Description

Chosen Password: wD05@Ag9$J
possibilities
1. Lower case letter (a-z) 26 2. Upper case letter (A-Z) 26
3. Digit (0-9) 10
4. Digit (0-9) 10
5. @ 1
6. Upper/Lower case letter (a-z, A-Z) 52
7. Upper/Lower case letter (a-z, A-Z) 52
8. Symbol {$,9,5,v,w,J} 6 9. Symbol {$,9,5,v,w,J} 6
10. Symbol {$,9,5,v,w,J} 6

Entropy = L log2N
N = 26 x 26 x 10 x 10 x 1 x 52 x 52 x 6 x 6 x 6
= 39,482,726,400 or 3.95 x 1010
Entropy = 1 log2 (39,482,726,400)
≈ 35.20 bits
Entropy of Tiger Hash = 10 log2Tiger 3.95 x 1010
Tiger(wD05@Ag9$J) = 357c723ff871393085c9e40f401679187fad4f78f3959d52
Q2

O1 O2 O3 O4 O5 O6
S1 R R R R R RW
S2 R W W W
S3 R RW RW W W
S4 R R W
S5 R
S6 R R R R

Subjects from every level can read object O1 and is dominated by all subject, hence it is at the lowest level

O1 O2 O3 O4 O5 O6
S1 R R R R R RW
S2 R W W W
S3 R RW RW W W
S4 R R W
S5 R
S6 R R R R

Subject S3 can read and write objects O2 and O3, hence S3, O2, O3 must be at the same level.

O1 O2 O3 O4 O5 O6
S1 R R R R R RW
S2 R W W W
S3 R RW RW W W
S4 R R W
S5 R
S6 R R R R

Subject S5 can only read object O1, hence subject S5 can only dominate object O1.

O1 O2 O3 O4 O5 O6
S1 R R R R R RW
S2 R W W W
S3 R RW RW W W
S4 R R W
S5 R
S6 R R R R
O1 O2 O3 O4 O5 O6
S1 R R R R R RW
S2 R W W W
S3 R RW RW W W
S4 R R W
S5 R
S6 R R R R
Subjects S1 and S6 must dominate Object O2 and O3 to allow reading

Subject S1 and S4 must dominate object O4 to allow reading.

O1 O2 O3 O4 O5 O6
S1 R R R R R RW
S2 R W W W
S3 R RW RW W W
S4 R R W
S5 R
S6 R R R R
Subject S1 must dominate object O5 to allow reading.
O5 must dominate Subject S2 and S3 to allow writing.

O1 O2 O3 O4 O5 O6
S1 R R R R R RW
S2 R W W W
S3 R RW RW W W
S4 R R W
S5 R
S6 R R R R
O6 must dominate S4 to allow writing.
Top level introduced to complete the lattice.

Q3
Statement Subject Objects Actions
Alice can climb trees and eat apples Alice Trees and Apples Climb, Eat
Bob can climb fences, eat apples, and wave flags Bob Fences, Apples, Flags Climb, Eat, Wave
Trees can hurt apples. Trees Apples Hurt
Carol can jump waves and wave flags Carol Waves, Flags Jump, Wave

Legends: Climb = C , Eat = E, Wave = W, Hurt = H, Jump = J
Subject/Objects Apples Fences Flags Trees Waves
Alice E C
Bob E C W
Trees H
Carol W J