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 [...]

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