Part III. Asymmetric Ciphers

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  1. The RSA cipher and its algorithmic foundations
  2. Cryptanalysis of RSA
  3. Primality Tests
  4. The discrete logarithm with cryptographic applications
  5. Hard number theoretic problems
  6. Equivalences of basic cryptographic functions
This part has two mathematical appendices:

The complete Part III as PDF file.


Asymmetric encryption introduces a new idea into cryptography that makes a fundamental difference with the formerly treated classic or bitblock ciphers:

Encryption and decryption are significantly different processes. Who knows the encryption function (including its key) has no means to efficiently derive the decryption function (or key).
The derivation of the decryption function from the encryption function is a »one-way« process. As an everyday analog think of a postbox: Who can insert letters in it is not able to get something out of the box, except when she has the key. In this situation for every participant there exists a pair of functions. The first part of this pair is the encryption function—represented by a parameter called »public key«—and is publically available and usable by everyone. The second part is the decryption function—represented by a »private key«—and is a personal secret shared by no one else.

The existence of a strictly personal secret has further interesting applications:

The latter is simply the reverse application of private and public keys:

Historical Notes

Author: Klaus Pommerening, 1997-Apr-09; last change: 2021-Mar-06