Computer Security and Cryptography

2.7 DERIVING THE PARAMETERS OF A MARKOV MODEL FROM SLIDING WINDOW COUNTS

The Markov model parameters are defined from the sliding window counts of 2-grams {N(i, j)} derived from a large sample x = (x₀, x₁, …, x_n−1) of text as follows:

We assume the sample size n is large enough so that for 0 ≤ i < m and that π satisfies

To prove Equation (2.16), we start with Equations (2.13) to (2.15), writing

This book provides three sets of Markov source parameters:

• Smarkov1 and Smarkov2: These Markov source parameters were derived from a nonsliding window count of 67,320 2-grams in the alphabet {A, B, …, Z} appearing in Abraham Sinkov's book [Sinkov, 1968]. P(j/i) was derived using Equation (2.15) from Sinkov's 2-gram counts and written to Smarkov2; thereafter, π(i) was calculated to satisfy Equation (2.3) and written to Smarkov1.
• Gmarkov1 and Gmarkov2: These Markov source parameters were derived ...