Abstract
A problem of the symmetric cryptosystems that we have described so far is key distribution and key management. When Alice and Bob use a symmetric cryptosystem, they must exchange a secret key before they can secretly communicate. For the key exchange, they need, for example, a secure channel or a courier. The key exchange problem becomes even more difficult if many people want to exchange encrypted messages, for example, on the Internet. If a communication network has n users and any two of them exchange a key, then n(n − 1)/2 secret key exchanges are necessary and all those keys have to be stored securely. According to [34] there were approximately 6 · 108 Internet users in 2002. If any two Internet users exchanged a secret key then 1.8 · 1017 keys would be necessary. This would be impossible to organize.
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© 2004 Springer Science+Business Media New York
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Buchmann, J.A. (2004). Public-Key Encryption. In: Introduction to Cryptography. Undergraduate Texts in Mathematics. Springer, New York, NY. https://doi.org/10.1007/978-1-4419-9003-7_8
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DOI: https://doi.org/10.1007/978-1-4419-9003-7_8
Publisher Name: Springer, New York, NY
Print ISBN: 978-0-387-20756-8
Online ISBN: 978-1-4419-9003-7
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