Henk C. A. van Tilborg (auth.)'s An Introduction to Cryptology PDF

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

ISBN-10: 1461289556

ISBN-13: 9781461289555

ISBN-10: 1461316936

ISBN-13: 9781461316930

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S,,_I) of the shift register. The function fisa mapping of (0,1)" in {0,1} and is called the feedback function. Since f is a boolean function it can easily be made with logical switches. After the tirst time unit the shift register will output s" = f (s o, SI, . . • S,,_I)' So and go to the state (SJ,S2' ••• , s,,), where Continuing in this way the shift register will generate an infinite sequence We shall first study the special case that f is a linear function, say: (Si }i~O. 7) (0,1}, O:;; i :;; where Ci E (Si }i~O can now be described by the starting values n -1, and alI the additions are taken modulo 2.

1". Because of this ordering and ,,-1 since L ldi < 1 we can define the vectors fi i=1 1 Ci,l Ci,2 L-=-+-+ 2/ 2 22 i-I ;=1 So fi = (O, O, ... , O) of length Il> f2 ~ n, by Ci'/i +-/.. 5) 2' j I h etc.. By definition fi, 1 ~ i = (Ci,I>Ci,2' ... ), , 1::;;; i = (O, O, ... , O, 1, O, ... , O) oflength 12 , with alon coordinate n, has length li' It remains to show that no fu can be the prefix of a codeword f •. Suppose the contrary. Clearly 1" 1•• So 1" < 1. and thus u < v. -1 L -/. - L -/.

2. Consider a memoryless message source that genemtes uniformIy distributed Ietters X from (O,l,2). After tmnsmission over a channei the symboi Y, that is received, will be equal 10 X with probability l-p , OS P SI, and will be equal to any of the other two letters in the alphabet with probability p/2. Compute the mutual information 1 (X ,Y) . 3. Proof that the one-time pad is unconditionally secure. 6» that the security of a cryp- tosystem can be increased by reducing the redundancy in the plaintext.

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


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