[수체계] The ElGamal Cryptosystem & An Application to the splicing of telephone cables(영문)
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추천 연관자료
- 목차
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1. Introduction
2. main subject
1) ElGamal Cryptosystem
<Example 1>
<Example 2>
2) ElGamal Signature Scheme
(1) Signature Scheme
(2) ElGamal Signature Scheme
<Example 3>
(3) Security of ElGamal Signatures
<Example 4>
3) An Application to the splicing of Telephone Cables
<Example 5>
<Example 6>
3. conclusion
[ Bibliography ]
- 본문내용
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1. Introduction
We all use math every day to predict the weather, tell the time, handle money and etc. Math is more than formulas and equations, math is related with our lifes so deeply and it is almost everywhere. So our team members are interested in the application of the math, especially ElGamal cryptosystem and the application to the splicing telephone cables.
Sometimes we use math for cryptology to solve the criminal misteries by code-breaking like computer hacking, eavesdropping and wiretapping. Also include the security of ATM cards, computer passwords, and the electronic commerce, which all depend on cryptography. So These days the importance of cryptology is increasing more and more.
Around 50 B.C. the earlist cryptographic system was used by Julius Caesar and the cryptography was investigated and used for protecting military practices. Today, by a rapid growth of computer technology, it is a practical means for protecting information and for safe transmitting information.
In modern times there are so many ways of cryptology and among those A New Approach To The ElGamal Encryption scheme. Czeslaw Koscielny.
Int. J. Appl. Math. comput. Sci. 2004, Vol.14.No.2, 265~267
public-key cryptographic algorithms are designed to resist chosen-plaintext attacks. And their security is based both on the difficulty of finding the secret key from the public key and the difficulty of determining the plaintext from the cryptogram. At present, the most common public-key cryptosystem is the RSA algorithm. The RSA cryptosystem is related to the difficulty of factoring large numbers. But it is conceivable that an entirely different way to break RSA can be discovered.(perhaps this way is already known for some cryptanalysts.) Therefore cryptographers attempt to activate alternative public-key encryption algorithm, like the ElGamal encryption scheme.
Because of that we pick the subject of ElGamal cryptosystem especially, actually the fact that its security is based on the difficulty of finding discrete logarithms modulo a large prime in a finite field is quite interesting.
And also the fact that math is used for splicing telephone cables attracts us and we are curious about how the number theory can help to make the splicing telephone cables. Telephone lines are constructed by splicing together sections of cable. But when two wires are adjacent in the same layer in multiple sections of the cable, there are so many problems with interference and crosstalk. So we need the mathematical rules in this time.
Like this, math is very useful in many ways. Above all the fact that the number theory we've learned can explain the cryptosystem and the splicing telephone cables motivates us to study harder and make us feel the joy of learning number theory.
2. main subject
1) ElGamal Cryptosystem
ElGamal Cryptosystem is invented by T. ElGamal in 1985 and its security is based on the difficulty of finding discrete logarithms modulo a large prime in a finite field. In other words, it is difficult to determine the private key a from the public key (p, r, b). A disadvantage of the ElGamal system is that the encrypted message becomes very big, about twice the size of the original message. For this reason it is only used for small messages such as secret keys.
The ElGamal cryptosystem consists of two parts, ElGamal encryption scheme and ElGamal signature scheme.
Before the encryption, we have to translate the letters into their numerical equivalents and then form blocks with an even number of digits.
There are so many ways of translation but here we take the alphabet of English and translate them into the integers from 0 to 25, as shown in the next table.
A
B
C
D
E
F
G
H
I
J
K
L
M
N
O
P
Q
R
S
T
U
V
W
X
Y
Z
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01
02
03
04
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- 참고문헌
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<암호학과 네트워크 보안>Forouzan, Behrouz A, 한국맥그로힐, 2008
< 암호학의 이해> 김철, 영풍문고, 1996
<수론과 암호학> 서광석 외, 경문사, 1998
Stinson, Douglas R., Chapman & Hall/CRC , 2002
Smart, Nigel P., McGraw-Hill, 2003
Stallings, William., Prentice Hall, 1999
Man Young Rhee., McGraw-Hill, 1994
Richard E. Smith ,Addison Wesley ,1997
Implementation of the ElGamal cryptosystem, 김민경, 이화여자대학교 대학원 2005학년도 석사학위 청구논문
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