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 Takahiro Okubo /Group Member 1009084 Keisuke Aotuka 1009085 Takahumi Inaguma 1009087 Takahiro Okubo Masaaki Shirase Advisor Osamu Konishi 2012 1 18 Date of Submission January, 2011
PARI/GP RSA 4 RSA RSA RSA RSA RSA RSA - i -
Abstract This project implements a device for person who are not interested in to enjoy by visualization of decryption. Firstly, we learn about basics of cryptography using PARI/GP.Then, we divide into for groups, Birthday paradox, RSA cryptography, Elliptic Curve Cryptography, Implementation and learn it about a code.implementation made environment for Application.Birthday paradox, RSA cryptography and Elliptic Curve Cryptography were active toward the implementation of the application while learning basic knowledge each.rsa cryptography is generally used widely because safety is secured by prime factoring of big numerical of the figure. Elliptic Curve Cryptography is a relatively new code.elliptic Curve Cryptography can handle the processing that is equal to RSA cryptography in short time.decipher 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 world of the code.we want to implement plain visualization of the decryption by this project. Keyword Public key cryptosystem, Birthday Paradox, RSA cryptography, Elliptic Curve Cryptography - ii -
1 1 1.1..................................... 1 1.2................................. 1 1.3...................................... 1 2 2 2.1............................ 2 2.2................. 2 2.3............................... 3 2.3.1...................................... 3 2.3.2.................................... 4 3 5 3.1 RSA....................................... 5 3.1.1...................................... 5 3.1.2 PGP(Pretty Good Privacy)............... 5 3.2..................................... 6 3.2.1...................................... 6 3.2.2..................................... 6 3.3 ID.................................... 7 3.3.1...................................... 7 3.3.2..................................... 7 3.3.3 PKI( )............................... 8 3.3.4................................. 8 3.4 ID............................. 8 3.4.1 ID............................. 8 3.4.2 ID............................. 8 3.5................................. 9 3.5.1...................................... 9 3.5.2.................... 9 4 10 4.1..................... 10 4.2....................... 10 4.2.1.............................. 10 4.2.2............................... 10 4.2.3............................... 10 5 12 - iii -
5.1.............................. 12 5.2............... 13 5.2.1.............................. 13 5.2.2.............................. 13 5.2.3............................. 14 5.3............................... 14 5.3.1.................................... 14 5.3.2.................................... 15 5.3.3................................... 16 6 18 6.1.................................... 18 6.2............................... 18 6.3..................... 19 6.4.......................... 19 6.5......................... 19 6.6............................ 20 7 21 7.1...................................... 21 7.2...................................... 21 7.3....................................... 21 7.4....................................... 22 7.5....................................... 22 7.6..................................... 23 8 24 8.1.......................................... 24 8.2.................................... 24 8.2.1................................. 24 8.2.2................................. 25 9 27 9.1............................... 27 9.2............................... 28 10 29 10.1............................... 29 10.2................................ 29 10.3................................ 29 11 30 11.1................................. 30 11.2...................................... 30 - iv -
11.3...................................... 30 A 32 B 33 34 - v -
1 1.1 1.2 1.3 Group Report of 2011 SISP - 1 - Group Number 13-C
2 2.1 RSA 2.2 1 Group Report of 2011 SISP - 2 - Group Number 13-C
2.3 2.3.1 4 4 RSA RSA RSA RSA RSA RSA Group Report of 2011 SISP - 3 - Group Number 13-C
2.3.2 ipad PARI/GP 2 RSA RSA PARI/GP RSA Mac ipad Group Report of 2011 SISP - 4 - Group Number 13-C
3 3.1 RSA RSA 3.1.1 RSA RSA MIT 3 (Rivest, Shamir, Adleman) RSA RSA RSA RSA RSA Philip R. Zimmermann PGP PGP RSA RSA 3.1.2 PGP(Pretty Good Privacy) RSA RSA MIT 3 (Rivest, Shamir, Adleman) RSA RSA RSA RSA RSA Philip R. Zimmermann PGP PGP RSA Group Report of 2011 SISP - 5 - Group Number 13-C
RSA 3.2 3.2.1 (EC-DLP) 1985 (Victor Miller) (Neal Koblitz) RSA RSA DSA DSA (EC-DSA) DH DH EC-DLP RSA RSA P=NP EC-DLP ECC 1 1 ElGamal DLP 3.2.2 (EC-DLP) 1985 (Victor Miller) (Neal Koblitz) RSA RSA DSA DSA (EC-DSA) DH DH EC-DLP RSA RSA P=NP EC-DLP ECC 1 1 ElGamal DLP Group Report of 2011 SISP - 6 - Group Number 13-C
3.3 ID ID ID 3.3.1 ID ( ) IP ID(Identity) IBE(Identity Based Encryption) ID ID ID ID ID ID ID ID ID ID ID 1 3.3.2 ID (Private Key Generator:PKG) ID ID ID PKI(Public Key Infrastructure) Group Report of 2011 SISP - 7 - Group Number 13-C
3.3.3 PKI( ) PKI (CA) (RA) PKI ( ) (VPN) Web 3.3.4 ( ) 3.4 ID 3.4.1 ID ( ID ) ID( ) RSA 3.4.2 ID Group Report of 2011 SISP - 8 - Group Number 13-C
( ) 3.5 3.5.1 1 RSA ID ID 1 3.5.2 ID 2 ID ID Group Report of 2011 SISP - 9 - Group Number 13-C
4 4.1 ipad 4.2 4.2.1 4.2.2 hidden Yes No 4.2.3 Objective-C Group Report of 2011 SISP - 10 - Group Number 13-C
Open Office 4.1 4.1 Group Report of 2011 SISP - 11 - Group Number 13-C
5 5.1 ipad PARI/GP 2 RSA RSA PARI/GP RSA Mac ipad 4 4 RSA RSA RSA RSA RSA RSA Group Report of 2011 SISP - 12 - Group Number 13-C
5.2 5.2.1 4 5 6 Objective-C 7 Objective-C 8 Objective-C 9 10 11 12 5.2.2 4 5 6 Objective-C 7 Objective-C 8 Objective-C 9 10 11 12 Group Report of 2011 SISP - 13 - Group Number 13-C
5.2.3 4 5 6 Objective-C 7 Objective-C 8 Objective-C 9 10 11 12 5.3 5.3.1 4 PARI RSA 5 RSA PARI ipad 6 Objective-C Group Report of 2011 SISP - 14 - Group Number 13-C
7 Objective-C ipad Objective-C 8 Objective-C 9 Objective-C 10 Mac Apple Developer Center X-Code ipad Developer Center ipad 11 12 5.3.2 4 PARI RSA 5 RSA PARI ipad 6 Objective-C Group Report of 2011 SISP - 15 - Group Number 13-C
7 Objective-C ipad Objective-C 8 Objective-C 9 Objective-C 10 Mac Apple Developer Center X-Code ipad Developer Center ipad 11 12 5.3.3 4 PARI RSA 5 RSA PARI ipad 6 Objective-C Group Report of 2011 SISP - 16 - Group Number 13-C
7 Objective-C ipad Objective-C 8 Objective-C 9 Objective-C 10 Mac Apple Developer Center X-Code ipad Developer Center ipad 11 12 Group Report of 2011 SISP - 17 - Group Number 13-C
6 6.1 e a b a b 6.2 c a z 26 a c b c, 3 a d b e z 3 c 26 Group Report of 2011 SISP - 18 - Group Number 13-C
6.3 a z 26 1 a z 6.4. 6.5 PARI/GP PARI/GP PARI/GP RSA Group Report of 2011 SISP - 19 - Group Number 13-C
ipad PC 6.6 Group Report of 2011 SISP - 20 - Group Number 13-C
7 7.1 7.2 pc 18 55 10 7.3 pc pc 2 Group Report of 2011 SISP - 21 - Group Number 13-C
7.4 10 7.5 10 Group Report of 2011 SISP - 22 - Group Number 13-C
7.6 ipad PC Group Report of 2011 SISP - 23 - Group Number 13-C
8 8.1 ipad Objective-C RSA Objective-C ipad 8.1 8.2 8.2.1 Objective-C Objective-C Macmini Objective-C Objective-C ipad MAC Macmini Macmini Objective-C MacbookAir Objective-C Objective-C (2010) Objective-C2.0. (2011) Group Report of 2011 SISP - 24 - Group Number 13-C
8.1 iphone. Objective-C Objective-C 8.2.2 Group Report of 2011 SISP - 25 - Group Number 13-C
Group Report of 2011 SISP - 26 - Group Number 13-C
9 9.1 Group Report of 2011 SISP - 27 - Group Number 13-C
9.2 RSA RSA ipad RSA ipad Group Report of 2011 SISP - 28 - Group Number 13-C
10 10.1 10.2 10.3 Group Report of 2011 SISP - 29 - Group Number 13-C
11 11.1 RSA RSA 11.2 11.3 RSA ipad Group Report of 2011 SISP - 30 - Group Number 13-C
ipad ipad RSA ipad RSA ipad Group Report of 2011 SISP - 31 - Group Number 13-C
A PARI/GP PARI/GP PARI/GP PARI/GP RSA TeX TeX TeX Adobe Illustrator CS4 Adobe Illustrator CS4 Group Report of 2011 SISP - 32 - Group Number 13-C
B Tex Group Report of 2011 SISP - 33 - Group Number 13-C
[1],,, Java,, 2008. [2],,, 2008. [3] J.H., J.,, 1995. [4],,,, 2001. [5], iphone, 2011. [6], Objective-C2.0, 2010. [7] PARI/GP, newblock http://pari.math.u-bordeaux.fr/ [8], newblock http://dev.sbins.co.jp/cryptography/crypto graphy01.html Group Report of 2011 SISP - 34 - Group Number 13-C