Chapter 2 — Discrete mathematics

Lesson map

Lesson 02 published. Map, example, EX004.

flowchart TD
  N0["Learning outcomes"]
  N1["2.1 Policies as logic"]
  N2["2.2 Sets of access"]
  N3["2.3 Counting combinations"]
  N4["Synthesis"]
  N0 --> N1 --> N2 --> N3 --> N4
  N4 --> EX["Worked example"]
  EX --> Q["Exercise EX004"]

Logical drawing

flowchart LR
  N0["Learning outcomes"]
  N1["2.1 Policies as logic"]
  N2["2.2 Sets of access"]
  N3["2.3 Counting combinations"]
  N4["Synthesis"]
  N0 --> N1 --> N2 --> N3 --> N4 --> Q["EX004"]

[Learning outcomes]
    |
    v
[2.1 Policies as logic]
    |
    v
[2.2 Sets of access]
    |
    v
[2.3 Counting combinations]
    |
    v
[Synthesis]
    |
    v
[Worked example] --> [Exercise EX004]

Learning outcomes

You will (1) write policy rules in logic; (2) find conflicts between rules; (3) use sets to compare who holds access with who should.

2.1 Policies as logic

Nadia translates two Ardwell policies into logic. One says every remote session to the control system must use multi-factor authentication. Another says vendors may connect during emergencies without delay. Written as statements, the two clash when a vendor's token fails during an outage. Precise logic exposes the conflict before an engineer must decide under pressure which rule to break. Nadia proposes an explicit emergency rule with a pre-approved fallback and after-the-fact review, so the exception becomes part of the policy instead of an undocumented workaround.

2.2 Sets of access

Using sets, Nadia compares people with control system access against people whose role requires it. The set difference reveals seven accounts belonging to staff who moved to other jobs. The intersection of vendors and accounts without multi-factor authentication shows two vendor accounts at risk. Sets turn vague concerns into exact lists that owners can act on. They also make it easy to test whether a proposed change widens or narrows access, which is the basic question in every access governance decision Ardwell makes.

2.3 Counting combinations

Nadia counts segregation of duties conflicts in Ardwell's finance system. Five sensitive permissions exist, and policy forbids any person from holding both create supplier and approve payment, or both approve payment and reconcile bank. She counts pairs of permissions and lists which are forbidden, then checks staff permission sets against the list. Counting makes the rule testable by a simple script. It also shows how quickly checks grow as permissions are added, a reason to keep role design simple and to automate conflict detection.

Worked example

Nadia exposes a policy conflict in logic, finds seven stale accounts by set difference and counts forbidden permission pairs.

Synthetic case. Policies, accounts and counts are synthetic.

Errors and limits

Logic captures written rules, not actual practice. Set lists go stale quickly.

Exercises

• EX004 — Emergency clash. Which two policies clash during an outage?
  Show marking criteria

  Rubric: 3 = mandatory MFA and immediate vendor emergency access;; 2 = conflict;; 1 = vague;; 0 = none.
• EX005 — Stale accounts. How many stale control-system accounts did the set difference reveal?
  Show marking criteria

  Rubric: 3 = seven;; 2 = 7;; 1 = vague;; 0 = none.
• EX006 — Forbidden pairs. Name one forbidden permission pair.
  Show marking criteria

  Rubric: 3 = create supplier with approve payment;; 2 = SoD pair;; 1 = vague;; 0 = none.

Synthesis

Logic, sets and counting turn governance rules into precise, testable statements.

Continue studying — chapter 02 of 50

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