This book is a step towards showing the practicability of Public Key Cryptography (PKC) and in particular Elliptic Curve Cryptography (ECC) on low-end constrained devices like sensor nodes and RF-ID chips. The book presents the flexibility that ECC provides in the choice of parameters and algorithms at different hierarchies for efficient implementations on constrained platforms like 8-bit micro-processors. Architectural enhancements with software/hardware co-design including instruction set extensions were investigated for low-level finite field arithmetic used in ECC. Finally, a highly area optimized ASIC implementation of an ECC co-processor using standard 0.35um CMOS libraries is presented using an innovative arithmetic and architectural design. The book is intended for students and researchers involved in realizing practical public-key cryptographic implementations on constrained devices used in ambient intelligent (AmI) environments, sensor networks and RF-ID applications.