Number Theory and Cryptography

Question 1

What is divisibility in number theory?

Answer 1

Question 2

What are properties of divisibility?

Answer 2

Question 3

What is integer division?

Answer 3

Question 4

What is congruence?

Answer 4

Question 5

What are the properties of congruence?

Answer 5

Question 6

What is modular arithmetic?

Answer 6

Question 7

What are the properties of modular arithmetic?

Answer 7

Question 8

Examples of modular arithmetic

Answer 8

Question 9

What is modular arithmetic and congruence classes?

Answer 9

Question 10

What is the fundamental theorem of arithmetic? (primes)

Answer 10

Question 11

What is the Sieve of Eratosthenes?

Answer 11

Question 12

Example of the Sieve of Eratosthenes

Answer 12

Question 13

What are Mersenne primes?

Answer 13

Question 14

What is the gcd?

Answer 14

Question 15

gcd example

Answer 15

Question 16

What is the Euclidean Algorithm?

Answer 16

Question 17

What is the lcm?

Answer 17

Question 18

What is the Cute theorem?

Answer 18

Question 19

What is Bezout’s Theorem?

Answer 19

Question 20

Example of Bezout’s Theorem

Answer 20

Review slides 37-42

Question 21

What are some collaries of Bezouts Theorem?

Answer 21

Question 22

What are linear congruences?

Answer 22

Question 23

Example of linear congruences

Answer 23

Question 24

What are systems of linear congruences?

Answer 24

Question 25

Example of systems of linear congruences

Answer 25

Question 26

How does the Caesar cipher work?

Answer 26

Question 27

How do Affine ciphers work?

Answer 27

Question 28

What is the difference between a public and private key?

Answer 28

Question 29

What is the RSA cryptosystem

Answer 29