Computer Security and Cryptography

5.1 WEAKNESSES IN A CRYPTOSYSTEM

Cryptographic systems might be cryptanalyzed by

• Exhaustive key trial, or
• Exploitation of systemic weakness, often in conjunction with a selective nonexhaustive key trial.

The recent cracking of DES involved exhaustive key trial, but the Enigma machine was cryptanalyzed by exploiting a weakness in the design and defective operational protocol used in encipherment.

The only perfectly secure encipherment uses a one-time system and this only when used properly. The practical limitation of one-time encipherment led to design of cryptographic systems that use a short key k₀, k₁,…, k_n−1 to generate a larger operational key. It is an act of faith that as the basic key length n increases, the security of the derived ciphertext also improves. The design of cryptographic systems has therefore focused on ways of generating long keys that appear to be random.

The methods discussed thus far in these notes have dealt with uncovering some systemic weakness. Here we examine some of the statistical methods that might be used to detect hidden relationships between the key, plaintext, and ciphertext. One such statistical measure, the χ²-test has already been described in Chapter 3.