It is widely recognized that security issues will play a crucial role in the majority of future computer and communication systems. Central tools for achieving system security are cryptographic algorithms. This contribution proposes arithmetic architectures which are optimized for modern field programmable gate arrays (FPGAs). The proposed architectures perform modular exponentiation with very long integers. This operation is at the heart of many practical public-key algorithms such as RSA and discrete logarithm schemes. We combine a high