Public-Key Encryption

  • Johannes A. Buchmann
Part of the Undergraduate Texts in Mathematics book series (UTM)


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.


Discrete Logarithm Chinese Remainder Theorem Choose Ciphertext Attack Extended Euclidean Algorithm ElGamal Encryption 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


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Copyright information

© Springer Science+Business Media New York 2004

Authors and Affiliations

  • Johannes A. Buchmann
    • 1
  1. 1.Department of Computer ScienceTechnical UniversityDarmstadtGermany

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