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Basis of Cryptography • Chapter 9 535

rithms are generally larger than those used by symmetric algorithms, because the
most common asymmetric attack (factoring) is more efficient than the most
common symmetric attack (brute-force).
Because of this, asymmetric algorithms are typically used only for encrypting
small amounts of information. In this section, we examine the RSA, Diffie-
Hellman, and El Gamal algorithms.

EXAM WARNING

If this is your first exposure to cryptography, make sure you understand
the differences between public keys, private keys, and secret keys.
Asymmetric algorithms use two keys, a private key and a public key, one
of which does the encryption and the other the decryption. Symmetric
algorithms use a single secret key, shared between the two parties, to
perform both the encryption and the decryption. Secret keys and private
keys need to be closely guarded, while public keys can be given out
freely.

Diffie-Hellman

The biggest problem in symmetric cryptography is the security of the secret key.
Obviously, you cannot transmit the key over the same medium as the ciphertext,
since any unauthorized parties observing the communications could use the key to
decode the messages. Prior to the development of asymmetric cryptography and the
Diffie-Hellman key exchange, secret keys were exchanged using trusted private
couriers and other out-of-band methods.
In the mid-1970s,Whitfield Diffie and Martin Hellman published the Diffie-
Hellman algorithm for key exchange, which allowed a secret key to be transmitted
securely over an insecure line.This was the first published use of public-key cryp-
tography, and one of the cryptography field’s greatest advances.With the Diffie-
Hellman algorithm, the DES secret key (sent with a DES-encrypted payload
message) could be encrypted via Diffie-Hellman by one party, and decrypted only
by the intended recipient.
Because of the inherent slowness of asymmetric cryptography, the Diffie-
Hellman algorithm was not intended for use as a general encryption scheme.
Rather, its purpose was to transmit a private key for DES (or a similar symmetric
algorithm) across an insecure medium. In most cases, Diffie-Hellman is not used

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