shw2 - IS2150/TEL2810 Introduction to Security - Fall 2011...

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IS2150/TEL2810 Introduction to Security - Fall 2011 Homework 2: Sample Solution Question 1
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Question 2-a Step 1: Step 2: Step 3: V 1 V 3 V 2 V 4 V 5 V 6 {g} {a 3 ,a 6 ,a 10 ,g} {a 8 ,g} {a 2 ,a 4 ,a 5 ,a 7 ,g} {a 1 ,a 9 ,g} V 1 V 3 V 2 V 4 V 5 V 6 {g} {a 3 } {a 8 ,g} {a 2 ,a 4 ,a 5 ,a 7 ,g} {a 1 ,a 9 ,g} {a 8 } {a 10 } {a 6 } {a 9 } {a 5 } {a 7 } V 1 V 3 V 2 V 4 V 5 V 6 {a 3 } {a 2 } {a 1 } {a 8 } {a 10 } {a 6 } {a 9 } {a 5 } {a 7 }
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Question 2-b Access sets: A(x)={x,a1,a2,a3} A(a1)={a1,a2,a3} A(a2)={a2,a3} A(a3)={a3} A(b)={a3,b,c} A(c)={c,d} A(d)={d} A(e)={d,e} Deletion sets: δ(x,a1)={a1} δ(x,a2)={a2} δ(x,a3)={a3} δ(a1,a2)={a2} δ(a1,a3)={a3} δ(a2,a3)={a3} δ(a3,b)={a3} δ(b,c)={c} δ(c,d)={d} δ(c,e)={d} δ(d,e)={d} Conspiracy graph: Theft of r by x: Conspirators set: {x,a3,b,c,e} Witness: 1. e grants (r to z) to d 2. c takes (r to z) from d 3. b gets (r to z) from c (Lemma 3-2) a. b creates (tg to new vertex) t1 b. b grants (g to t1) to c c. c grants (r to z) to t1 d. b takes (r to z) from t1 4. b grants (r to z) to a3 5. x takes (t to a2) from a1 6. x takes (g to a3) from a2 7. x gets (r to z) from a3 (Lemma 3-2) a. x creates (tg to new vertex) t2 b. x grants (g to t2) to a3 c. a3 grants (r to z) to t2 h(x) h(a1) h(a2) h(a3) h(b) h(c) h(d) h(e)
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d. x takes (r to z) from t2
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shw2 - IS2150/TEL2810 Introduction to Security - Fall 2011...

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