2011 Future University Hakodate 2011 System Information Science Practice Group Report Project Name Visualization of Code-Breaking RSA Group Name RSA C
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1 2011 Future University Hakodate 2011 System Information Science Practice Group Report Project Name RSA Group Name RSA Code Elliptic Curve Cryptograrhy Group /Project No. 13-B /Project Leader Takahiro Okubo /Group Leader Takumi Ito /Group Member Takumi Ito Hanako Hakodate Yoshitaka Nagai Manami Oikawa Masaaki Shirase Advisor Osamu Konishi Date of Submission January 18, 2012
2 RSA 4 RSA RSA RSA RSA RSA RSA - i -
3 Abstract This project implements a device for person who are not interested in cryptography to enjoy by visualization of break. Then, we divide into four groups, Birthday paradox, RSA cryptography, Elliptic Curve Cryptography, Implementation and learn it about a code the first term. The RSA cryptograph group and the Elliptic Curve Cryptography were united and learned the second term. RSA cryptography is generally used widely because safety is secured by the hardness prime factoring of big numerical. Elliptic Curve Cryptography is a relatively new cryptography. Elliptic Curve Cryptography can handle the processing that is equal to RSA cryptography in short time. Attacker of Symmetric key cryptography which many persons images needs thought such as the Frequency analysis. On the other hand, public key cryptosystems such as RSA and elliptic curve cryptographies can decipher by using a way of thinking of Birthday paradox. Therefore the birthday paradox is very important in the fild of the cryptography. We want to implement plain visualization of the decryption by this project. Keyword Public key cryptosystem, Birthday Paradox, RSA cryptography, Elliptic Curve Cryptography - ii -
4 DES RSA RSA iii -
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6 A 50 B v -
7 Group Report of 2011 SISP Group Number 13-B
8 2 2.1 RSA 2.2 RSA 3 4 RSA RSA 3 RSA RSA RSA RSA RSA RSA Group Report of 2011 SISP Group Number 13-B
9 ipad Group Report of 2011 SISP Group Number 13-B
10 3 ipad RSA PARI/GP RSA RSA PARI/GP RSA 3.2 PARI/GP Group Report of 2011 SISP Group Number 13-B
11 ( ) Group Report of 2011 SISP Group Number 13-B
12 RSA ElGamal DES 64bit 64bit 64bit 1024bit ElGamal 1024bit 2024bit 1024bit RSA RSA RSA ElGamal, Group Report of 2011 SISP Group Number 13-B
13 4.9 DES 4.10 DES DES DES DES 3 DES UNIX DES UNIX DES /etc/passwd UNIX 8 DES 56 DES Group Report of 2011 SISP Group Number 13-B
14 4.12 IC Group Report of 2011 SISP Group Number 13-B
15 Group Report of 2011 SISP Group Number 13-B
16 DES Group Report of 2011 SISP Group Number 13-B
17 5 RSA Ronald Rivest Adi Shamir Leonard Adleman RSA 5.1 RSA RSA RSA 5.2 RSA 1 p q 2 n = p q (n) (p 1)(q 1) n 3.gcd, ( ) 1 e( ) gcd e n e,n 4 de mod (n) d d n d,n 5 e,n p,q,d 5.3 ( ) Group Report of 2011 SISP Group Number 13-B
18 (1. C = M e mod n (2. M = C d mod n RSA RSA RSA RSA, RSA n d n f(x) ( ) X X0 Xi = f(xi 1) mod n X0 = 2, f(x) = X 2 + 1, n=1133 X0 = 2, X1 = 5, X2 = 26, X3 = Y i = Xi mod d d=11 Yi Y 0 = 2, Y 1 = 5, Y 2 = 4, Y 3 = 6... Xi = f(xi 1) mod n Yi d f(y i 1) d ( d ) i j Y i = Y j t Y i + t = Y j + t Yi Yj Xi = Xj(mod d) d Xi Xj Xi Xj gcd(n, Xi Xj) n c c j-i i j Group Report of 2011 SISP Group Number 13-B
19 RSA RSA p q p = 7, q = 13 n = p q = 72 e = 5 (n) = (p 1) (q 1) = 220 e 1 ed 1(mod ( )) n d d = 29 e n (e, n) = (5, 72) n x e (mod n) x = 33 e (mod n) = 335(mod 72) = 6 6 d 6 d (mod n) = 33 d (n) = 72 (n) n Group Report of 2011 SISP Group Number 13-B
20 n p q (n) Group Report of 2011 SISP Group Number 13-B
21 ( ) 6.4 Group Report of 2011 SISP Group Number 13-B
22 7 7.1 RSA RSA RSA C ASCII RSA p,q N e d e (p 1) (q 1) d (p 1) (q 1) e d RSA N 7.2 a, b (a b) a b r a b b r b r r 0 a b m, n (m n) 2. n = 0 m 3. m n n n m 2. Group Report of 2011 SISP Group Number 13-B
23 7.3 m, n gcd(m,n) am + bn = gcd(m, n) a, b = = = = = ( ) = m, n 1 am + bn = c c (a, b) e d 7.4 p=7 q=13 e=5 April P r e s s ASCII 33 e mod N) Group Report of 2011 SISP Group Number 13-B
24 j * x (p 1)*(q 1) e d (p 1) (q 1) = 6 12 = 72 e = 5 72 = = = = 5 ( ) 2 = d = j * x d P r e s s Group Report of 2011 SISP Group Number 13-B
25 7.6 p q N e p q d N N=91 e=7 Me[6vC N f(x) = x2 + 1 mod N x = 2 y = 2 d = 1 x = f(x) = 5 y = f(f(y)) = f(5) = 26 d = gcd( x y, N) = gcd(21, 91) = 7 p = 7 q f(x) = x mod N x = f(x) = 14 y = f(f(y)) = f(14) = 24 d = gcd( x y, N) = gcd(10, 91) = 1 d 1 x = f(x) = 24 Group Report of 2011 SISP Group Number 13-B
26 y = f(f(y)) = f(40) = 63 d = gcd( x y, N) = gcd(39, 91) = 13 q = 13 p q e d (p 1) (q 1) = 6 12 = 72 e = 7 72 = = = = 7 ( ) 3 = d = M e [ 6 v C d w e i g h t Group Report of 2011 SISP Group Number 13-B
27 8 8.1 y 2 = x 3 + ax + b 4a b x y E : y 2 = x 3 + ax + b P Q R = P + Q 1. P Q L 2. E L R 3.R x R R R R = R R P + Q E : y 2 = x 3 + ax + b P(x1,y1) Q(x2,y2) R(x3,y3) Group Report of 2011 SISP Group Number 13-B
28 P Q x3 = 2 x1 x2 y3 = (x1 x3) y1 = (y2 y1)/(x2 x1) P Q x3 = 2 2x1 y3 = (x1 x3) y1 = (3x1 2 + a)/2y1 8.4 x y E : y 2 = x 3 + ax + b P S = 2P 1. P 2. E S 3.S x S S P 2P 8.5 P d P d d * P = P + + P d * P d? 1 8 * P = P + P + P + P + P + P + P + P Group Report of 2011 SISP Group Number 13-B
29 8 * P = 2 * (2 * (2 * P)) 8.6 Z p Z mod p m ( p - 1)2 m ( p + 1)2 P Q ip = Q i 8.7 y 2 = x 3 + ax + b P s s Q Q = sp Q P s P Q s s P Q s 8.8 RSA Group Report of 2011 SISP Group Number 13-B
30 RSA RSA RSA RSA k P, Q = kp, y 2 = x 3 + ax + b ( ) Group Report of 2011 SISP Group Number 13-B
31 ( ) X r A = rp B = X + rq A B (A,B) ( ) k B ka B ka = (X + rq) k(rp ) = X + rkp krp = X P, Q = kp, y 2 = x 3 + x + b k = 13 P = (1, 1) P = (1, 1), 2P = (2, 16), 3P = (13, 9), 4P = (16, 8), 5P = (11, 7) 6P = (18, 4), 7P = (7, 8), 8P = (15, 8), 9P = (8, 5), 10P = (8, 14) 11P = (15, 11), 12P = (7, 11), 13P = (18, 15), 14P = (11, 12), 15P = (16, 11) 16P = (13, 10), 17P = (2, 3), 18P = (1, 18), 19P = (0, 0) 19 Q = kp = 13P = 13(1, 1) = (18, 15) X = (15, 11) r = 3 A = rp = 3(1, 1) = (13, 9) B = X + 3 Q = (15, 11) + 3(18, 15) = (15, 11) P = (15, 11) + (13, 10) = (9, 2) = ((13, 9), (9, 2)) k = 13 (9, 2) 13(13, 9) = (9, 2) (13, 10) = ( 4, 8) = (19 4, 19 8) = (15, 11) Group Report of 2011 SISP Group Number 13-B
32 = X 8.10 PARI/GP s p q q = sp p q s p q p 100 p = ; p = nextprime(p); q = p + 1 ellap(e, p); P (x, y) x = Mod(1, p); y = Mod(2, p); s s = 1 + random(q 1); m p m m = random(p); m m C1 r = 1 + random(q 1); C1 = ellpow(e, P, r); Group Report of 2011 SISP Group Number 13-B
33 a b a1 b1 A1 q A1 = f(a1, b1, R1); a = A[1]b=A[2]a1 = A1[1]b1=A1[2] a b a1 b1 s s1 if(gcd(b b1, l) == 1, s1 = Mod((a1 a)/(b b1), l); s1 = lift(s1); s1 s s1 s s m Group Report of 2011 SISP Group Number 13-B
34 PARI/GP 6 RSA 7 RSA RSA RSA Group Report of 2011 SISP Group Number 13-B
35 4 PARI/GP PARI/GP PARI/GP 5 RSA RSA Mod PARI/GP PARI/GP 6 RSA PARI/GP RSA Mod RSA Group Report of 2011 SISP Group Number 13-B
36 1 4 PARI/GP PARI/GP PARI/GP 5 RSA RSA Mod PARI/GP PARI/GP 6 RSA PARI/GP Mod RSA Group Report of 2011 SISP Group Number 13-B
37 10 11 RSA PARI/GP PARI/GP PARI/GP 5 RSA RSA Mod Group Report of 2011 SISP Group Number 13-B
38 PARI/GP PARI/GP C 9 RSA RSA RSA 10 RSA Java Java C RSA 11 Group Report of 2011 SISP Group Number 13-B
39 RSA 12 RSA RSA 1 4 PARI/GP PARI/GP PARI/GP 5 RSA RSA Mod PARI/GP PARI/GP 6 7 Group Report of 2011 SISP Group Number 13-B
40 SAR SAR 11 SAR 12 Group Report of 2011 SISP Group Number 13-B
41 RSA RSA RSA RSA Group Report of 2011 SISP Group Number 13-B
42 Group Report of 2011 SISP Group Number 13-B
43 RSA Group Report of 2011 SISP Group Number 13-B
44 i Pad Group Report of 2011 SISP Group Number 13-B
45 Group Report of 2011 SISP Group Number 13-B
46 RSA i Pad Group Report of 2011 SISP Group Number 13-B
47 RSA Group Report of 2011 SISP Group Number 13-B
48 RSA PARI/GP RSA od RSA PARI/GP PARI/GP RSA RSA PARI/GP RSA RSA 1975 RSA RSA RSA RSA RARI/GP RSA Group Report of 2011 SISP Group Number 13-B
49 RSA PARI/GP RSA RSA RSA Group Report of 2011 SISP Group Number 13-B
50 12 RSA RARI/GP RSA Group Report of 2011 SISP Group Number 13-B
51 13 RSA RSA RSA RSA RSA RSA RSA SA Group Report of 2011 SISP Group Number 13-B
52 RSA RSA RSA RSA RSA PARI/GP RSA Group Report of 2011 SISP Group Number 13-B
53 RSA RSA RSA RSA RSA Group Report of 2011 SISP Group Number 13-B
54 RSA RSA RSA RSA RSA RSA Group Report of 2011 SISP Group Number 13-B
55 Group Report of 2011 SISP Group Number 13-B
56 A PARI/GP PARI/GP PARI/GP PARI/GP RSA TeX TeX TeX Adobe Illustrator CS4 Adobe Illustrator CS4 Group Report of 2011 SISP Group Number 13-B
57 B Tex Group Report of 2011 SISP Group Number 13-B
58 [1],,, Java,, [2],,, [3] J.H., J.,, [4],,,, [5],,, [6] PARI/GP, [7], graphy01.html Group Report of 2011 SISP Group Number 13-B
2011 Future University Hakodate 2011 System Information Science Practice Group Report Project Name Visualization of Code-Breaking Group Name Implemati
2011 Future University Hakodate 2011 System Information Science Practice Group Report Project Name Group Name Implemation Group /Project No. 13-C /Project Leader 1009087 Takahiro Okubo /Group Leader 1009087
2013 Future University Hakodate 2013 System Information Science Practice Group Report biblive : Project Name biblive : Recording and sharing experienc
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2015 Future University Hakodate 2015 System Information Science Practice Group Report Project Name Improvement of Environment for Learning Mathematics at FUN C (PR ) Group Name GroupC (PR) /Project No.
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2015 Future University Hakodate 2015 System Information Science Practice Group Report Project Name Improvement of Environment for Learning Mathematics at FUN A ( ) Group Name GroupA (System) /Project No.
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2015 Future University Hakodate 2015 System Information Science Practice Group Report Boat Map Project Name Development of Boat map to display the position of boats A Group Name Group A /Project No. 14-A
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2015 Future University-Hakodate 2015 System Information Science Practice Group Report - Project Name HAKODATE - SORACAM, UMICAM, YAMACAM - Part SORACAM Program production and tool development Group Name
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2013 Future University-Hakodate 2013 System Information Science Practice Group Report Project Name Exploring recipe for a new concept of food C Group Name Group C /Project No. 1-C /Project Leader 1011013
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2013 Future University-Hakodate 2013 System Information Science Practice Group Report Project Name Exploring recipe for a new concept of food B Group Name Group B /Project No. 1-B /Project Leader 1011013
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2016 Future University Hakodate 2016 System Information Science Practice Group Report AI Project Name AI Love Deep Learning AI Group Name AI Scope /Project No. 14-A /Project Leader 1014041 Daichi Fukuda
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23 Research of the authentication method on the two dimensional code 1145111 2012 2 13 7,, i Abstract Research of the authentication method on the two dimensional code Karita Koichiro Recently, the two
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24 Development of the programming s learning tool for children be derived from maze 1130353 2013 3 1 ,,,,., C Java,,.,,.,., 1 6 1 2.,,.,, i Abstract Development of the programming s learning tool for children
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2011 Vol.60 No.2 p.138 147 Performance of the Japanese long-term care benefit: An International comparison based on OECD health data Mie MORIKAWA[1] Takako TSUTSUI[2] [1]National Institute of Public Health,
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22 Web Research of a Web search support system based on individual sensitivity 1135117 2011 2 14 Web Web Web Web Web, i Abstract Research of a Web search support system based on individual sensitivity
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2012 Future University Hakodate 2012 System Information Science Practice Group Report Project Name Biological Information for Social Welfare Development of Myoelectric hand Group Name Measurement of Myoelectric
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19 Development of moving image delivery system for elementary school 1080337 2008 3 10 Web Basic Web SAS-2 Web SAS-2 i Abstract Development of moving image delivery system for elementary school Ayuko INOUE
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