Resistance against side-channel analysis (SCA) attacks is an important requirement for many secure embedded systems. Microprocessors and microcontrollers which include suitable countermeasures can be a vital building block for such systems. In this paper, we present a detailed concept for building embedded processors with SCA countermeasures. Our concept is based on ideas for the secure implementation of cryptographic instruction set extensions. On the one hand, it draws from known SCA countermeasures like DPA-resistant logic styles. On the other hand, our protection scheme is geared towards use in modern embedded applications like PDAs and smart phones. It supports multi-tasking and a separation of secure system software and (potentially insecure) user applications. Furthermore, our concept affords support for a wide range of cryptographic algorithms. Based on this concept, embedded processor cores with support for a selected set of cryptographic algorithms can be built using a fully automated design flow.