Homework #5

Due: March 15, 2024
Points: 100

Questions

1. (30 points) Let L = (S_L, ≤_L) be a lattice. Define:
   1. S_IL = { [a, b] | a, b ∈ S_L ⋀ a ≤_L b }
   2. ≤_IL = { ([a₁, b₁], [a₂, b₂]) | a₁≤_L a₂ ⋀ b₁ ≤_L b₂ }
   3. lub_IL([a₁, b₁], [a₂, b₂]) = (lub_L(a₁, a₂), lub_L(b₁, b₂))
   4. glb_IL([a₁, b₁], [a₂, b₂]) = (glb_L(a₁, a₂), glb_L(b₁, b₂))
   Prove that the structure IL = (S_IL, ≤_IL) is a lattice.

2. (30 points) The following system call adds read permission for a process (for_pid) if the caller (call_pid) owns the file, and does nothing otherwise. (The operating system supplies call_ pid; the caller supplies the two latter parameters.)

   
   function addread(call_pid, for_pid: process_id; fid: file_id): integer;
   begin
   	if (call_pid = filelist[fid].owner) then
   		addright(filelist[fid].access_control_list, for_pid, "r");
   	result := (call_pid - filelist[fid].owner);
   	return result
   end.
   

   1. Is the variable result directly or indirectly visible, or not visible?
   2. Is the variable filelist[fid].owner directly or indirectly visible, or not visible?
   3. Is the variable filelist[fid].access_control directly or indirectly visible, or not visible?

3. (40 points) Section 18.3.2.3 derives a formula for I(A; X). Prove that this formula is a maximum with respect to p when p = M^1/m/(1+mM^1/m}, with M and m as defined in that section. (The value of p in the book is incorrect.)

Matt Bishop Office: 2209 Watershed Sciences Phone: +1 (530) 752-8060 Email: mabishop@ucdavis.edu

ECS 235B, Foundations of Computer and Information Security Version of March 8, 2024 at 11:36AM

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