Number Theory & Classical Cryptography (part 1) Flashcards
Quiz #2
Greatest Common Divisor (GCD)
the greatest common divisor (gcd) is the largest integer that divides two numbers
Prime Number
an integer is prime if and only if its only divisors are 1 and the integer itself
Relative Prime Number
two integers are relatively prime if their only common positive integer factor is 1
Fundamental Theorem of Arithmetic
states that every integer greater than 1 can be represented uniquely as a product of prime numbers, up to the order of the factors
Modulus
given two integers a and n, mod n is the remainder when a is divided by n
Congruent Modulo
(a mod n) = (b mod n) or a = b (mod n)
Euler’s Totient Function
the number of positive integers less than n and relatively prime to n
Exponentiation
repeated multiplication
Plaintext
an original message
Ciphertext
the coded message
Enciphering/Encryption
the process of converting from plaintext to ciphertext
Deciphering/Decryption
restoring the plaintext from the ciphertext
Cryptography
the area of study of the many schemes used for encryption
Cryptographic System/Cipher
a scheme or particular algorithm
Cryptanalysis
techniques used for deciphering a message without any knowledge of the enciphering details
Cryptology
the areas of cryptography and cryptanalysis
Substitution
replace one element in plaintext with another
Transposition
re-arrange elements
Symmetric
single-key, secret-key, conventional encryption
Asymmetric
two-key, or public-key encryption
Block Cipher
process one block of elements at a time
Stream Cipher
process input elements continuously
Brute-Force Attack
attacker tries every possible key on a piece of ciphertext until an intelligible translation into plaintext is obtained
Unconditionally Secure
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
Computationally Secure
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
Strong Encryption
encryption schemes that make it impractically difficult for unauthorized persons or systems to gain access to plaintext that has been encrypted
Caesar Cipher
involves replacing each letter of the alphabet with the letter standing x places further down the alphabet
Monoalphabetic Cipher
use a single alphabet for both plaintext and ciphertext (a single cipher alphabet is used per message)
Digram
two-letter combination
Trigram
three-letter combination
Playfair Cipher
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)
One-Time Pad
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
