The keys, please ... (RSA)

• Your secret key is a pair of big prime numbers, P and Q
• Your public key is the even bigger composite number N that's the product of these primes
• (The actual encryption/decryption function is a bunch of hocus-pocus derived from Euler's theorem)
• If a bad guy could find the prime factors P & Q of your public key N, he could break the cipher ... but we don't know how to do this efficiently!
  • (The "schoolkid's algorithm" of repeated division is combinatorial/exponential in the size of the composite number N. The current best algorithm, the "number field sieve," is better, but still combinatorial/exponential.)

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