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Security of data by means of cryptography is becoming more and more important in many areas of our lives. Public-key cryptosystems (PKC) form an important part of cryptography as they allow convenient and secure communication between all users. Theobjective is to develop PKCs that provide a high level of security while being fast and easy to use. The author Robert Niebuhr analyses the application of Algebraic-Geometric Codes (AGC) in Cryptographic Systems. Starting with a brief discussion of Algebraic Geometry and the general construction of PKCs, he showshow to use AGC including encoding, decoding and error-correction.To demonstrate the concrete application he develops a Cryptosystem using the McEliece Scheme and evaluates its properties. This book is a useful reference for students, professors, and everybody with some mathematical background and an interest in cryptography.