Intro + Number Theory

Question 1

What is cryptography?

Answer 1

The study of mathematical techniques related to information security

Question 2

What are the four main goals of cryptography?

Answer 2

Confidentiality
Data integrity
Authentication
Non-repudiation

Question 3

Non-repudiation means?

Answer 3

It ensures that a party cannot deny sending a message or signing a document, typically achieved using digital signatures.

Question 4

Data Integrity means?

Answer 4

Ensures that data is not altered or tampered with during transmission (e.g., using checksums or hash functions).

Question 5

Confirms a user’s or system’s identity (e.g., verifying a password or digital signature) is the definition of

Answer 5

Authentication

Question 6

Ensures that information is only accessible to authorized users, preventing unauthorized access (e.g., encryption) is the definition of

Answer 6

Confidentiality

Question 7

What is symmetric-key encryption?

Answer 7

A type of encryption where the same key is used for both encryption and decryption

Question 8

An encryption method where two different keys (public and private) are used for encryption and decryption is called

Answer 8

Public-key encryption

Question 9

Ensuring that information has not been altered by unauthorized means during transmission is

Answer 9

Data integrity

Question 10

What is a digital signature?

Answer 10

A cryptographic mechanism is used to bind an entity’s identity to a piece of information, ensuring authenticity and integrity.

Question 11

A function that converts an input into a fixed-size string of bytes, typically used to ensure data integrity is called

Answer 11

Hash function

Question 12

It deals with the generation, distribution, storage, and destruction of keys to ensure secure communication is the purpose of

Answer 12

Key management in cryptography

Question 13

What is key escrow?

Answer 13

A system where encryption keys are stored by a third party to allow access under certain conditions, such as in legal cases.

Question 14

It states that for any integer a and positive integer n, there are unique integers q (quotient) and r (remainder) such that:
𝑎=𝑞𝑛+𝑟 where 0≤𝑟<𝑛

Answer 14

The Division Algorithm

Question 15

What is the Euclidean Algorithm used for?

Answer 15

It is used to find the greatest common divisor (GCD) of two integers.

Question 16

What is modular arithmetic?

Answer 16

It’s a system of arithmetic for integers, where numbers “wrap around” upon reaching a certain value, known as the modulus.

Question 17

If p is a prime number and a is an integer not divisible by p, then
a ^(p−1 )≡1 modp.

Answer 17

Fermat’s Little Theorem

Question 18

What is Euler’s Totient Function ϕ(n)?

Answer 18

The count of integers less than n is relatively prime to n. For a prime number p, ϕ(p)=p−1.

Question 19

What does the Chinese Remainder Theorem state?

Answer 19

It provides conditions under which a system of simultaneous congruences has a unique solution modulo the product of the moduli.

Question 20

Tntegers greater than 1 that have no divisors other than 1 and themselves.

Answer 20

Prime numbers

Question 21

The largest integer that divides two numbers without leaving a remainder.

Answer 21

Greatest common divisor(GCD)

Question 22

What are discrete logarithms?

Answer 22

Given a number
b=g ^(x) modn, the discrete logarithm problem involves finding x, given b, g, and n.