Number Theory & Classical Cryptography (part 1)

Question 1

Greatest Common Divisor (GCD)

Answer 1

the greatest common divisor (gcd) is the largest integer that divides two numbers

Question 2

Prime Number

Answer 2

an integer is prime if and only if its only divisors are 1 and the integer itself

Question 3

Relative Prime Number

Answer 3

two integers are relatively prime if their only common positive integer factor is 1

Question 4

Fundamental Theorem of Arithmetic

Answer 4

states that every integer greater than 1 can be represented uniquely as a product of prime numbers, up to the order of the factors

Question 5

Modulus

Answer 5

given two integers a and n, mod n is the remainder when a is divided by n

Question 6

Congruent Modulo

Answer 6

(a mod n) = (b mod n) or a = b (mod n)

Question 7

Euler’s Totient Function

Answer 7

the number of positive integers less than n and relatively prime to n

Question 8

Exponentiation

Answer 8

repeated multiplication

Question 9

Plaintext

Answer 9

an original message

Question 10

Ciphertext

Answer 10

the coded message

Question 11

Enciphering/Encryption

Answer 11

the process of converting from plaintext to ciphertext

Question 12

Deciphering/Decryption

Answer 12

restoring the plaintext from the ciphertext

Question 13

Cryptography

Answer 13

the area of study of the many schemes used for encryption

Question 14

Cryptographic System/Cipher

Answer 14

a scheme or particular algorithm

Question 15

Cryptanalysis

Answer 15

techniques used for deciphering a message without any knowledge of the enciphering details

Question 16

Cryptology

Answer 16

the areas of cryptography and cryptanalysis

Question 17

Substitution

Answer 17

replace one element in plaintext with another

Question 18

Transposition

Answer 18

re-arrange elements

Question 19

Symmetric

Answer 19

single-key, secret-key, conventional encryption

Question 20

Asymmetric

Answer 20

two-key, or public-key encryption

Question 21

Block Cipher

Answer 21

process one block of elements at a time

Question 22

Stream Cipher

Answer 22

process input elements continuously

Question 23

Brute-Force Attack

Answer 23

attacker tries every possible key on a piece of ciphertext until an intelligible translation into plaintext is obtained

Question 24

Unconditionally Secure

Answer 24

no matter how much time an opponent has, it is impossible for them to decrypt the ciphertext simply because the required information is not there

Question 25

Computationally Secure

Answer 25

the cost of breaking the cipher exceeds the value of the encrypted information or the time required to break the cipher exceeds the useful lifetime of the information

Question 26

Strong Encryption

Answer 26

encryption schemes that make it impractically difficult for unauthorized persons or systems to gain access to plaintext that has been encrypted

Question 27

Caesar Cipher

Answer 27

involves replacing each letter of the alphabet with the letter standing x places further down the alphabet

Question 28

Monoalphabetic Cipher

Answer 28

use a single alphabet for both plaintext and ciphertext (a single cipher alphabet is used per message)

Question 29

Digram

Answer 29

two-letter combination

Question 30

Trigram

Answer 30

three-letter combination

Question 31

Playfair Cipher

Answer 31

treats digrams in the plaintext as single units and translates these units into ciphertext digrams (based on the use of a 5x5 matrix of letter constructed using a keyword)

Question 32

One-Time Pad

Answer 32

use a random key that is as long as the message so that the key need not be repeated; key is used to encrypt and decrypt a single message and then is discarded