고전 암호원리 및 개념 1주차 발표 자료

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전이식 암호, 더하기 암호, 비제네르암호, 아핀 암호, 힐 암호 등을 수식화 하고 예를들어 원리를 설명 하였다. 고전 암호화의 입문 단계에서 발표 자료로 사용 하였기에. 발표 점수 및 ppt 자료는 당연히 A+이 였습니다.

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본문내용

Divede a and b by m, obtaining integer quotients and remainders.
Remainders: Between 0 and m-1. a = q1 r1, b = q2m + r2
0 ≤ r1 ≤ m-1, 0 ≤ r2 ≤ m-1
To compute 101mod 7=3 ∴101=7*14+3 ,0≤3≤6(7-1)
(-101) mod 7=4 ∴-101=7*(-15)+4 , 0≤4≤6
Define aritmetic modulo m: Zm is the set{0,…m-1},equipped with two operation, + and *. Addition and multiplication in Zm work exactly like real addition and multiplication, except that the results are reduced modulo m.
11*13in Z166= 15 and hence 11*13=15Z16
Suppose a and b are integers, and m is a positive integer. Then we write a≡b(mod m) if m divides b-a. the phrase a≡b(mod m) is called a congruence, and it is read as “a is congruent to b moduo m.” The integer mled the modulus.
The Shift Cipher
Basics properties
1. addition is closed, a,b∈Zm, a+b ∈Zm
2. addition is commutative a,b∈Zm, a+b=b+a
3. addition is commutative a,b,c ∈Zm, (a+b)+c=a+(b+c)
4. 0 is an additive identity a ∈Zm, a+0=0+a=a
5. multiplication is closed, a,b ∈Zm, ab ∈Zm
6. multiplication is commutative a,b ∈ Zm ab=ba
7. multiplication is associative a,b,c ∈Zm, (ab)c=a(bc)
8. 1 is a multiplicative identity a ∈ Zm, a*1=1*a=a
add) a*b =1 , b is inverse.
Shift Cipher
0

참고 자료

"Cryptography",-> Therory and practice