Intro + Number Theory Flashcards
Chapter 1-2
What is cryptography?
The study of mathematical techniques related to information security
What are the four main goals of cryptography?
Confidentiality
Data integrity
Authentication
Non-repudiation
Non-repudiation means?
It ensures that a party cannot deny sending a message or signing a document, typically achieved using digital signatures.
Data Integrity means?
Ensures that data is not altered or tampered with during transmission (e.g., using checksums or hash functions).
Confirms a user’s or system’s identity (e.g., verifying a password or digital signature) is the definition of
Authentication
Ensures that information is only accessible to authorized users, preventing unauthorized access (e.g., encryption) is the definition of
Confidentiality
What is symmetric-key encryption?
A type of encryption where the same key is used for both encryption and decryption
An encryption method where two different keys (public and private) are used for encryption and decryption is called
Public-key encryption
Ensuring that information has not been altered by unauthorized means during transmission is
Data integrity
What is a digital signature?
A cryptographic mechanism is used to bind an entity’s identity to a piece of information, ensuring authenticity and integrity.
A function that converts an input into a fixed-size string of bytes, typically used to ensure data integrity is called
Hash function
It deals with the generation, distribution, storage, and destruction of keys to ensure secure communication is the purpose of
Key management in cryptography
What is key escrow?
A system where encryption keys are stored by a third party to allow access under certain conditions, such as in legal cases.
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
The Division Algorithm
What is the Euclidean Algorithm used for?
It is used to find the greatest common divisor (GCD) of two integers.
What is modular arithmetic?
It’s a system of arithmetic for integers, where numbers “wrap around” upon reaching a certain value, known as the modulus.
If p is a prime number and a is an integer not divisible by p, then
a ^(p−1 )≡1 modp.
Fermat’s Little Theorem
What is Euler’s Totient Function ϕ(n)?
The count of integers less than n is relatively prime to n. For a prime number p, ϕ(p)=p−1.
What does the Chinese Remainder Theorem state?
It provides conditions under which a system of simultaneous congruences has a unique solution modulo the product of the moduli.
Tntegers greater than 1 that have no divisors other than 1 and themselves.
Prime numbers
The largest integer that divides two numbers without leaving a remainder.
Greatest common divisor(GCD)
What are discrete logarithms?
Given a number
b=g ^(x) modn, the discrete logarithm problem involves finding x, given b, g, and n.
