final result or product is cryptographically stronger than any of the component ciphers.
3.5 What is the difference between diffusion and confusion?
In diffusion, the statistical structure of the plaintext is dissipated into long-range statistics of the ciphertext. This is achieved by having each plaintext digit affect the value of many ciphertext digits, which is equivalent to saying that each ciphertext digit is affected by many plaintext digits. Confusion seeks to make the relationship between the statistics of the ciphertext and the value of the encryption key as complex as possible, again to thwart attempts to discover the key. Thus, even if the attacker can get some handle on the statistics of the ciphertext, the way in which the key was used to produce that ciphertext is so complex as to make it difficult to deduce the key. This is achieved by the use of a complex substitution algorithm.
3.6 Please give the Feistel Cipher Structure?
3.7 What is the purpose of the S-boxes in DES?
The S-box is a substitution function that introduces nonlinearity and adds to the complexity of the
transformation.
3.8 Explain the avalanche effect.
The avalanche effect is a property of any encryption algorithm such that a small change in either the plaintext or the key produces a significant change in the ciphertext.
In particular, a change in one bit of the plaintext or one bit of the key should produce a change in many bits of the ciphertext. This is referred to as the avalanche effect.
please illustrate The overall scheme for DES encryption.
Please give the internal structure of a single round As in any classic Feistel cipher .
In DES, the substitution consists of a set of eight S-boxes, each of which accepts 6 bits as input
and produces 4 bits as output. Please give the outputs of the inputs in from s1 to s8 ? S(18 09 12 3d 11 17 38 39) = 5fd25e03
18(01|1000) 09(00|1001) 12(01|0010) 3d(11|1101) (00,12)5 (01,4)f-15 (00,9)d-13 (11,14)2 11(01|0001) 17(01|0111) 38(11|1000) 39(11|1001) (01,8)5 (01,11)e-14 (10,12)0 (11,12)3
4.6 For each of the following equations, find an integer that satisfies the equation. a. b. c.
a. 2 b. 3 c. 4
There are other correct answers.
4.13 Find the multiplicative inverse of each nonzero element in1–1 = 1, 2–1 = 3, 3–1 = 2, 4–1 = 4
4.15 a. Determine . gcd(24140, 16762) b. Determine . gcd(4655, 12075)
4.15 a. gcd(24140, 16762) = gcd(16762, 7378) = gcd(7378, 2006) = gcd(2006, 1360) =
gcd(1360, 646) = gcd (646, 68) = gcd(68, 34) = gcd(34, 0) = 34
b. gcd(4655, 12075) = gcd(4655, 2765) = gcd(2765, 1890) = gcd(1890, 875) = gcd(875,
140) = gcd (140,35) = gcd(35, 0) = 35
gcd(2152, 764) = gcd(764, 624) = gcd(624, 140) = gcd(140, 64) = gcd(64, 12) = gcd(12, 4) =
gcd(4, 0) = 4
4.20 Develop a set of tables similar to Table 4.5 for .GF(5)
+ 0 1 2 3 4
? 0 1 2 3 4
0
1
2
3
4
w
–w
w–1 — 1 3 2 4 0 0 1 2 3 4 1 1 2 3 4 0 2 2 3 4 0 1 3 3 4 0 1 2 4 4 0 1 2 3 0 0 0 0 0 0 1 2 3 4 0 2 4 1 3 0 3 1 4 2 0 4 3 2 1
0 1 2 3 4 0 4 3 2 1 4.23 For polynomial arithmetic with coefficients in , perform the following calculations. a. b. a. b.
9x2 + 7x + 7 5x3 + 7x2 + 2x + 6
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