We present techniques for the implementation of a key exchange protocol and digital signature scheme based on the Curve25519 elliptic curve and its Edwards form, respectively, in resource-constrained ARM devices. A possible application of this work consists of TLS deployments in the ARM Cortex-M family of processors and beyond. These devices are located towards the lower to mid-end spectrum of ARM cores, and are typically used on embedded devices. Our implementations improve the state-of-the-art substantially by making use of novel implementation techniques and features specific to the target platforms.