1
. Excel RSA .
. Visual Basic for Applications, . Excel / RSA. .
- . , Microsoft Office.
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2. VBA Excel.
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Uml; Visual Basic .
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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} |
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() (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 .
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, , , (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 ).