Asymmetric key algorithm

In cryptography, an asymmetric key algorithm uses a pair of different, though related, cryptographic keys to encrypt and decrypt. The two keys are related mathematically; a message encrypted by the algorithm using one key can be decrypted by the same algorithm using the other. In a sense, one key "locks" a lock (encrypts); but a different key is required to unlock it (decrypt).

A postal analogy

An analogy which can be used to understand the advantages of an asymmetric system is to imagine two people, Alice and Bob, sending a secret message through the public mail.

With a symmetric key system, Alice first puts the secret message in a box, and then padlocks the box using a lock to which she has a key. She then sends the box to Bob through regular mail. When Bob receives the box, he uses an identical copy of Alice's key (which he has somehow obtained previously) to open the box, and reads the message.

In an asymmetric key system, instead of opening the box when he receives it, he simply adds his own personal lock to the box, then returns the box to Alice. Alice uses her key to remove her lock, and returns the box to Bob, with Bob's lock still in place. Finally, Bob then uses his key to remove his lock, and reads the message from Alice.

The critical advantage in an asymmetric key system is that Alice never need send a copy of her key to Bob. This substantially reduces the chance that a third party (perhaps, in the example, an corrupted postal worker) will copy a key while is in transit to Bob, allowing said third party to spy on all future messages sent by Alice. In addition, if Bob were to be careless and allow someone else to copy his key, Alice's messages to Bob will be compromised, but Alice's messages to other people would remain secret.

Actual algorithms -- two linked keys

Fortunately cryptography is not concerned with actual padlocks, but with encryption algorithms which aren't vulnerable to hacksaws, bolt cutters, or liquid nitrogen attacks.

Not all asymmetric key algorithms operate in precisely this fashion. The most common have the property that Alice and Bob each own two keys; neither of which is (so far as is known) deducible from the other. This is known as public-key_cryptography, since one key of the pair can be published without affecting message security. In the analogy above, Bob might publish instructions on how to make a lock ("public key"), but the lock is such that it is impossible (so far as is known) to deduce from these instructions how to make a key which will open that lock ("private key"). Those wishing to send messages to Bob use the public key to encrypt the message; Bob uses his private key to decrypt it.

Weaknesses

Of course, there is the possibility that someone could "pick" either of Bob's or Alice's locks. Unlike the case of the one-time pad or its equivalents, there is no currently known asymmetric key algorithm which has been proven to be secure against a mathematical attack. That is, it is not known to be impossible that some relation between the keys in a key pair, or a weakness in an algorithm's operation, might be found which would allow decryption without either key, or using only the encryption key. The security of asymmetric key algorithms is based on estimates of how difficult the underlying mathematical problem is to solve. Such estimates have changed both with the decreasing cost of computer power, and with new mathematical discoveries.

Weaknesses have been found for promising asymmetric key algorithms in the past. The 'knapsack packing' algorithm was found to be insecure when an unsuspected attack came to light. Recently, some attacks based on careful measurements of the exact amount of time it takes known hardware to encrypt plain text have been used to simplify the search for likely decryption keys. Thus, use of asymmetric key algorithms does not ensure security; it is an area of active research to discover and protect against new and unexpected attacks.

History

The first known asymmetric key algorithm was invented by Clifford Cocks of GCHQ in the UK. It was not made public at the time, and was reinvented by Rivest, Shamir, and Adleman at MIT in 1976. It is usually referred to as RSA as a result. RSA relies for its security on the difficulty of factoring very large integers. A breakthrough in that field would cause considerable problems for RSA's security. Currently, RSA is vulnerable to an attack by factoring the 'modulus' part of the public key, even when keys are properly chosen, for keys shorter than perhaps 700 bits. Most authorities suggest that 1024 bit keys will be secure for some time, barring a fundamental breakthrough in factoring practice, but others favor even longer keys.

At least two other asymmetric algorithms were invented after the GCHQ work, but before the RSA publication. These were the Ralph Merkle puzzle cryptographic system and the Diffie-Hellman system. Well after RSA's publication, Taher Elgamal invented the Elgamal discrete log cryptosystem which relies on the difficulty of inverting logs in a finite field. It is used in the SSL, TSL, and DSA protocols.

A relatively new addition to the class of asymmetric key algorithms is elliptic curve cryptography. While it is more complex computationally, many believe it to represent a more difficult mathematical problem than either the factorisation or discrete logarithm problems.

Practical limitations & hybrid cryptosystems

One drawback of asymmetric key algorithms is that they are much slower (factors of 1000+ are typical) than 'comparably' secure symmetric key algorithms. In many quality crypto systems, both algorithm types are used. The receiver's public key encrypts a symmetric algorithm key which is used to encrypt the main message. This combines the virtues of both algorithm types when properly done.