An Introduction to Cryptology - download pdf or read online

By Henk C. A. van Tilborg (auth.)

ISBN-10: 1461289556

ISBN-13: 9781461289555

ISBN-10: 1461316936

ISBN-13: 9781461316930

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Extra resources for An Introduction to Cryptology

Example text

S,,_I) = boolean function g in n - 1 variables. So + g feedback function (SI. S2 • . . • S,,_I) for some Prooi' Since 1 is a Boolean function one can write 1 (SO,SI' soh (SJ,S2 • . . • :;. If h (SI>S2 • . . S2' . . • S,,_I) then (O,SI>S2>"" S,,_I) and S,,_I) have the same successor states. Thus a branch point would exist We conclude that h == 1. <:= The state (0,SI>S2 •. • has successor with s,. • S.. _I), while So there are no branch points. • s .. ) S,,_I) bas successor (SI>S2' . . ).

So G2 says that certain n-grams occur with the right probabilities. The interpretation of G3 is more difficult It does say that counting the number of agreements between a sequence and a shifted version of that sequence does not give any information about the period of that sequence, unless one shifts over a multiple of the period. 3, where this comparison gives the length of the key used in a Vigenere cipher. In cryptographical applications p will be too large for such an approach. The value of the constant in G3 follows from G 1 and G3, as we shall now prove.

3: (McMillan inequality, [McMS6]) A necessary and sufficient condition for the existence of a uniquely decodable code C with codewords oflength 1;. 1 SiS Il, is " 1 1:-,. SI. D. code with codeword lengths li' 1 SiS Il. 2) is also sufficient will be proved later in this chapter. e. 11 S 12 S ... SI". 3) where Ni is the number of ways to write j as IiI + li 2 + + liN' or altematively Ni is the number of ways to make a concatenation of N codewords of total length j. D. no two different choices of N concatenated codewords will give rise to the same string of length j.

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An Introduction to Cryptology by Henk C. A. van Tilborg (auth.)

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