Why it matters

Cryptography rests on number theory. Understanding shapes crypto intuition.

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The architecture

Miller-Rabin: probabilistic primality via modular exponentiation.

Pollard rho: birthday paradox for factorization.

Advanced number theoryMiller-Rabinprimality testPollard rhofactorizationDiscrete logBSGS or Pohlig-HellmanMiller-Rabin deterministic under GRH; probabilistic with specific witnesses in practice
Advanced techniques.
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How it works end to end

Miller-Rabin: choose witnesses (first few primes); test each.

Pollard rho: O(n^0.25) expected. Uses cycle detection.

Baby-step giant-step: O(√n) discrete log.

RSA + Diffie-Hellman rely on hard factorization + discrete log.