ECDH

Elliptic curve Diffie-Hellman (ECDH) is a elliptic curve variant of the Diffie-Hellman key exchange protocol. It allows two parties to establish a shared secret over an insecure channel. The shared secret can then be used to encrypt messages between the two parties.

See the Diffie-Hellman section for more information on the key exchange protocol.

Attacks

Bad Parameters

• Small secret - CryptoHack

  If one of the secret integers is small and the order of the curve is rather smooth (i.e has very few lage, over $10^{12}$, factors), using Pohlig-Hellman to solve the discrete logarithm problem on the subgrups of the small factors can be enough to recover the secret.