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In recent years, the use of cryptography has become §more widespread, due to the advent and expansion of §the electronic communication age. This has been §fuelled by the growing popularity of services such §as e-mail, and on-line shopping and banking. §Therefore, the security industry has a requirement §to produce high-speed, low cost, and high-strength §cryptographic products in order to satisfy customer §demands for real-time encryption. In particular, §hardware based algorithms, architectures, and §implementations of encryption algorithms offer §several key benefits over software solutions. §Therefore, the overall aim of the work presented in §this book has been to develop reusable hardware §based public-key cryptographic solutions, capable of §performing high-strength encryption in real-time. §Particular focus has been on the RSA cryptosystem, §Montgomery modular multiplication and inversion, §elliptic curve cryptosystems, and public-key §cryptography for wireless sensor networks and RFID §tags. Worked examples are provided throughout the §book in order to provide a more detailed insight §into the many cryptographic algorithms and §architectures described.