姓名： 袁孟華
學號： 110550004
密碼學概論 homework #1
Q1. ( P.44 1.2) List and briefly define the three key objectives of computer security.
Ans:
1. Confidentiality: Make sure that private information can only be accessed and
disclosed by authorized individuals.
2. Integrity: Make sure that the information can only be modified by authorized and
specified manner. Make sure a system is unimpaired and can only be manipulated
under authentication.
3. Availability: Make sure that the information can be accessed to and used timely
and reliable by authorized individuals.
Q2. Use Stein‘s Algo. to find gcd(1735,975).
Ans: gcd(1735, 975) = 5
1
姓名： 袁孟華
學號： 110550004
Q3. ( P.82 2.37 )
Ans:
2
姓名： 袁孟華
學號： 110550004
Q4. ( P.115 3.11 )
Ans:
a.
IO NL YR EG RE TX TH AT IH AV EB UT ON EL IF ET OG IV EF OR MY CO UN TR TX
-> MA PA ZO QH GJ HW HM LI TM IA JH PB AS DG MC DH RO CA FJ RA FO FA NP BL HW
b.
A
I
C
N
V
L
T
D
P
W
G
H
E
Q
X
O
M
F
S
Y
R
B
J/K
U
Z
3
姓名： 袁孟華
學號： 110550004
IO NL YR EG RE TX TH AT IH AV EB UT ON EL IF ET OG IV EF OR MY CO UN TR TX
-> MA PA ZO QH GJ HW HM LI TM IA JH PB AS DG MC DH RO CA FJ RA FO FA NP BL HW
c. 我們可以擴大這個(b)的 matrix: 將左邊4個colomns複製到最右邊，上面4個rows 複製道
下方，變成一個9*9的matrix:
A
I
C
N
V
A
I
C
N
L
T
D
P
W
L
T
D
P
G
H
E
Q
X
G
H
E
Q
O
M
F
S
Y
O
M
F
S
R
B
J/K
U
Z
R
B
J/K
U
A
I
C
N
V
A
I
C
N
L
T
D
P
W
L
T
D
P
G
H
E
Q
X
G
H
E
Q
O
M
F
S
Y
O
M
F
S
如此便可以發現兩件事:
1. 9*9 matrix 的加密方法與原先5*5 matrix的加密方法相同，不必考慮5*5 matrix
最右邊和最下方字母的特殊情形，因為已經擴充了。
2. (a)和(b)的matrix都包含在這個大matrix裡面，(b)的左上角在(1,1)，(a)的左上
角在(3,5)
因此兩個matrix加密出來的結果相同。
Q5. ( P.116 3.18 )
Ans:
a.
b.
4
姓名： 袁孟華
學號： 110550004
Q6. ( P.138 4.6 )
Ans:
1. The DES encryption function would still permute and substitute the input block.
2. The decryption function of DES is the same as the encryption function, except that
the order of the subkeys is reversed.
Q7. ( P.169 5.3 ) Briefly define a field.
Ans:
Field is a set with 2 binary operations, addition and multiplication. The operations
satisfy some axioms, including closure property, communicative law, associative law,
distributive law, and existence of inverse and identity.
Q8. ( P.170 5.11 )
Ans:
So the multiplicative inverse is x.
5