Why it matters

DLP hardness enables crypto. Understanding shapes crypto foundations.

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The architecture

Baby-step giant-step O(sqrt(n)).

Pollard's rho O(sqrt(n)) memory-efficient.

Index calculus for special groups.

DLP algorithmsBSGSO(sqrt(n)) time + memPollard rhoO(sqrt(n)) timeIndex calculusfor suitable groupsOrdinary curves resist index calculus; ECDLP still hard
DLP.
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How it works end to end

Baby-step giant-step precomputes half.

Pollard rho memory-cheaper.

Index calculus breaks weak DH.