RT Formulas - TobTu

chainLen = chainLenRCrack − 1

keySpace =

maxPwLen

∑

i = minPwLen

charSetLen

i

=

charSetLen

maxPwLen + 1

− charSetLen

minPwLen

charSetLen − 1

tableWorkFactor =

chainLen ∙ chainCount

keySpace

totalWorkFactor = numTables ∙ tableWorkFactor

preWork =

chainLen ∙ (chainLen + 1)

2

bruteForcePoint ≲

keySpace

preWork ∙ numTables

expectedUniqueChains = euc(chainLen) ≈

chainCount

tableWorkFactor

2

+ 1

euc(1) = chainCount

euc(i) = keySpace ∙

(

1 − e

-euc(i − 1)

keySpace

)

tableGenerationTime =

keySpace ∙ tableWorkFactor

stepSpeed

=

chainCount ∙ chainLen

stepSpeed

perfectTableSuccessRate ≈ 1 −

(

1 −

uniqueChains

keySpace

)

chainLen

≈ 1 −

(

1 −

expectedUniqueChains

keySpace

)

chainLen

imperfectTableSuccessRate ≈ 1 −

chainLen

∏

i = 1

(

1 −

euc(i)

keySpace

)

totalSuccessRate ≈ 1 −

numTables

∏

i = 1

(

1 − tableSuccessRate

i

)

≈ 1 − (1 − tableSuccessRate)

numTables

1

tableWorkFactor

≈

1

chainLen ∙ (1 − (1 − perfectTableSuccessRate)

1

∕

chainLen

)

−

1

2

perfectTableSuccessRate ≈ 1 −

(

1 −

tableWorkFactor

chainLen ∙ (1 +

tableWorkFactor

2

)

)

chainLen

chainCount ≈

expectedUniqueChains

1 −

expectedUniqueChains ∙ chainLen

2 ∙ keySpace

chainCount ≈

√

8 ∙ keySpace

numTables ∙ bruteForcePoint

+ 1

− 1

2

tableSuccessRate ≈ 1 − (1 − totalSuccessRate)

1

∕

numTables

minTables = ceiling

(

log(1 − totalSuccessRate)

log(1 − maxTableSuccessRate)

)

maxTableSuccessRate > 0.859