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Cryptology

I.10 Theoretical Security
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Contents

  1. A Priori and A Posteriori Probabilities [PDF]
  2. Perfect Security [PDF]
  3. Examples of Perfect Security [PDF]
  4. Density and Redundancy of a Language [PDF]
  5. Unicity Distance [PDF]
  6. Cryptological Applications [PDF]
  7. References [PDF]

[The complete section is available as one PDF file.]

Introduction

The theory of this section goes back to Claude SHANNON (1916-2001) (with later simplifications):

C. E. Shannon: Communication theory of secrecy systems.
Bell System Technical Journal 28 (1949), 656 - 715 [online]
In this paper SHANNON developed the first general mathematical model of cryptology as well as the analysis of cryptosystems by information theoretical methods. The basic question this theory asks is:
How much information about the plaintext is preserved in the ciphertext?
(no matter how difficult or expensive the extraction of this information is.) If this information doesn't suffice to determine the plaintext, then the cipher is secure.

SHANNON's ideas are based on the information theory that he had developed before. The basic paper is:

C. E. Shannon: A mathematical theory of communication.
Bell System Technical Journal 27 (1948), 379 - 423, 623 - 656 [online]

The practical value of SHANNON's theory is limited. But besides it there are almost no sufficient criteria for the security of cryptographic methods that are mathematically proved. In contrast there are lots of necessary criteria derived from cryptanalytic procedures. Lacking better ideas one tries to optimize the cryptographic procedures for these necessary conditions. We saw and shall see many instances of this in these lecture notes.

Author: Klaus Pommerening, 2000-Feb-06; last change: 2014-Sep-02.