crypto4_newx

crypto4_newx - CIS CIS 5371 Cryptography 4. Computational...

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IS 5371 Cryptography CIS 5371 4. Computational Complexity 1
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Turing Machines A finite state control unit k 1 tapes and read or write tapeheads FSC unit tapeheads 2
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Deterministic Polynomial Time Class P he class of languages L such that: The class of languages any x L can be recognized by a TM in time bounded y a polynomial p(n) where n is the length of x by a polynomial p(n), where n is the length of x. A language recognition problem is a decisional problem. Class P can also be used to capture computational problems. Polynomial-time computational problems These must be computed by a TM in polynomial-time. 3
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The Euclidean Algorithm Input : integers a > b 0 utput cd b Output : gcd ( a,b ) 1. i 0; r -1 a ; r 0 b ; hil ( )d 2 .w hile ( r i 0 ) do a) . r i+ 1 . r i- 1 (mod r i ) ; ) b) . i i+ 1 3. return( r i- 1 ) 4
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An example a = 60, b = 9 r r i- 1 i 60 9 96 6 3 3 = cd 60,9) 3 0 5 g (, )
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The Extended Euclidean Algorithm Input : integers a > b 0 Output : integers , satisfying a +b = gcd ( a,b ) 1. i 0; r -1 a ; r 0 b ; q 0 -1 1 ; -1 0 ; 0 0 ; 0 1 hil ( )d 2 .w hile ( r i = a i + b i 0 ) do a) . q = r i -1 r i b)   - q ;   - q . i+ 1 . i- 1 i i+ 1 . i- 1 i
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This note was uploaded on 12/11/2011 for the course CIS 5371 taught by Professor Mascagni during the Fall '11 term at FSU.

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crypto4_newx - CIS CIS 5371 Cryptography 4. Computational...

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