# Discrete Mathematics Questions and Answers – Cryptography – Ciphers

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This set of Discrete Mathematics Multiple Choice Questions & Answers (MCQs) focuses on “Cryptography – Ciphers”.

1. _______ is an example of asymmetric ciphers.
a) Block cipher
b) RSA encryption
c) AES encryption

Explanation: The asymmetric ciphers use asymmetric algorithms that use one key to encrypt data and a different key to decrypt ciphers. These algorithms are used in RSA encryption and public-key cryptography in which the public key is used to encrypt data and the private key is used to decrypt data.

2. There is no secret key in case of ____________
a) Symmetric ciphers
b) Asymmetric ciphers
c) RSA encryption
d) Alpha-numeric cryptography

Explanation: A symmetric algorithm uses the same key to encrypt data as well as to decrypt data. For example, a symmetric algorithm will use the key to encrypt some plaintext information like a password into a ciphertext. Then, it uses again to take that ciphertext and turn it back into the password.

3. Suppose in order to get a message across enemy lines, we need to choose an initial secret key say, 100110. What will be the decrypted cipher when the original message is 010010011.
a) 110100
b) 1001011
c) 0011010
d) 011011

Explanation: In order to decrypt the given cipher text, we need to XOR each bit with the corresponding bit in the secret key. As, the cipher text is longer than the secret key, wrap around the remaining cipher text and begin again at the starting. When there will be a chance to decrypt the 7th bit of the cipher text, XOR it with the first bit of the secret key. Hence, after decrypting every bit in the cipher text, the original message will be 110100.

4. Electronic Code Book process is used in ________
a) caesar cipher
b) antisymmetric cipher
c) block cipher
d) stream cipher

Explanation: The block cipher takes a plaintext in the chuck of bits and the bits of key are used to produce bits of ciphertext. They operate on blocks of bits at a time and so it is termed as block ciphers. TIn current cryptomeric systems, the messages that are larger than one block long that need to be split up into smaller messages by using a process called Electronic Code Book (ECB).

5. ______ uses the concept of pseudo-random sequence.
a) Stream cipher
b) DES encryption
c) Caesar cipher
d) Block cipher

Explanation: The stream cipher is the one-time pad that uses the XOR function on the plaintext with a pseudo-random sequence. The input plaintext is encrypted one byte at a time incrementally. As the random sequence is not possible, a pseudo-random sequence is used. These pseudo-random sequence are the outputs of a generator given an initial seed which is a number used to initialize a pseudo-random number generator.

6. How many bits are there for random bits and error detection bits in the case of DES block ciphers?
a) 72, 1024
b) 56, 8
c) 104, 45
d) 32, 198

Explanation: DES is a symmetric system that uses block ciphers which consist of 56 random bits, and 8 more bits are used for error detection. First the data is sent into the system and then divided into two 32-bit blocks. Those two blocks are sent through the entire system using criss-cross which is known as the Feistel system. There are 16 layers in DES. At each layer, one half of the data passes through the Fiestel function and after its completion, it is XORd with the other half of the data. Each layer has its own subkey which is derived from the main 56-bit key by using a key scheduler.

7. What are the steps in the Feistel function?
a) expansion, mixing, substitution, permutation
d) expansion, divide, mixing, permutation

Explanation: The Feistel function which occurs in every block has 3 steps
i) Expansion:- The incoming 32-bit block has half of its bits duplicated, making it a 48-bit block.
ii) Mixing:- The new, 48-bit input block is put through an XOR gate with this round’s unique subkey.
iii) Substitution:- The mixed, 48-bit block is divided into 8 6-bit pieces. Each of these 8 pieces is put through an S-block which will output only 4-bits using non-linear-transformation. Permutation: The 32 output bits are then arranged in a specific permutation that ensures that they will be distributed among different S-blocks in the next round. This is the most important part of security in DES and it helps to avoid simple, algebra-based attacks.

8. What type of algorithm does AES encryption use?
a) Stream cipher
b) Symmetric block cipher
c) Asymmetric caesar cipher
d) DES encryption

Explanation: AES encryption uses symmetric block ciphers to encrypt the messages. It is at least 6 times faster than 3 DES. AES uses a substitution-permutation network and this network is a series of operations that either replaces input with output bits (substitution) or shuffles the bits (permutation). It uses 128-bit input plaintext and it operates on bytes rather than bits. Here, the input is represented as 16 bytes (because 128 bits = 16 bytes) and is arranged in a 4 x 4 matrix.

9. What is the block size of blowfish block cipher?
a) 64 bits
b) 128 bits
c) 1043 bits
d) 10 bits

Explanation: Blowfish symmetric block cipher was created after DES but before AES. Its block size is 64 bits, and it can use key lengths from 32 up to 448 bits. It is a 16-round Feistel cipher and unlike in DES it’s S-boxes are key-dependent and so they are generated dynamically.

10. In which cipher each letter of the plaintext is substituted by any other letter to form the cipher message?
a) Shift cipher
b) DES encryption
c) Block cipher
d) AES encryption 