Diffie–Hellman key exchange
For example, in the Diffie–Hellman key exchange, an eavesdropper observes "gx" and "gy" exchanged as part of the protocol, and the two parties both compute the shared key "gxy". A fast means of solving the DHP would allow an eavesdropper to violate the privacy of the Diffie–Hellman key exchange and many of its variants, including ElGamal encryption.