网络与信息安全第2次作业
Secret and Public Key Cryptography
密钥和公钥的密码技术
1. H ow many DES keys, on the average, encrypt a particular plaintext block to
a particular ciphertext block? [Kaufman
§3.3]
(10 points)
一般来说，把一段详细的评述文字加密成一段加密文字，需要多少位DES 密码？
2. S uppose the DES mangler function mapped every 32-bit value to zero,
regardless of the value of its input. What function would DES then
compute? [Kaufman §3.5] (10 points)
假设这种DES切割函数就是不管输入什么值每32位的值都映射成0，那么DES是什么函数又是怎么计算的呢？
3. I t is said that the initial and final permutations of all 64 bits in DES operation
do not enhance the cryptographic strength of the encryption algorithm.
Could you provide an explanation without using sophisticated
mathematics? (10 points)
据说，64位前后交换位置这种DES方法不能提高加密算法的密码强度。
不使用复杂的数学理论你能提供一个解释来说明吗？
4. C ompute the number of 64-bit encryption operations performed for an n bit
plaintext using CBC, k-bit OFB and k-bit CFB. Count all encryption
operations, not just operations performed on the plaintext itself. Take as
an example, n = 1024 and k =
32. (10
points)
计算64位的数字加密操作通过使用CBC，k位OFB和k位CFB把它变成一个n位的评述文字。
计算所有的加密操作，这些操作不仅仅运行在这个评述文字本身。
举个例子n=1024和k =32。
5. C onsider the following method of encrypting a message using CBC mode.
To encrypt a message, one uses the algorithm for doing a CBC decryption.
To decrypt a message, one uses the algorithm for doing a CBC encryption.
Would this work? How secure is this alternative method in comparison
with the normal CBC mode? (10 points)
考虑以下这种方法，通过CBC模式加密一个消息。
为了加密一个消息，可以使用一个CBC解码算法。
为了解密一个消息，可以使用一个CBC加密算法。
这是怎么实现的呢？这种转换方法与一般的CBC模式比起来有多安全呢？
6. W hat pseudo-random bit stream is generated by 64-bit OFB with a weak
DES key? (10 points)
Note: please refer to Kaufman §3.3.6 for the definition of weak key.
通过使用一个弱的DES密码加密而成的64位OFB，将产生什么伪随机的比特流呢？
注：请参考Kaufman §3.3.6相关章节弱密码的定义
7. I n RSA algorithm, is it possible for more than one d to work with a given e, p,
and q? [Kaufman §6.3] (10 points)
在RSA算法中，当我们知道e,p,g，是否可能得到超过一个d？
8. I n RSA algorithm, what is the probability that something to be encrypted will
not be in Z*n? [Kaufman §7.11] (10 points)
在RSA算法中，被加密的一些不属于Z*n, ,什么情况下是可能发生的？
9. I n the description of possible defense against Man-in-the-Middle Attack
[Kaufman §6.4.2, 3], it stated that encrypting the Diffie-Hellman value with
the other sides’s public key shall prevent the attack. Why is t his case
assumption that an attacker can encrypt whatever it wants with the other
sides’ public key? [Kaufman §6.2] (10 points)
在描述defense against Man-in-the-Middle Attack这种可能性时，它说用另外种方面的普通密码加密这个Diffie-Hellman值可以预防这方面的攻击。
为什么一个攻击可以用另一方面的普通密码加密任何它想要的呢？
10. In modular arithmetic, why must the operand x be relatively prime with the
modulus n in order for x to have a unique multiplicative
inverse? (10
points)
在模运算中，为什么一定要把操作数x设置成模数的相关初始值，是为了让x有一个唯一的乘法倒数吗？。