Prime Numbers in Cryptography: How Large Primes Protect RSA and Online Banking
Explore how the fundamental building blocks of arithmetic secure global financial transactions, HTTPS TLS connections, and military cryptosystems.
The Fundamental Building Blocks of Mathematics
Prime numbers are integers greater than 1 that have no positive divisors other than 1 and themselves (2, 3, 5, 7, 11, 13...). Under the Fundamental Theorem of Arithmetic, every positive integer can be uniquely represented as a product of prime factors.
The Trapdoor Function: Asymmetric RSA Cryptography
In 1977, Ron Rivest, Adi Shamir, and Leonard Adleman created RSA public-key cryptography, which protects modern internet traffic (HTTPS, SSH, banking portals).
RSA is built on an asymmetric trapdoor function:
- Computing $N = p \times q$ (multiplying two 300-digit prime numbers) is trivial.
- Factoring $N$ back into $p$ and $q$ without the private key is practically impossible with classical computers.
Test any number's primality and view canonical prime factor trees on our **Prime Number Checker**.
Frequently Asked Questions
Published by AnantAstra's engineering and research desk. All calculations, privacy guarantees, and algorithms referenced in this article are open-source and run client-side in the browser.
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