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/ RSA




1

. Excel RSA .

. Visual Basic for Applications, . Excel / RSA. .

- . , Microsoft Office.

1. .

2. VBA Excel.

3. Excel RSA, / .

4. / , . , .

5. .

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1 , Excel.

Uml; Visual Basic .

¨ RSA. , RSA, , . , , .

Uml; / , .

Uml; RSA, RSA. .

( 1- 2- ) (N,E)
  [50;100], [75; 125] (N,e)=(78937, 19) M={44389, 31974, 50020, 41406, 29866}
  [70;120], [90; 140] (N,e)=(55357, 37) M={13389, 33602, 11685, 33602, 40522, 47755, 10459, 15507, 33602}
  - [40;90], [80; 130] (N,e)=(41869, 23) M={21618, 16457, 36520, 31771, 22233, 32135 }
  [70;120], [60; 110] (N,e)=(111557, 113) M={49096, 63084, 8557, 3743, 4162, 63084, 8557}
  [30;70], [70; 120] (N,e)=(96091,113) M={61768, 80113, 95437, 80113, 53070, 75177, 82879}
  - [60;100], [110; 150] (N,e)=(139331, 113) M={84929, 101535, 89665, 31645, 48847, 48310, 101535, 89665}
  [70;120], [60; 110] (N,e)=(85039, 113) M={30454, 11454, 54678, 37720, 28540, 13779, 22807, 63035}
  [40;80], [70; 120] (N,e)=(150737, 113) M={104318, 143945, 19327, 69783, 112451, 105094}
  - [70;110], [120; 150] (N,e)=(94697,113) M={10546, 67178, 84721, 4306, 78944, 1251, 27204}
  [75;110], [100; 130] (N,e)=(156031,113) M={29152, 59889, 6814, 115388, 93780, 105567, 31230, 108149}
  [35;70], [80; 120] (N,e)=(157379, 113) M={113065, 45393, 45393, 77288, 102351, 90053, 4109, 122125}
  - [75;100], [120; 160] (N,e)=(65041, 113) M={11965, 10878, 61241, 39494, 43796, 59735, 10878}
  [60;90], [90; 140] (N,e)=(95371, 113) M={73636, 91819, 93589, 82293, 75385, 63153, 27478}
  [70;100], [1200; 150] (N,e)=(103861, 113) M={31152, 63308, 38428, 91454, 4476, 10515, 70086, 63308, 84514, 83370}
  - [65;100], [105; 140] (N,e)=(169921, 113) M={39823, 108107, 55814, 75107, 158616, 145959, 18054}

 

 

 

() (one way function) - f, X -> Y, X Y - , :

1. x . , , f(x) x.

2. y, , . , , , .

 

N ( N) : p q, N=p q, p q N , .

RSA. 1977 , , , , , , 40 , , , 132- ( 40 ). RSA . 129- N ( 428 ), , p q, 65 64 .

. , RSA, 1994 (Quadratic Sieve Factoring), , , . 600 , 1700 , 7 .

, , , (Generalizad Number Field Sieve - GNFS), . , , 2008 , 1000-. RSA 1024, , .

 

/ RSA.

 

1. p q. p q 100 200. N=p q 10 12 . N 512, 768 1024 ( 2048 ).

2. N=p q.

3. . , N, (.. k < N , (N; k)=1).

4. e, RSA, , N, . e L/3, L N. e , N p q, , ().

5. d, RSA, . d , . A B C=(,), x y , . d . C=(,) 1. , . x y , . , . , d y . , y , , d , y < 0,

RSA . (N, e) , d (d ).

 





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