Key encapsulation

Key encapsulation mechanisms (KEMs) are a class of encryption techniques designed to secure symmetric cryptographic key material for transmission using asymmetric (public-key) algorithms. In practice, public key systems are clumsy to use in transmitting long messages. Instead they are often used to exchange symmetric keys, which are relatively short. The symmetric key is then used to encrypt the longer message.

The traditional approach to sending a symmetric key with public key systems is to first generate a random symmetric key and then encrypt it using the chosen public key algorithm. The recipient then decrypts the public key message to recover the symmetric key. As the symmetric key is generally short, padding is required for full security and proofs of security for padding schemes are often less than complete. KEMs simplify the process by generating a random element in the finite group underlying the public key system and deriving the symmetric key by hashing that element, eliminating the need for padding.

Using the same notation employed in the RSA system article, say Alice has transmitted her public key ${\displaystyle (n,e)}$ to Bob, while keeping her private key secret, as usual. Bob then wishes to send symmetric key M to Alice. M might be a 128 or 256-bit AES key, for example. Note that the public key n is typically 1024-bits or even longer, thus much larger than typical symmetric keys. If e is small enough that ${\displaystyle M^{e}<n}$, then the encryption can be quickly broken using ordinary integer arithmetic.

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