---
title: 資訊安全導論期末
---
# 前引
*　目前只有９７、９８以及１０７年的紀錄，因此較難猜題
*　110 下學期因為遠距課程，期末改以報告形式進行，本文作業暫停
# 題目
## 1. (送分)For each type of the following attacks, list all information and/or encryption/decryption programs the attacker of a cryptosystem can have?
* 107
* 12%
### Ciphertext-only attack
* 攻擊者僅有密文。
* 攻擊者有encryption/decryption program
### Known-plaintext attack
* 攻擊者有一組以上密文與明文。
* 攻擊者有encryption/decryption program
### Chosen-Plaintext Attack
* 攻擊者可將明文轉為密文。
* 攻擊者有encryption/decryption program
### Chosen-Ciphertext Attack
* 攻擊者可將密文轉為明文。
* 攻擊者有encryption/decryption program
#### Kerckhoffs原理
* 『對於一密碼系統的安全性，應假設敵人是知道所使用的方法。』
* 攻擊者有encryption/decryption program
## 2. S-boxes
* 98, 107
### Which type of (Ciphertext-only attack, Known-plaintext attack, Chosen-Plaintext Attack or Chosen-Ciphertext Attack) should **linear attack** be classified as?
* Known-plaintext attack
### Which type of (Ciphertext-only attack, Known-plaintext attack, Chosen-Plaintext Attack or Chosen-Ciphertext Attack) should **differential** be classified as?
* chosen-plaintext attack
### probability holds
* if + means XOR
* We are checking for equals to 0 to hold. If we split x and y into two groups to process , remember that the results of the two groups has to be equal for XOR to result in 0.
* Bias is the probility -1/2
* 
#### Find the probability that $x_1+x_2+y_3+y_4=0$ holds
|$x_1+x_2$ | $y_3+y_4$ | $x_1+x_2=y_3+y_4$ |
| -------- | -------- | -------- |
| 0 | 1 | 0 |
| 0 | 0 | 1 |
| 0 | 1 | 0 |
| 0 | 1 | 0 |
| 1 | 1 | 1 |
| 1 | 0 | 0 |
| 1 | 0 | 0 |
| 1 | 0 | 0 |
| 0 | 0 | 1 |
| 0 | 1 | 0 |
| 0 | 1 | 0 |
| 0 | 0 | 1 |
| 1 | 1 | 1 |
| 1 | 1 | 1 |
| 1 | 0 | 0 |
| 1 | 0 | 0 |
* Ans: 7/16
#### Find the probability that $x_1+x_4+y_1+y_2+y_4=0$ holds

|$x_1+x_4$ | $y_1+y_2+y_4$ | $x_1+x_4=y_1+y_2+y_4$ |
| -------- | -------- | -------- |
| 0 | 0 | 1 |
| 1 | 1 | 1 |
| 0 | 1 | 0 |
| 1 | 1 | 1 |
| 0 | 0 | 1 |
| 1 | 1 | 1 |
| 0 | 0 | 1 |
| 1 | 1 | 1 |
| 1 | 1 | 1 |
| 0 | 1 | 0 |
| 1 | 1 | 1 |
| 0 | 0 | 1 |
| 1 | 0 | 0 |
| 0 | 0 | 1 |
| 1 | 0 | 0 |
| 0 | 0 | 1 |
* Ans:12/16
### condition probability
#### Find the conditional probability that $\Delta y=1000$ and $\Delta x=1010$
#### Find the conditional probability that $\Delta y=0101$ and $\Delta x=0110$
## 3. Questions for AES
* 97
### List the advantages of AES over DES
### Write out AES-128 (10-round) encryption algorithm. The SubByte, ShiftRow, MixColumn, and AddRoundkey procedures can be called as a command.
#### Encryption

AddRoundKey(S,K[0]);
for(i=1;i<=9;i++)
{
    SubByte(S);
    ShiftRow(S);
    MixColumn(S);
    AddRoundKey(S,K[i]);
}
SubByte(S);
ShiftRow(S);
AddRoundKey(S,K[10]);

#### Decryption

AddRoundKey(S,K[10]);
InverseShiftRow(S);
InverseSubByte(S);
for(i=9;i>=1;i--)
{
    AddRoundKey(S,K[i]);
    InverseMixColumn(S);
    InverseShiftRow(S);
    InverseSubByte(S);
}
AddRoundKey(S,K[0]);

## 4. Consider an RSA crypto-system whose public key is ...
* 107 $(n,e)=(5767,4493)$
* 98 $(n,e)=(221,77)$
### Find prime numbers *p* and *q* such that $n =pq$
#### 107
* n = 79 * 73
#### 98
* n = 13 * 17
### Find the private key(d,n)
#### 98
* $\phi (221)=lcm((13-1),(17-1)) = 48$
* $d=e^{-1}(mod\ \phi(n))$
* $1=77*d\ mod 48\rightarrow d=5$
* Ans: (5,221)
#### 107
* $\phi (5767)=lcm((79-1),(73-1)) = 936$
* $d=e^{-1}(mod\ \phi(n))$
* $1=4493*d\ mod\ 976\rightarrow d=517$
* Ans: (517,4493)
### Decrypt the ciphertext
* $m(c) = c^d mod(n)$
#### 98. $88$
* 88^5 mod 221 = 219
#### 107. $1000$
* 1000^517 mod 4493 = ?
* 算得出來?
### Is it possible to find a different value of $d$ in the range of $0\lt d \lt(p-1)(q-1)$ that also works in decryption. Explain why it is impossible, or find all possible values of $d$
### RSA Key gen
1. find prime numbers $p$ and $q$.
2. Calculate $n=p*q$
3. Calculate $\phi (n)=(p-1)(q-1)$
4. Select e, s.t. $1<e<\phi(n), gcd(e, \phi(n))=1 has to be singular$
5. Calculate $d=e^{-1}(mod \phi(n))$
6. Public key: $(e, n)$
7. Private key: $(d, n)$
## 5. Answer the following questions about RSA cryptosystem
* 107
### What is common modulus attack
*　same n
* Choose different n's
### What is Small-e attack
* e too small

* choose large e
### What is cycling attack

### How to avoid cycling attack
* choose better p,q
* p,q are large prime and
* $p=2p^*+1, p*$ is prime
* $q=2q^*+1, q*$ is prime

## 6. Describe algorithms(flow charts) to
* 107
### Create a digital envelope
#### Open a digital envelope
## 7. Use flow charts to explain the RSA signature with hash function
* 97,98,107
### Alice wants to sign a document M
* Hash plaintext and encrypt with Alice's private key
### Bob wants to verify a signed document (M,s) from Alice
* decrypt signature with Alices's public key
* Generate hash value from plaintext and check if it matches the signature
#### 教授版
[](https://i.imgur.com/p9DhCd6.png)

## 8. Certificates of public key
* 97,98, 107
### Why certificates are necessary
* proves the authenticity of a device, server, or user
### Which information items should be contained in a certificate?
*　things mentioned by x.509 Authentication framework
*　includinge
* 使用者名稱 A
* 該使用者的公鑰 KUA
* 由 CA 對(A, KUA)所簽署的簽章*
* CA: certificate authority　
### Let a Certificate issued from A for B be denoted as A[B]
* 需要確認答案是否正確
#### 107
* A,B,F
#### 98
* ans: A,E,D
## 9. What is a "Computer Virus"? Describe the life cycle of a computer virus.
*　107
*　Currently no PPT for this question
## 10. What are the differences between "Information Hiding" and "Encryption"? What are the differences of "Steganography" and "Watermarking"
*　107
*　Currently no PPT for this question
## 11. Common Modulus attack
* 98, 98

## 12. Consider a Rabin cryptosystem where the encryption function is $E(x) = x^2 mod 77$. Find all possible plaintexts that encrypt to the ciphertext 23
* 97,98
### Decrypt method
* $p\equiv q \equiv 3(mod4)$
* $n = p*q$
* $m_p= c^{\dfrac{p+1}{4}}mod\ p$
* $m_q= c^{\dfrac{q+1}{4}}mod\ q$
* $ap+bq=1$
* $M_1 = (a*p*m_p+n*q*m_q) mod\ p$
* $M_2 = n-M_1$
* $M_3 = (a*p*m_p-n*q*m_q) mod\ q$
* $M_4 = n-M_3$
### Answer
* $p*q=n=77, \rightarrow p=7,q=11$
* $4= 23^{\dfrac{7+1}{4}}mod\ 7$
* $1= 23^{\dfrac{11+1}{4}}mod\ 11$
* $7a+11b = 1 \rightarrow a=-3 , b=2$
* $M_1 = (-3*7*4+ 2*11*1)mod\ 7=1$
* $M_2 = 77-1$
* $M_3 = (-3*7*4-2*11*1)mod\ 11 = 4$
* $M_4 = 77-4 = 73$
## 13. In a Diffie-Hellman key agreement between two persons A and B, (g,p) = (5,97). User A randomly choose x=4, and user B randomly selects y=9.
* 97, 98
### Which number should be sent from A to B
* $A = 5^4\ mod\ 97=43$
### Which number should be sent from B to A
* $B = 5^9 mod 97=30$
### What is the agreed key
* $S = B^x mod p = A^y\ mod\ p = 30^4 mod 97 = 43^9 mod 97 = 50$
## 14. Please draw a diagram to explain the Dual Signature scheme used in SET(Secure Electronic Transaction).
* 97
## 15. Is it possible to apply the technology such as encryption/decryption and digital signature in information security to multimedia. say images or videos? If it is possible, describe some applications; otherwise, explain why it is impossible
* Currently no PPT for this question
* Probably watermarking
###### tags: `Introduction to Information Security` `CSnote`