Exploring Cryptography and Number Theory

Explain the concept of primality testing.

• Primality testing is the process of determining if a number is prime.

• Primality testing is used to find the factors of a number.

• Primality testing is a method for generating random numbers.

• Primality testing determines the largest prime number.

What is the purpose of Euler's totient function?

• To determine the number of divisors of n.

• To count the integers up to n that are coprime to n.

• To calculate the prime factors of n.

• To find the largest integer less than n.

State Fermat's Little Theorem.

• If p is a prime and a is an integer not divisible by p, then a^(p-1) ≡ 1 (mod p).

• If p is a prime, then a^(p-1) ≡ a (mod p).

• If p is a prime and a is divisible by p, then a^(p-1) ≡ 0 (mod p).

• If p is a prime, then a^(p+1) ≡ 1 (mod p).

What is the Chinese Remainder Theorem used for?

• To calculate the greatest common divisor.

• To solve systems of simultaneous congruences.

• To find the least common multiple.

• To solve linear equations in one variable.

How does RSA encryption work?

• RSA encryption is based on the properties of small composite numbers.

• RSA encryption uses a pair of keys (public and private) for secure data transmission, relying on the mathematical properties of large prime numbers.

• RSA encryption relies on symmetric key algorithms for security.

• RSA encryption uses a single key for encryption and decryption.

What is HMAC and how is it used in message authentication?

• HMAC is a mechanism for message authentication that uses a cryptographic hash function and a secret key to ensure message integrity and authenticity.

• HMAC is a method for compressing data to reduce file size.

• HMAC is a protocol for establishing secure connections over the internet.

• HMAC is a type of encryption algorithm used for securing data transmission.

Explain the Diffie-Hellman key exchange method.

• The Diffie-Hellman key exchange method enables two parties to securely share a secret key over a public channel.

• It allows two parties to create a public key together.

• It requires both parties to meet in person to exchange keys.

• It is a method for encrypting messages directly.

What are elliptic curves in mathematics?

• Elliptic curves are linear equations of the form y = mx + b.

• Elliptic curves are defined by the equation x^2 + y^2 = r^2.

• Elliptic curves are algebraic curves defined by equations of the form y^2 = x^3 + ax + b.

• Elliptic curves are polynomial functions that only include integer coefficients.

What is the significance of secure hash functions in cryptography?

• Secure hash functions ensure data integrity, enable digital signatures, and protect sensitive information.

• Secure hash functions are used for data compression.

• Secure hash functions are primarily for encrypting passwords.

• Secure hash functions are only relevant for file storage.

What is the role of elliptic curves in cryptography?

• Elliptic curves are used to solve linear equations.

• Elliptic curves are used to create secure digital signatures and encryption methods.

• Elliptic curves are only relevant in number theory.

• Elliptic curves are primarily used for data compression.