Lattice Estimator

Documentation

• Introduction
  • Quick Start
  • Status
  • Evolution
  • Bugs
  • Contributions
  • Citing
  • License
  • Third Party Tools Using this Estimator
  • Acknowledgements
• LWE Primal Attacks
• LWE Dual Attacks
• Coded-BKW for LWE
• Arora-GB
• Contributing
  • Design & Tips
  • Tests
  • Documentation

Parameters from the Literature

• NIST PQC Round 3 Finalists
• Homomorphic Encryption Standard

API Reference

• estimator.cost
  • estimator.cost.Cost
    • Cost
      • Cost.__call__()
    • estimator.cost.Cost.__init__
      • Cost.__init__()
    • estimator.cost.Cost.clear
      • Cost.clear()
    • estimator.cost.Cost.combine
      • Cost.combine()
    • estimator.cost.Cost.copy
      • Cost.copy()
    • estimator.cost.Cost.filter
      • Cost.filter()
    • estimator.cost.Cost.fromkeys
      • Cost.fromkeys()
    • estimator.cost.Cost.get
      • Cost.get()
    • estimator.cost.Cost.items
      • Cost.items()
    • estimator.cost.Cost.keys
      • Cost.keys()
    • estimator.cost.Cost.pop
      • Cost.pop()
    • estimator.cost.Cost.popitem
      • Cost.popitem()
    • estimator.cost.Cost.register_impermanent
      • Cost.register_impermanent()
    • estimator.cost.Cost.reorder
      • Cost.reorder()
    • estimator.cost.Cost.repeat
      • Cost.repeat()
    • estimator.cost.Cost.sanity_check
      • Cost.sanity_check()
    • estimator.cost.Cost.setdefault
      • Cost.setdefault()
    • estimator.cost.Cost.str
      • Cost.str()
    • estimator.cost.Cost.update
      • Cost.update()
    • estimator.cost.Cost.values
      • Cost.values()
    • estimator.cost.Cost.impermanents
      • Cost.impermanents
    • estimator.cost.Cost.key_map
      • Cost.key_map
    • estimator.cost.Cost.val_map
      • Cost.val_map
• estimator.errors
• estimator.gb
  • estimator.gb.AroraGB
    • AroraGB
      • AroraGB.__call__()
    • estimator.gb.AroraGB.__init__
      • AroraGB.__init__()
    • estimator.gb.AroraGB.cost_Gaussian_like
      • AroraGB.cost_Gaussian_like()
    • estimator.gb.AroraGB.cost_bounded
      • AroraGB.cost_bounded()
    • estimator.gb.AroraGB.equations_for_secret
      • AroraGB.equations_for_secret()
    • estimator.gb.AroraGB.ps_single
      • AroraGB.ps_single()
  • estimator.gb.gb_cost
    • gb_cost()
• estimator.io
  • estimator.io.Logging
    • Logging
      • Logging.__call__()
    • estimator.io.Logging.__init__
      • Logging.__init__()
    • estimator.io.Logging.log
      • Logging.log()
    • estimator.io.Logging.set_level
      • Logging.set_level()
    • estimator.io.Logging.CRITICAL
      • Logging.CRITICAL
    • estimator.io.Logging.DEBUG
      • Logging.DEBUG
    • estimator.io.Logging.ERROR
      • Logging.ERROR
    • estimator.io.Logging.INFO
      • Logging.INFO
    • estimator.io.Logging.LEVEL0
      • Logging.LEVEL0
    • estimator.io.Logging.LEVEL1
      • Logging.LEVEL1
    • estimator.io.Logging.LEVEL2
      • Logging.LEVEL2
    • estimator.io.Logging.LEVEL3
      • Logging.LEVEL3
    • estimator.io.Logging.LEVEL4
      • Logging.LEVEL4
    • estimator.io.Logging.LEVEL5
      • Logging.LEVEL5
    • estimator.io.Logging.NOTSET
      • Logging.NOTSET
    • estimator.io.Logging.WARNING
      • Logging.WARNING
    • estimator.io.Logging.detail_logger
      • Logging.detail_logger
    • estimator.io.Logging.logger
      • Logging.logger
    • estimator.io.Logging.loggers
      • Logging.loggers
    • estimator.io.Logging.plain_logger
      • Logging.plain_logger
• estimator.lwe
  • estimator.lwe.Estimate
    • Estimate
      • Estimate.__call__()
    • estimator.lwe.Estimate.__init__
      • Estimate.__init__()
    • estimator.lwe.Estimate.rough
      • Estimate.rough()
• estimator.lwe_bkw
  • estimator.lwe_bkw.CodedBKW
    • CodedBKW
      • CodedBKW.__call__()
    • estimator.lwe_bkw.CodedBKW.N
      • CodedBKW.N()
    • estimator.lwe_bkw.CodedBKW.__init__
      • CodedBKW.__init__()
    • estimator.lwe_bkw.CodedBKW.b
      • CodedBKW.b()
    • estimator.lwe_bkw.CodedBKW.cost
      • CodedBKW.cost()
    • estimator.lwe_bkw.CodedBKW.t1
      • CodedBKW.t1()
    • estimator.lwe_bkw.CodedBKW.ntest
      • CodedBKW.ntest
• estimator.lwe_dual
  • estimator.lwe_dual.DualHybrid
    • DualHybrid
      • DualHybrid.__call__()
    • estimator.lwe_dual.DualHybrid.__init__
      • DualHybrid.__init__()
    • estimator.lwe_dual.DualHybrid.fft_solver
      • DualHybrid.fft_solver()
    • estimator.lwe_dual.DualHybrid.optimize_blocksize
      • DualHybrid.optimize_blocksize()
    • estimator.lwe_dual.DualHybrid.cost
      • DualHybrid.cost
    • estimator.lwe_dual.DualHybrid.dual_reduce
      • DualHybrid.dual_reduce
  • estimator.lwe_dual.dual
    • dual()
  • estimator.lwe_dual.dual_hybrid
    • dual_hybrid()
• estimator.lwe_guess
  • estimator.lwe_guess.Distinguisher
    • Distinguisher
      • Distinguisher.__call__()
    • estimator.lwe_guess.Distinguisher.__init__
      • Distinguisher.__init__()
  • estimator.lwe_guess.ExhaustiveSearch
    • ExhaustiveSearch
      • ExhaustiveSearch.__call__()
    • estimator.lwe_guess.ExhaustiveSearch.__init__
      • ExhaustiveSearch.__init__()
  • estimator.lwe_guess.MITM
    • MITM
      • MITM.__call__()
    • estimator.lwe_guess.MITM.X_range
      • MITM.X_range()
    • estimator.lwe_guess.MITM.__init__
      • MITM.__init__()
    • estimator.lwe_guess.MITM.cost
      • MITM.cost()
    • estimator.lwe_guess.MITM.local_range
      • MITM.local_range()
    • estimator.lwe_guess.MITM.mitm_analytical
      • MITM.mitm_analytical()
    • estimator.lwe_guess.MITM.locality
      • MITM.locality
  • estimator.lwe_guess.guess_composition
    • guess_composition
      • guess_composition.__call__()
    • estimator.lwe_guess.guess_composition.__init__
      • guess_composition.__init__()
    • estimator.lwe_guess.guess_composition.dense_solve
      • guess_composition.dense_solve()
    • estimator.lwe_guess.guess_composition.gammaf
      • guess_composition.gammaf()
    • estimator.lwe_guess.guess_composition.sparse_solve
      • guess_composition.sparse_solve()
• estimator.lwe_parameters
  • estimator.lwe_parameters.LWEParameters
    • LWEParameters
      • LWEParameters.__call__()
    • estimator.lwe_parameters.LWEParameters.__init__
      • LWEParameters.__init__()
    • estimator.lwe_parameters.LWEParameters.amplify_m
      • LWEParameters.amplify_m()
    • estimator.lwe_parameters.LWEParameters.normalize
      • LWEParameters.normalize()
    • estimator.lwe_parameters.LWEParameters.switch_modulus
      • LWEParameters.switch_modulus()
    • estimator.lwe_parameters.LWEParameters.updated
      • LWEParameters.updated()
    • estimator.lwe_parameters.LWEParameters.m
      • LWEParameters.m
    • estimator.lwe_parameters.LWEParameters.tag
      • LWEParameters.tag
    • estimator.lwe_parameters.LWEParameters.n
      • LWEParameters.n
    • estimator.lwe_parameters.LWEParameters.q
      • LWEParameters.q
    • estimator.lwe_parameters.LWEParameters.Xs
      • LWEParameters.Xs
    • estimator.lwe_parameters.LWEParameters.Xe
      • LWEParameters.Xe
• estimator.lwe_primal
  • estimator.lwe_primal.PrimalHybrid
    • PrimalHybrid
      • PrimalHybrid.__call__()
    • estimator.lwe_primal.PrimalHybrid.__init__
      • PrimalHybrid.__init__()
    • estimator.lwe_primal.PrimalHybrid.babai_cost
      • PrimalHybrid.babai_cost()
    • estimator.lwe_primal.PrimalHybrid.cost_zeta
      • PrimalHybrid.cost_zeta()
    • estimator.lwe_primal.PrimalHybrid.svp_dimension
      • PrimalHybrid.svp_dimension()
    • estimator.lwe_primal.PrimalHybrid.cost
      • PrimalHybrid.cost
  • estimator.lwe_primal.PrimalUSVP
    • PrimalUSVP
      • PrimalUSVP.__call__()
    • estimator.lwe_primal.PrimalUSVP.__init__
      • PrimalUSVP.__init__()
    • estimator.lwe_primal.PrimalUSVP.cost_gsa
      • PrimalUSVP.cost_gsa
    • estimator.lwe_primal.PrimalUSVP.cost_simulator
      • PrimalUSVP.cost_simulator
  • estimator.lwe_primal.primal_bdd
    • primal_bdd()
• estimator.nd
  • estimator.nd.NoiseDistribution
    • NoiseDistribution
      • NoiseDistribution.__call__()
    • estimator.nd.NoiseDistribution.CenteredBinomial
      • NoiseDistribution.CenteredBinomial()
    • estimator.nd.NoiseDistribution.DiscreteGaussian
      • NoiseDistribution.DiscreteGaussian()
    • estimator.nd.NoiseDistribution.DiscreteGaussianAlpha
      • NoiseDistribution.DiscreteGaussianAlpha()
    • estimator.nd.NoiseDistribution.SparseTernary
      • NoiseDistribution.SparseTernary()
    • estimator.nd.NoiseDistribution.Uniform
      • NoiseDistribution.Uniform()
    • estimator.nd.NoiseDistribution.UniformMod
      • NoiseDistribution.UniformMod()
    • estimator.nd.NoiseDistribution.__init__
      • NoiseDistribution.__init__()
    • estimator.nd.NoiseDistribution.get_hamming_weight
      • NoiseDistribution.get_hamming_weight()
    • estimator.nd.NoiseDistribution.support_size
      • NoiseDistribution.support_size()
    • estimator.nd.NoiseDistribution.bounds
      • NoiseDistribution.bounds
    • estimator.nd.NoiseDistribution.density
      • NoiseDistribution.density
    • estimator.nd.NoiseDistribution.gaussian_tail_bound
      • NoiseDistribution.gaussian_tail_bound
    • estimator.nd.NoiseDistribution.gaussian_tail_prob
      • NoiseDistribution.gaussian_tail_prob
    • estimator.nd.NoiseDistribution.is_Gaussian_like
      • NoiseDistribution.is_Gaussian_like
    • estimator.nd.NoiseDistribution.is_bounded
      • NoiseDistribution.is_bounded
    • estimator.nd.NoiseDistribution.is_sparse
      • NoiseDistribution.is_sparse
    • estimator.nd.NoiseDistribution.mean
      • NoiseDistribution.mean
    • estimator.nd.NoiseDistribution.n
      • NoiseDistribution.n
    • estimator.nd.NoiseDistribution.tag
      • NoiseDistribution.tag
    • estimator.nd.NoiseDistribution.stddev
      • NoiseDistribution.stddev
  • estimator.nd.sigmaf
    • sigmaf()
  • estimator.nd.stddevf
    • stddevf()
• estimator.prob
  • estimator.prob.amplify
    • amplify()
  • estimator.prob.amplify_sigma
    • amplify_sigma()
  • estimator.prob.babai
    • babai()
  • estimator.prob.drop
    • drop()
  • estimator.prob.mitm_babai_probability
    • mitm_babai_probability()
• estimator.reduction
  • estimator.reduction.ABFKSW20
    • ABFKSW20
      • ABFKSW20.__call__()
    • estimator.reduction.ABFKSW20.LLL
      • ABFKSW20.LLL()
    • estimator.reduction.ABFKSW20.__init__
      • ABFKSW20.__init__()
    • estimator.reduction.ABFKSW20.beta
      • ABFKSW20.beta()
    • estimator.reduction.ABFKSW20.delta
      • ABFKSW20.delta()
    • estimator.reduction.ABFKSW20.short_vectors
      • ABFKSW20.short_vectors()
    • estimator.reduction.ABFKSW20.short_vectors_simple
      • ABFKSW20.short_vectors_simple()
    • estimator.reduction.ABFKSW20.svp_repeat
      • ABFKSW20.svp_repeat()
  • estimator.reduction.ABLR21
    • ABLR21
      • ABLR21.__call__()
    • estimator.reduction.ABLR21.LLL
      • ABLR21.LLL()
    • estimator.reduction.ABLR21.__init__
      • ABLR21.__init__()
    • estimator.reduction.ABLR21.beta
      • ABLR21.beta()
    • estimator.reduction.ABLR21.delta
      • ABLR21.delta()
    • estimator.reduction.ABLR21.short_vectors
      • ABLR21.short_vectors()
    • estimator.reduction.ABLR21.short_vectors_simple
      • ABLR21.short_vectors_simple()
    • estimator.reduction.ABLR21.svp_repeat
      • ABLR21.svp_repeat()
  • estimator.reduction.ADPS16
    • ADPS16
      • ADPS16.__call__()
    • estimator.reduction.ADPS16.LLL
      • ADPS16.LLL()
    • estimator.reduction.ADPS16.__init__
      • ADPS16.__init__()
    • estimator.reduction.ADPS16.beta
      • ADPS16.beta()
    • estimator.reduction.ADPS16.delta
      • ADPS16.delta()
    • estimator.reduction.ADPS16.short_vectors
      • ADPS16.short_vectors()
    • estimator.reduction.ADPS16.short_vectors_simple
      • ADPS16.short_vectors_simple()
    • estimator.reduction.ADPS16.svp_repeat
      • ADPS16.svp_repeat()
  • estimator.reduction.BDGL16
    • BDGL16
      • BDGL16.__call__()
    • estimator.reduction.BDGL16.LLL
      • BDGL16.LLL()
    • estimator.reduction.BDGL16.__init__
      • BDGL16.__init__()
    • estimator.reduction.BDGL16.beta
      • BDGL16.beta()
    • estimator.reduction.BDGL16.delta
      • BDGL16.delta()
    • estimator.reduction.BDGL16.short_vectors
      • BDGL16.short_vectors()
    • estimator.reduction.BDGL16.short_vectors_simple
      • BDGL16.short_vectors_simple()
    • estimator.reduction.BDGL16.svp_repeat
      • BDGL16.svp_repeat()
  • estimator.reduction.CheNgu12
    • CheNgu12
      • CheNgu12.__call__()
    • estimator.reduction.CheNgu12.LLL
      • CheNgu12.LLL()
    • estimator.reduction.CheNgu12.__init__
      • CheNgu12.__init__()
    • estimator.reduction.CheNgu12.beta
      • CheNgu12.beta()
    • estimator.reduction.CheNgu12.delta
      • CheNgu12.delta()
    • estimator.reduction.CheNgu12.short_vectors
      • CheNgu12.short_vectors()
    • estimator.reduction.CheNgu12.short_vectors_simple
      • CheNgu12.short_vectors_simple()
    • estimator.reduction.CheNgu12.svp_repeat
      • CheNgu12.svp_repeat()
  • estimator.reduction.GJ21
    • GJ21
      • GJ21.__call__()
    • estimator.reduction.GJ21.LLL
      • GJ21.LLL()
    • estimator.reduction.GJ21.__init__
      • GJ21.__init__()
    • estimator.reduction.GJ21.beta
      • GJ21.beta()
    • estimator.reduction.GJ21.d4f
      • GJ21.d4f()
    • estimator.reduction.GJ21.delta
      • GJ21.delta()
    • estimator.reduction.GJ21.short_vectors
      • GJ21.short_vectors()
    • estimator.reduction.GJ21.short_vectors_simple
      • GJ21.short_vectors_simple()
    • estimator.reduction.GJ21.svp_repeat
      • GJ21.svp_repeat()
    • estimator.reduction.GJ21.NN_AGPS
      • GJ21.NN_AGPS
  • estimator.reduction.Kyber
    • Kyber
      • Kyber.__call__()
    • estimator.reduction.Kyber.LLL
      • Kyber.LLL()
    • estimator.reduction.Kyber.__init__
      • Kyber.__init__()
    • estimator.reduction.Kyber.beta
      • Kyber.beta()
    • estimator.reduction.Kyber.d4f
      • Kyber.d4f()
    • estimator.reduction.Kyber.delta
      • Kyber.delta()
    • estimator.reduction.Kyber.short_vectors
      • Kyber.short_vectors()
    • estimator.reduction.Kyber.short_vectors_simple
      • Kyber.short_vectors_simple()
    • estimator.reduction.Kyber.svp_repeat
      • Kyber.svp_repeat()
    • estimator.reduction.Kyber.NN_AGPS
      • Kyber.NN_AGPS
  • estimator.reduction.LaaMosPol14
    • LaaMosPol14
      • LaaMosPol14.__call__()
    • estimator.reduction.LaaMosPol14.LLL
      • LaaMosPol14.LLL()
    • estimator.reduction.LaaMosPol14.__init__
      • LaaMosPol14.__init__()
    • estimator.reduction.LaaMosPol14.beta
      • LaaMosPol14.beta()
    • estimator.reduction.LaaMosPol14.delta
      • LaaMosPol14.delta()
    • estimator.reduction.LaaMosPol14.short_vectors
      • LaaMosPol14.short_vectors()
    • estimator.reduction.LaaMosPol14.short_vectors_simple
      • LaaMosPol14.short_vectors_simple()
    • estimator.reduction.LaaMosPol14.svp_repeat
      • LaaMosPol14.svp_repeat()
  • estimator.reduction.MATZOV
    • MATZOV
      • MATZOV.__call__()
    • estimator.reduction.MATZOV.LLL
      • MATZOV.LLL()
    • estimator.reduction.MATZOV.__init__
      • MATZOV.__init__()
    • estimator.reduction.MATZOV.beta
      • MATZOV.beta()
    • estimator.reduction.MATZOV.d4f
      • MATZOV.d4f()
    • estimator.reduction.MATZOV.delta
      • MATZOV.delta()
    • estimator.reduction.MATZOV.short_vectors
      • MATZOV.short_vectors()
    • estimator.reduction.MATZOV.short_vectors_simple
      • MATZOV.short_vectors_simple()
    • estimator.reduction.MATZOV.svp_repeat
      • MATZOV.svp_repeat()
    • estimator.reduction.MATZOV.NN_AGPS
      • MATZOV.NN_AGPS
  • estimator.reduction.RC
    • RC
      • RC.__call__()
    • estimator.reduction.RC.LLL
      • RC.LLL()
    • estimator.reduction.RC.__init__
      • RC.__init__()
    • estimator.reduction.RC.beta
      • RC.beta()
    • estimator.reduction.RC.delta
      • RC.delta()
    • estimator.reduction.RC.ABFKSW20
      • RC.ABFKSW20
    • estimator.reduction.RC.ABLR21
      • RC.ABLR21
    • estimator.reduction.RC.ADPS16
      • RC.ADPS16
    • estimator.reduction.RC.BDGL16
      • RC.BDGL16
    • estimator.reduction.RC.CheNgu12
      • RC.CheNgu12
    • estimator.reduction.RC.GJ21
      • RC.GJ21
    • estimator.reduction.RC.Kyber
      • RC.Kyber
    • estimator.reduction.RC.LaaMosPol14
      • RC.LaaMosPol14
    • estimator.reduction.RC.MATZOV
      • RC.MATZOV
  • estimator.reduction.ReductionCost
    • ReductionCost
      • ReductionCost.__call__()
    • estimator.reduction.ReductionCost.LLL
      • ReductionCost.LLL()
    • estimator.reduction.ReductionCost.__init__
      • ReductionCost.__init__()
    • estimator.reduction.ReductionCost.beta
      • ReductionCost.beta()
    • estimator.reduction.ReductionCost.delta
      • ReductionCost.delta()
    • estimator.reduction.ReductionCost.short_vectors
      • ReductionCost.short_vectors()
    • estimator.reduction.ReductionCost.short_vectors_simple
      • ReductionCost.short_vectors_simple()
    • estimator.reduction.ReductionCost.svp_repeat
      • ReductionCost.svp_repeat()
  • estimator.reduction.beta
    • beta()
  • estimator.reduction.cost
    • cost()
  • estimator.reduction.delta
    • delta()
• estimator.simulator
  • estimator.simulator.CN11
    • CN11()
  • estimator.simulator.GSA
    • GSA()
  • estimator.simulator.normalize
    • normalize()
  • estimator.simulator.plot_gso
    • plot_gso()
  • estimator.simulator.qary_simulator
    • qary_simulator()
• estimator.util
  • estimator.util.Bounds
    • Bounds
      • Bounds.__call__()
    • estimator.util.Bounds.__init__
      • Bounds.__init__()
    • estimator.util.Bounds.count
      • Bounds.count()
    • estimator.util.Bounds.index
      • Bounds.index()
    • estimator.util.Bounds.high
      • Bounds.high
    • estimator.util.Bounds.low
      • Bounds.low
  • estimator.util.Task
    • Task
      • Task.__call__()
    • estimator.util.Task.__init__
      • Task.__init__()
    • estimator.util.Task.count
      • Task.count()
    • estimator.util.Task.index
      • Task.index()
    • estimator.util.Task.catch_exceptions
      • Task.catch_exceptions
    • estimator.util.Task.f
      • Task.f
    • estimator.util.Task.f_name
      • Task.f_name
    • estimator.util.Task.log_level
      • Task.log_level
    • estimator.util.Task.x
      • Task.x
  • estimator.util.TaskResults
    • TaskResults
      • TaskResults.__call__()
    • estimator.util.TaskResults.__init__
      • TaskResults.__init__()
  • estimator.util.early_abort_range
    • early_abort_range
      • early_abort_range.__call__()
    • estimator.util.early_abort_range.__init__
      • early_abort_range.__init__()
    • estimator.util.early_abort_range.update
      • early_abort_range.update()
    • estimator.util.early_abort_range.x
      • early_abort_range.x
    • estimator.util.early_abort_range.y
      • early_abort_range.y
  • estimator.util.local_minimum
    • local_minimum
      • local_minimum.__call__()
    • estimator.util.local_minimum.__init__
      • local_minimum.__init__()
    • estimator.util.local_minimum.update
      • local_minimum.update()
    • estimator.util.local_minimum.neighborhood
      • local_minimum.neighborhood
    • estimator.util.local_minimum.x
      • local_minimum.x
    • estimator.util.local_minimum.y
      • local_minimum.y
  • estimator.util.local_minimum_base
    • local_minimum_base
      • local_minimum_base.__call__()
    • estimator.util.local_minimum_base.__init__
      • local_minimum_base.__init__()
    • estimator.util.local_minimum_base.update
      • local_minimum_base.update()
    • estimator.util.local_minimum_base.x
      • local_minimum_base.x
    • estimator.util.local_minimum_base.y
      • local_minimum_base.y
  • estimator.util.batch_estimate
    • batch_estimate()
  • estimator.util.binary_search
    • binary_search()
  • estimator.util.f_name
    • f_name()
  • estimator.util.log2
    • log2()

Appendix

• Index
• References