You are here
HomeDiffieHellman key exchange
Primary tabs
DiffieHellman key exchange
The DiffieHellman 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 DiffieHellman key exchange.

1) Alice and Bob publicly agree on an elliptic curve $E$ over a large finite field $F$ and a point $P$ on that curve.

3) Using elliptic curve pointaddition, Alice computes $aP$ on $E$ and sends it to Bob. Bob computes $bP$ on $E$ and sends it to Alice.

4) Both Alice and Bob can now compute the point $abP$, Alice by multipliying the received value of $bP$ by her secret number $a$, and Bob viceversa.

5) Alice and Bob agree that the $x$ 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 $E$, $P$, $aP$, and $bP$. She can succeed in determining the final secret value by gaining knowledge of either of the values $a$ or $b$. Thus, the security of the exchange depends on the hardness of that problem, known as the elliptic curve discrete logarithm problem. For large $a$ and $b$, it is a computationally “difficult” problem.
Mathematics Subject Classification
94A60 no label found Forums
 Planetary Bugs
 HS/Secondary
 University/Tertiary
 Graduate/Advanced
 Industry/Practice
 Research Topics
 LaTeX help
 Math Comptetitions
 Math History
 Math Humor
 PlanetMath Comments
 PlanetMath System Updates and News
 PlanetMath help
 PlanetMath.ORG
 Strategic Communications Development
 The Math Pub
 Testing messages (ignore)
 Other useful stuff
Recent Activity
new question: Prime numbers out of sequence by Rubens373
Oct 7
new question: Lorenz system by David Bankom
Oct 19
new correction: examples and OEIS sequences by fizzie
Oct 13
new correction: Define Galois correspondence by porton
Oct 7
new correction: Closure properties on languages: DCFL not closed under reversal by babou
new correction: DCFLs are not closed under reversal by petey
Oct 2
new correction: Many corrections by Smarandache
Sep 28
new question: how to contest an entry? by zorba
new question: simple question by parag