Generic group model, discrete log algorithms (brute force and BSGS) and lower bound - #83
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Generic group model, discrete log algorithms (brute force and BSGS) and lower bound#83fharding1 wants to merge 1 commit into
fharding1 wants to merge 1 commit into
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The generic group model is a nice cryptography target for this project because you can prove some interesting lower bounds without computational assumptions. This formalization follows Maurer's. * Models/GenericGroup.lean - generic model * Algorithms/DiscreteLog.lean - brute-force discrete log algorithm is correct and Theta(p) element-producing group operations (add and neg) * Algorithms/BabyStepGiantStep.lean - baby-step giant-step discrete log algorithm is correct and Theta(sqrt(p)) element-producing group ops * LowerBounds/DiscreteLog.lean - any (generic) discrete log algorithm that is correct on all inputs uses Omega(sqrt(p)) element-producing group ops AI disclosure: prepared with significant AI assistance (mainly Opus 5). I scrutinized the model, algorithm descriptions, top-level theorems, and skimmed the proofs to make sure they were what I expected. There are also some tests in AlgoleanTests/GroupExamples.lean which are meant to give some intuition for how the model works, and show off some examples of using the algorithms.
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The generic group model is a nice cryptography target for this project because you can prove some interesting lower bounds without computational assumptions. This formalization follows Maurer's.
Models/GenericGroup.lean- generic model. See some more discussion on the formalization in the doc-string.Algorithms/DiscreteLog.lean- brute-force discrete log algorithm is correct andAlgorithms/BabyStepGiantStep.lean- baby-step giant-step discrete log algorithm is correct andLowerBounds/DiscreteLog.lean- any (generic) discrete log algorithm that is correct on all inputs usesAI disclosure: this PR was prepared with significant AI assistance (mainly Opus 5). I scrutinized the model, algorithm descriptions, top-level theorems, doc-strings, and skimmed the proofs to make sure they were what I expected. There are also some tests in
AlgoleanTests/GroupExamples.leanwhich are meant to give some intuition for how the model works, and show off some examples of using the algorithms.