Number Trick - (q - 1). m = (3 - (11 - 1) = 20 p h 1) h 1)...

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Sheet1 Page 1 Number Trick Pick any number from 1 to 32. M Raise this to the 7th power. M 7 Divide by 33 and tell me the remainder. R =(M 7 )mod33 I will tell you the original number. What happened? 7 R =(M )mod33 3 (R )mod33 = M M Where did 7, 33, and 3 come from? I chose two prime numbers p & q. 3 & 11 a = q 33 = 3 11 Let m = ( p -
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Unformatted text preview: (q - 1). m = (3 - (11 - 1) = 20 p h 1) h 1) h Sheet1 Page 2 Choose any number e which has no common factors with m. [gcd( e, m) = 1] e = 7 gcd(7,20) = 1 Since gcd( e, m) = 1, then there are integers d & f d - f = 1. I want the d. -3 20 1 = 1 d = 3 With this setup, if (Me )mod a = R then (Rd )mod a = M M where e h m h 7 h...
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This note was uploaded on 04/19/2008 for the course MAED 310 taught by Professor Rogers during the Spring '08 term at SUNY Fredonia.

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Number Trick - (q - 1). m = (3 - (11 - 1) = 20 p h 1) h 1)...

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