RT Formulas - TobTu

chain Length

=

chain Length RCrack

− 1

keyspace

=

max Password Length

∑

i =

min Password Length

character Set Length

i

=

character Set Length

max Password Length

+ 1

−

character Set Length

min Password Length

character Set Length

− 1

table Work Factor

=

chain Length

∙

chain Count

keyspace

total Work Factor

=

number Of Tables

∙

table Work Factor

pre work

=

chain Length

∙ (

chain Length

+ 1)

2

brute Force Point

≲

keyspace

pre work

∙

number Of Tables

expected Unique Chains

= euc(

chain Length

) ≈

chain Count

table Work Factor

2

+ 1

euc(1) =

chain Count

euc(i) =

keyspace

∙

(

1 − e

-euc(

i

− 1)

keyspace

)

table Generation Time

=

keyspace

∙

table Work Factor

step Speedup

=

chain Count

∙

chain Length

step Speedup

perfect Table Success Rate

≈ 1 −

(

1 −

unique Chains

keyspace

)

chain Length

≈ 1 −

(

1 −

expected Unique Chains

keyspace

)

chain Length

imperfect Table Success Rate

≈ 1 −

chain Length

∏

i

= 1

(

1 −

euc(

i

)

keyspace

)

total Success Rate

≈ 1 −

number Of Tables

∏

i

= 1

(

1 −

table Success Rate

i

)

≈ 1 − (1 −

table Success Rate

)

number Of Tables

1

table Work Factor

≈

1

chain Length

∙ (1 − (1 −

perfect Table Success Rate

)

1

∕

chain Length

)

−

1

2

perfect Table Success Rate

≈ 1 −

(

1 −

table Work Factor

chain Length

∙ (1 +

table Work Factor

2

)

)

chain Length

chain Count

≈

expected Unique Chains

1 −

expected Unique Chains

∙

chain Length

2 ∙

keyspace

chain Count

≈

√

8 ∙

keyspace

number Of Tables

∙

brute Force Point

+ 1

− 1

2

table Success Rate

≈ 1 − (1 −

total Success Rate

)

1

∕

number Of Tables

min Tables

= ceiling

(

log(1 −

total Success Rate

)

log(1 −

max Table Success Rate

)

)

max Table Success Rate

> 0.859