Number theory and cryptography are fascinating fields of study that intertwine in many ways. Number theory deals with the properties of integers, while cryptography uses these properties to create secure communication systems. Here are some key concepts in both areas:

Key Concepts

  • Prime Numbers: These are numbers greater than 1 that have no positive divisors other than 1 and themselves.
  • Fermat's Little Theorem: A theorem stating that if ( p ) is a prime number and ( a ) is an integer not divisible by ( p ), then ( a^{p-1} \equiv 1 \mod p ).
  • Public Key Cryptography: A method where the public key is used to encrypt messages and the private key is used to decrypt them.
  • Hash Functions: Algorithms that map data of any size to a fixed-size hash value.

Learning Resources

For further learning on these topics, you can explore the following resources:

Prime Numbers

Practice Problems

To deepen your understanding, try solving some practice problems:

  • Find all prime numbers between 1 and 100.
  • Prove Fermat's Little Theorem for a given prime number ( p ).
  • Understand the concept of public key cryptography and how it works in practice.

Public Key Cryptography