I am searching for a algorithm to verify that a short message (size of about 20-30 bytes) was created by a specific device/user. The device/user can be partially offline.

Signing the data using rsa with 1024 bit is not possible since the content of the message will get to big. The size of the signature should not exceed ~100 bytes. Are there any algorithms or alternatives to create short signatures. The algorithm does not have neccessarily have to rely on public/private key. Both parties are ment to be secure and can use the same key if neccessary.

The purpose is to prevent other devices/users to create messages in the name of some else device/user.