Book: Computer Security Art and Science, Matt Bishop, Chapter 4 Section 4.7, 2003

a) Prove Theorem 4–1 of Bishops. Show all elements of your proof.

Theorem 4–1: Let m1 and m2 be secure protection mechanisms for a program p and policy c. Then m1 ∪ m2 is also a security protection mechanism for p and c. Furthermore, m1 ∪ m2 ≈ m1 and m1 ∪ m2 ≈ m2.

b) Expand the proof to show the details of the induction in Theorem 4-2.

Theorem 4–2: For any program p and security policy c, there exists a precise, secure mechanism m∗ such that, for all secure mechanisms m associated with p and c, m∗ ≈ m.