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?

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
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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
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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
$Δ y = 1000$ and
$Δ x = 1010$

Find the conditional probability that
$Δ y = 0101$ and
$Δ x = 0110$

3. Questions for AES

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
$n = p q$

107

n = 79 * 73

98

n = 13 * 17

Find the private key(d,n)

98

$ϕ (221) = l c m ((13 - 1), (17 - 1)) = 48$
$d = e^{- 1} (m o d ϕ (n))$
$1 = 77 * d m o d 48 \to d = 5$
Ans: (5,221)

107

$ϕ (5767) = l c m ((79 - 1), (73 - 1)) = 936$
$d = e^{- 1} (m o d ϕ (n))$
$1 = 4493 * d m o d 976 \to d = 517$
Ans: (517,4493)

Decrypt the ciphertext

$m (c) = c^{d} m o d (n)$

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
$0 < d < (p - 1) (q - 1)$ that also works in decryption. Explain why it is impossible, or find all possible values of
$d$

RSA Key gen

find prime numbers
$p$ and
$q$ .
Calculate
$n = p * q$
Calculate
$ϕ (n) = (p - 1) (q - 1)$
Select e, s.t.
$1 < e < ϕ (n), g c d (e, ϕ (n)) = 1 h a s t o b e s i n g u l a r$
Calculate
$d = e^{- 1} (m o d ϕ (n))$
Public key:
$(e, n)$
Private key:
$(d, n)$

5. Answer the following questions about RSA cryptosystem

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
- $p = 2 p^{*} + 1, p *$ is prime
- $q = 2 q^{*} + 1, q *$ is prime

6. Describe algorithms(flow charts) to

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

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
$E (x) = x^{2} m o d 77$ . Find all possible plaintexts that encrypt to the ciphertext 23

97,98

Decrypt method

$p \equiv q \equiv 3 (m o d 4)$
$n = p * q$
$m_{p} = c^{\frac{p + 1}{4}} m o d p$
$m_{q} = c^{\frac{q + 1}{4}} m o d q$
$a p + b q = 1$
$M_{1} = (a * p * m_{p} + n * q * m_{q}) m o d p$
$M_{2} = n - M_{1}$
$M_{3} = (a * p * m_{p} - n * q * m_{q}) m o d q$
$M_{4} = n - M_{3}$

Answer

$p * q = n = 77, \to p = 7, q = 11$
$4 = 23^{\frac{7 + 1}{4}} m o d 7$
$1 = 23^{\frac{11 + 1}{4}} m o d 11$
$7 a + 11 b = 1 \to a = - 3, b = 2$
$M_{1} = (- 3 * 7 * 4 + 2 * 11 * 1) m o d 7 = 1$
$M_{2} = 77 - 1$
$M_{3} = (- 3 * 7 * 4 - 2 * 11 * 1) m o d 11 = 4$
$M_{4} = 77 - 4 = 73$

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

$A = 5^{4} m o d 97 = 43$

Which number should be sent from B to A

$B = 5^{9} m o d 97 = 30$

What is the agreed key

$S = B^{x} m o d p = A^{y} m o d p = 30^{4} m o d 97 = 43^{9} m o d 97 = 50$

14. Please draw a diagram to explain the Dual Signature scheme used in SET(Secure Electronic Transaction).

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

前引

題目