Diffie-Hellman key exchange
The Diffie-Hellman key exchange is a cryptographic protocol for symmetric key exchange. There are various implementations of this protocol. The following interchange between Alice and Bob demonstrates the Elliptic Curve Diffie-Hellman key exchange.
2) Alice and Bob each privately choose large random integers, denoted and .
3) Using elliptic curve point-addition, Alice computes on and sends it to Bob. Bob computes on and sends it to Alice.
4) Both Alice and Bob can now compute the point , Alice by multipliying the received value of by her secret number , and Bob vice-versa.
5) Alice and Bob agree that the coordinate of this point will be their shared secret value.
An evil interloper Eve observing the communications will be able to intercept only the objects , , , and . She can succeed in determining the final secret value by gaining knowledge of either of the values or . Thus, the security of the exchange depends on the hardness of that problem, known as the elliptic curve discrete logarithm problem. For large and , it is a computationally “difficult” problem.
As a side note, some care has to be taken to choose an appropriate curve . Singular curves and ones with “bad” numbers of points on it (over the given field) have simplified solutions to the discrete log problem.
|Title||Diffie-Hellman key exchange|
|Date of creation||2013-03-22 13:45:58|
|Last modified on||2013-03-22 13:45:58|
|Last modified by||mathcam (2727)|