Embedded systems are so ubiquitous that they account for almost 90% of all the computing devices. They range from very small scale devices with an 8-bit microcontroller and few kilobytes of RAM to large-scale devices featuring PC-like performance with full-blown 32-bit or 64-bit processors, special-purpose acceleration hardware and several gigabytes of RAM. Each of these classes of embedded systems have unique set of challenges in terms of hardware utilization, performance and power consumption. As network connectivity becomes a standard feature in these devices, security becomes an important concern. Public Key Cryptography is an indispensable tool to implement various security features necessary on these embedded platforms. In this thesis, we provide optimized PKC solutions on platforms belonging to two extreme classes of the embedded system spectrum. First, we target high-end embedded platforms Qualcomm Snapdragon and Intel Atom. Each of these platforms features a dual-core processor, a GPU and a gigabyte of RAM. We use the SIMD coprocessor built into these processors to accelerate the modular arithmetic which accounts for the majority of execution time in Elliptic Curve Cryptography. We exploit the structure of NIST primes to perform the reduction step as we perform the multiplication. Our implementation runs over two times faster than OpenSSL implementations on the respective platforms. The second platform we targeted is an energy-harvested wireless sensor node which has a 16-bit MSP430 microcontroller and a low power RF interface. The system derives its power from a solar panel and is constrained in terms of available energy and computational power. We analyze the computation and communication energy requirements for different signature schemes, each with a different trade-off between computation and communication. We investigate the Elliptic Curve Digital Signature Algorithm (ECDSA), the Lamport-Diffie one-time hash-based signature scheme (LD-OTS) and the Winternitz one-time hash-based signature scheme (W-OTS). We demonstrate that there’s a trade-off between energy needs, security level and algorithm selection. However, when we consider the energy needs for the overall system, we show that all schemes are within one order of magnitude from each another. / Master of Science