The generation of a shared secret key K in the implementation of a key agreement protocol, for example MQV, may be optimized for accelerated computation by selecting the ephemeral public key and the long-term public key of a correspondent to be identical. One correspondent determines whether the pair of public keys of the other correspondent are identical. If it is, a simplified representation of the shared key K is used which reduces the number of scalar multiplication operations for an additive group or exponentiation operations for a multiplicative group. Further optimization may be obtained by performing simultaneous scalar multiplication or simultaneous exponentiation in the computation of K.