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elliptic curve cryptography

A public key cryptography method that provides fast decryption and digital signature processing. Elliptic curve cryptography (ECC) uses points on an elliptic curve to derive a 163-bit public key that is equivalent in strength to a 1024-bit RSA key. The public key is created by agreeing on a standard generator point in an elliptic curve group (elliptic curve mathematics is a branch of number theory) and multiplying that point by a random number (the private key). Although the starting point and public key are known, it is extremely difficult to backtrack and derive the private key.

Once the public key is computed by ECC, it can be used in various ways to encrypt and decrypt. One way is to encrypt with the public key and decrypt with the private one. Another is to use the Diffie-Hellman method which uses a key exchange to create a shared secret key by both parties. Finally, ECC allows a digital signature to be signed with a private key and verified with the public key. For an in-depth look at elliptic curve cryptography, visit Certicom's website at www.certicom.com. There are live examples that show the math and methods. See Diffie-Hellman.



Diffie-Hellman

A cryptographic key exchange method developed by Whitfield Diffie and Martin Hellman in 1976. Also known as the "Diffie-Hellman-Merkle" method and "exponential key agreement," it enables parties at both ends to derive a shared, secret key without ever sending it to each other.

Using a common number, both sides use a different random number as a power to raise the common number. The results are then sent to each other. The receiving party raises the received number to the same random power they used before, and the results are the same on both sides. See elliptic curve cryptography and key management.




Very Clever
There is more computation in actual practice, but this example, which uses tiny numbers to illustrate the concept, shows a very clever mathematical approach. Each party raises the common number, which is 2 in this example (this has nothing to do with binary-- it is just the number "2") to a random power and sends the result to the other. The received number is raised to the same random power. Note that both parties come up with the same secret key, which was never transmitted intact.






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