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Mobile computing has become popular over the last few years. Users need to have continuous access to information even when they are mobile, e.g., a doctor may need to constantly monitor a patient's health or a stock broker may need periodic information about the stock market, etc. Communication in such cases is typically over wireless links and it becomes critical to ensure secure message exchange. The traditional goals of secure computing have been to achieve confidentiality, integrity, availability, legitimacy and accountability. Messages exchanged between two hosts are usually coded by using symmetric or asymmetric ciphers, which makes it difficult for them to be seen by an outsider. This paper discusses issues concerned with mobility in a network and extensions of existing security schemes.