Computational Number Theory
Computational number theory, also known as algorithmic number theory, is a branch of mathematics and computer science that focuses on the use of computational methods to investigate and solve problems in number theory. This includes algorithms for primality testing, integer factorization, finding solutions to Diophantine equations, and explicit methods in arithmetic geometry.
Areas of application
- Cryptography
- Code-breaking
- Cryptocurrencies
- Computational algebra
- Number theory
- Arithmetic geometry
- Primality testing
- Integer factorization
Example
One example of an application of computational number theory is the development of fast and efficient algorithms for factoring large numbers, which has numerous applications in cryptography and code-breaking. Another example is the use of computational methods to study the properties of prime numbers and their distribution, which has implications for cryptography and other areas of mathematics.