Why it matters

Miller-Rabin is standard primality. Understanding shapes crypto.

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The architecture

Write n - 1 = 2^s * d.

Test witness a: a^d mod n or a^(2^r * d) mod n = n-1.

Repeat k witnesses.

Miller-RabinWrite n-1as 2^s * dTest witness aFermat-likek roundserr <= (1/4)^kk = 20-40 gives negligible error; deterministic for n < 3.3e14 with fixed witnesses
Miller-Rabin.
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How it works end to end

Error prob <= (1/4)^k per composite.

Deterministic for small n with specific witnesses.

Uses modexp.