapsulation scheme.
- Encrypts the message under the data encapsulation scheme, using the symmetric key just generated.
- Encrypt the symmetric key under the key encapsulation scheme, using Alice's public key.
- Send both of these encryptions to Alice.
To decrypt this hybrid ciphertext, Alice does the following: - uses her private key to decrypt the symmetric key contained in the key encapsulation segment.
- uses this symmetric key to decrypt the message contained in the data encapsulation segment.
## [edit]SecurityIf both the key encapsulation and data encapsulation schemes are secure against adaptive chosen ciphertext attacks, then the hybrid scheme inherits that property as well. |

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