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{-# LANGUAGE GeneralizedNewtypeDeriving, MultiParamTypeClasses #-}
module Cost where
import Entropy
import Utility.HumanTime
import Data.Monoid
-- | An estimated cost to perform an operation.
data Cost op
= CPUCost Seconds -- ^ using 1 CPU core
| GPUCost Seconds
| CombinedCost (Cost op) (Cost op)
deriving (Show)
newtype Seconds = Seconds Integer
deriving (Num)
instance Show Seconds where
show (Seconds n) = fromDuration (Duration n)
-- | Cost in seconds, with the type of hardware needed.
totalCost :: Cost op -> (Seconds, [UsingHardware])
totalCost (CPUCost s) = (s, [UsingCPU])
totalCost (GPUCost s) = (s, [UsingGPU])
totalCost (CombinedCost a b) =
let (s1, h1) = totalCost a
(s2, h2) = totalCost b
in (s1+s2, h1++h2)
data UsingHardware = UsingCPU | UsingGPU | UsingASIC
deriving (Show)
raiseCostPower :: Cost c -> Entropy e -> Cost c
raiseCostPower c (Entropy e) = adjustCost c (* 2^e)
adjustCost :: Cost c -> (Seconds -> Seconds) -> Cost c
adjustCost (CPUCost s) f = CPUCost (f s)
adjustCost (GPUCost s) f = GPUCost (f s)
adjustCost (CombinedCost a b) f = CombinedCost (adjustCost a f) (adjustCost b f)
castCost :: Cost a -> Cost b
castCost (CPUCost s) = CPUCost s
castCost (GPUCost s) = GPUCost s
castCost (CombinedCost a b) = CombinedCost (castCost a) (castCost b)
instance Monoid (Cost t) where
mempty = CPUCost (Seconds 0)
CPUCost (Seconds a) `mappend` CPUCost (Seconds b) =
CPUCost (Seconds (a+b))
GPUCost (Seconds a) `mappend` GPUCost (Seconds b) =
GPUCost (Seconds (a+b))
a `mappend` b = CombinedCost a b
-- | Operations whose cost can be measured.
data DecryptionOp
data CreationOp
data BruteForceOp
-- | Calculation of a cost that depends on some amount of entropy.
type CostCalc op t = Entropy t -> Cost op
-- | Number of bits of entropy
newtype Entropy t = Entropy Int
deriving (Num, Show)
-- | Entropy can never go negative when subtracting bits from it.
reduceEntropy :: Entropy t -> Int -> Entropy t
reduceEntropy (Entropy a) b = Entropy (max 0 (a - b))
-- | Things that can have entropy
data UnknownPassword
-- | CostCalc for a brute force linear search through an entropy space
-- in which each step entails paying a cost.
--
-- On average, the solution will be found half way through.
-- This is equivilant to one bit less of entropy.
bruteForceLinearSearch :: Cost step -> CostCalc BruteForceOp t
bruteForceLinearSearch stepcost e =
castCost stepcost `raiseCostPower` reduceEntropy e 1
-- | Things that can be brute-forced track their CostCalc.
class Bruteforceable t a where
getBruteCostCalc :: t -> CostCalc BruteForceOp a
-- | Estimate of cost of a brute force attack.
estimateBruteforceOf :: Bruteforceable t a => t -> Entropy a -> Cost BruteForceOp
estimateBruteforceOf t e = getBruteCostCalc t e
data DataCenterPrice = DataCenterPrice
{ instanceCpuCores :: Integer
, instanceCostPerHour :: Cents
}
-- August 2016 spot pricing: 36 CPU core c4.8xlarge at 33c/hour
spotAWS :: DataCenterPrice
spotAWS = DataCenterPrice
{ instanceCpuCores = 36
, instanceCostPerHour = Cents 33
}
-- | Estimate of cost of brute force attack using a datacenter.
--
-- Note that this assumes that CPU cores and GPU cores are of equal number,
-- which is unlikely to be the case; typically there will be many more
-- cores than GPUs. So, this underestimates the price to brute force
-- operations which run faster on GPUs.
estimateAttack :: DataCenterPrice -> Cost BruteForceOp -> Dollars
estimateAttack dc opcost = centsToDollars $ costcents
where
(Seconds cpuseconds) = fst (totalCost opcost)
cpuyears = cpuseconds `div` (60*60*24*365)
costpercpuyear = Cents $
fromIntegral (instanceCostPerHour dc) * 24 * 365
`div` instanceCpuCores dc
costcents = Cents cpuyears * costpercpuyear
newtype Cents = Cents Integer
deriving (Num, Integral, Enum, Real, Ord, Eq, Show)
newtype Dollars = Dollars Integer
deriving (Num, Integral, Enum, Real, Ord, Eq, Show)
centsToDollars :: Cents -> Dollars
centsToDollars (Cents c) = Dollars (c `div` 100)
|
