インターネット概論 第07回(2004/11/12) 「SFC-CNSの現状」
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- ふじよし つねざき
- 9 years ago
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Transcription
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14 AES 128bit) 196bit 256bit 128bit) bit) bit)
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16 (n, e) (n, d) M M : 2 ( 101 5) [e ] [e ] n = p * q (p q ) (n) = (p-1)(q-1) gcd( (n), e) = 1; 1 < e < (n) d = e^-1 (mod (n)) M e (mod n) [d ] [d ] C C : M = C d (mod n) = (M^e ^d (mod n) = M^ed (mod n) = M (mod n)
![(n) d = e^-1 (mod (n)) M e (mod n) [d ] [d ] C C : M](/docs-images/43/23116989/images/page_16.jpg "= C d (mod n) = (M^e ^d (mod n) = M^ed (mod n) = M")
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20 ( ) A A B B OK
21 MD
22 1 MD?? MD 1.? 2. 3.??? 4.
23 (1) challenge( (2) (3) response (4)
24 N Pass Phrase k Pass Phrase N+1 Pass Phrase k-1 Pass Phrase
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mahoro/2011autumn/crypto/
http://www.ss.u-tokai.ac.jp/ mahoro/2011autumn/crypto/ 1 1 2011.9.29, ( ) http://www.ss.u-tokai.ac.jp/ mahoro/2011autumn/crypto/ 1.1 1.1.1 DES MISTY AES 1.1.2 RSA ElGamal 2 1 1.2 1.2.1 1.2.2 1.3 Mathematica
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BIT -2-
2004.3.31 10 11 12-1- BIT -2- -3-256 258 932 524 585 -4- -5- A B A B AB A B A B C AB A B AB AB AB AB -6- -7- A B -8- -9- -10- mm -11- fax -12- -13- -14- -15- s58.10.1 1255 4.2 30.10-16- -17- -18- -19-6.12.10
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n=360 28.6% 34.4% 36.9% n=360 2.5% 17.8% 19.2% n=64 0.8% 0.3% n=69 1.7% 3.6% 0.6% 1.4% 1.9% < > n=218 1.4% 5.6% 3.1% 60.6% 0.6% 6.9% 10.8% 6.4% 10.3% 33.1% 1.4% 3.6% 1.1% 0.0% 3.1% n=360 0% 50%
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4 1 4 (1) (2) (3) (4) 1 4 2 (1) (B4:B6) (2) (B12:B14) (3) 1 (D4:H4) D5:H243 (4) 240 20 (B8:B10) (5) 240 (B8) 0 1 4 3 2 2.1 2 Excel 2 (A1:A14 D3:H3 B4,B5,B6) B5 0.035 4 4 2.2 3 1 1 B12: =B5+1 B13: =B12
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(1) %
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2001 Miller-Rabin Rabin-Solovay-Strassen self-contained RSA RSA RSA ( ) Shor RSA RSA 1 Solovay-Strassen Miller-Rabin [3, pp
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15 mod 12 = 3, 3 mod 12 = 3, 9 mod 12 = N N 0 x, y x y N x y (mod N) x y N mod N mod N N, x, y N > 0 (1) x x (mod N) (2) x y (mod N) y x
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0 (18) /12/13 (19) n Z (n Z ) 5 30 (5 30 ) (mod 5) (20) ( ) (12, 8) = 4
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