Why Does RSA Work?

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The Algorithm
The algorithm is divided into three stages: precalculation, encryption, and decryption. Precalculation is performed a single time for each person with a public/private key pair, and encryption/decryption is performed for each message.
Precalculation

Pick primes: Find two arbitrarily large prime numbers, p and q.

Determine the modulus: Multiply [...]

Number Theory, Hash Tables, and Geometric Progressions

Or, and Loathing in Los Vegas
What will this article focus on?
This particular article looks at geometric sequences (mod n), and how we can use them instead of linear hashes. A geometric sequence is simply a sequence of powers of some number: 1, , , , … So instead of adding the same number together [...]

Number Theory for Programmers, Part 2

What is Number Theory?
Number theory is the study of numbers, their properties, and what can be inferred from their properties. For programmers, it is most practical to focus on the theory of positive integers.
Who should use this guide?

Those who did not know the answer to the above question
Those who are interested in the math behind [...]