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Logic Basics for Cybersecurity, Part 2 Propositional Logic Basics
Welcome back, my aspiring cyberwarriors!
In an earlier post, I introduced you to logic. Logic is one of the most under-rated skills in cybersecurity. Without it, you are destined to fail or underperform. In this tutorial, I will attempt to advance your knowledge of logic by introducing you to propositional logic.
Propositional logic is used in AI, cybersecurity, mathematics, and data science but here we want to focus on propositional logic in cybersecurity.
Why Hackers Need Logic
Propositional logic is the backbone of cybersecurity – it’s how firewalls make decisions, how access controls work, and how attackers reverse-engineer your defenses. If you can’t think logically, you’ll get outmaneuvered. Period.
Propositional logic is a branch of logic that studies ways of combining or altering entire statements (called propositions) that have definite truth values—either true or false. It focuses on the logical relationships between these propositions and the rules for forming complex statements (compound propositions) using logical connectives like AND, OR, NOT, IF-THEN, and IF-AND-ONLY-IF.
Let’s break it down like a hacker dissecting a firewall rule.
Core Concepts: The Hacker’s Toolkit
Propositions are statements that are either true (1) or false (0):
P = "Port 22 is open"Q = "User is admin"R = "Malicious payload detected"
Logical Operators – Your Attack Vectors:
| Operator | Symbol | Real-World Example |
|---|---|---|
| NOT | ¬ | ¬P = "Port 22 is closed" |
| AND | ∧ | P ∧ Q = "Port 22 open AND user is admin" (Privilege escalation) |
| OR | ∨ | P ∨ R = "Port 22 open OR malware detected" (Alert condition) |
| IMPLIES | → | Q → R = "If user is admin, THEN check for malware" (Access policy) |
| IFF | ↔ | P ↔ Q = "Port 22 open IFF user is admin" (Hardened SSH rule) |
Truth Tables: Your Exploit Blueprint
Every firewall rule, IDS signature, or access policy boils down to truth tables. Here’s how to weaponize them:
Example: Phishing Detection Rule
(User_clicks_link ∧ Untrusted_domain) → Alert
| User_clicks_link | Untrusted_domain | Alert |
|---|---|---|
| 0 | 0 | 0 |
| 0 | 1 | 0 |
| 1 | 0 | 0 |
| 1 | 1 | 1 |
Attack insight: Evade detection by making either condition false (e.g., hijack trusted domain).
Cybersecurity Applications: Logic in Action
1. Firewall Rule Analysis
Corporate firewall rule:(IP ∈ whitelist ∧ Port ≠ 22) ∨ (MFA_verified)
Hacker’s playbook:
- If
MFA_verified = 0, focus onIP ∉ whitelistORPort = 22 - Bruteforce port 22 if IP spoofing succeeds
2. Malware Trigger Conditions
Ransomware activation logic:(Files_encrypted ∧ Time_delay_expired) → Deploy_payload
Reverse-engineering:
- If
Files_encrypted = 0, payload won’t deploy → disrupt encryption process - If
Time_delay_expired = 0, buy time for remediation
3. Access Control Bypass
Admin panel access rule:(Role = "admin" ∨ (Session_hijacked ∧ ¬2FA_enabled))
Exploit path:
- Set
Session_hijacked = 1(via XSS) - Force
2FA_enabled = 0(via config manipulation) - Access granted without admin role!
Hacker’s Lab: Practical Logic Drills
Exercise 1:
Rule: (Geolocation = "US" ∧ ¬Tor_connection) → Allow_access
Your mission: Bypass without VPN.
Hint: What combination makes Allow_access = 1?
Exercise 2:
IDS alert condition:(SQL_keywords ∧ HTTP_request) ∧ ¬Whitelisted_IP
Evasion strategy: Make one input false to kill the alert.
Exercise 3:
Build a truth table for:Alert_if = (Bruteforce_attempts > 5) ∧ ¬(IP ∈ whitelist)
Identify which conditions trigger alerts.
Pro Tips for Cyber Operators
- Policy Auditing:
Convert ACLs to logic formulas. Hunt for contradictions like(A ∧ ¬A)– guaranteed misconfiguration! - Attack Surface Mapping:
Write threat models as logical expressions:Data_breach_possible = (Vulnerability_exists ∧ Exploit_available) ∧ ¬Detection - SOC Automation:
Code SIEM rules with propositional logic: pythonif (unusual_login_location and not mfa_used) or (impossible_travel): trigger_alert()
The Bottom Line
Propositional logic turns vague security policies into hackable equations. Master truth tables, operator precedence, and real-world mappings – then weaponize them to expose flaws or harden systems.
Remember: In cybersecurity, logic isn’t philosophy – it’s your exploit roadmap.
“The difference between a script kiddie and a pro? The pro knows WHY the rule failed.”
Challenge: Take any firewall rule from your network. Convert it to propositional logic. Find one combination that breaks it. Report back.
The post Logic Basics for Cybersecurity, Part 2 Propositional Logic Basics first appeared on Hackers Arise.
