Definition:

• Username: A unique identifier used to distinguish users within a system.

• Password: A secret string of characters used in combination with the username to authenticate a user.

Common Devices:

• Computers: Password Login Example

• Websites: Website Login Example

• Email Accounts: Email Login Example

Pros:

• Widely Used: Standard method for authentication across many platforms.

• Customizable: Users can create their own passwords, adding complexity and variability.

Cons:

• Vulnerability to Brute Force Attacks: Weak passwords can be easily guessed or cracked.

• Risk of Phishing: Users may be tricked into revealing their passwords.

Best Practices:

• Length and Complexity: Use a minimum of 12 characters including upper and lower case letters, numbers, and special characters.

• Avoid Common Words: Do not use easily guessable words or common phrases.

• Unique Passwords: Use different passwords for different accounts.

Mathematical Improvement:

• Password Complexity: Increasing length exponentially increases security. For example, a password with 8 characters using 62 possible characters (lowercase, uppercase, and digits) has 62^8 (about 218 trillion) possible combinations. Increasing the length to 12 characters raises the combinations to 62^12 (about 3.2 x 10^21).

Definition:

• PIN: A numeric code used for authentication, usually 4 to 6 digits long.

Common Devices:

• ATMs: ATM PIN Example

• Mobile Phones: Phone PIN Entry Example

• Smart Lock Systems: Smart Lock PIN Entry Example

Pros:

• Simplicity: Easy to use and remember.

• Quick Access: Fast input and verification.

Cons:

• Limited Complexity: PINs are generally shorter and numeric, making them less secure compared to more complex passwords.

• Vulnerability to Shoulder Surfing: PINs can be observed and memorized by others.

Best Practices:

• Length: Use a minimum of 6 digits.

• Avoid Predictable Sequences: Do not use easily guessable patterns like 123456 or 000000.

• Change Regularly: Update PINs periodically to enhance security.

Mathematical Improvement:

• PIN Combinations: A 4-digit PIN has 10^4 (10,000) combinations. A 6-digit PIN has 10^6 (1 million) combinations. Thus, increasing the length from 4 to 6 digits increases security by a factor of 100.

Definition:

• Pattern: A drawable shape on a grid that the user draws to unlock a device, typically using a 3x3 grid.

Common Devices:

• Smartphones: Pattern Lock Example

• Tablets: Tablet Pattern Lock Example

Pros:

• Visual Nature: Easier for some users to remember and use compared to complex passwords.

• Speed: Quick to input compared to typing.

Cons:

• Predictable Patterns: Common patterns can be easily guessed or observed.

• Limited Combinations: Fewer possible combinations compared to passwords.

Best Practices:

• Complexity: Avoid simple shapes and predictable patterns. Use a pattern that covers more points on the grid.

• Avoid Reuse: Do not use the same pattern across multiple devices.

Mathematical Improvement:

• Pattern Complexity: A 3x3 grid has 9 points and patterns are usually 4-9 points long. The number of possible patterns increases with the length and complexity of the pattern. While specific numbers are complex to compute, more points and longer patterns exponentially increase security.

Definition:

• Biometrics: Authentication based on unique physiological characteristics such as fingerprints, facial recognition, or iris scans.

Common Devices:

• Smartphones: Fingerprint Scanner Example

• Laptops: Fingerprint Reader on Laptop

• Access Control Systems: Biometric Access Control Example

Pros:

• High Security: Difficult to replicate or forge.

• Convenience: Fast and easy access without the need to remember codes.

Cons:

• Privacy Concerns: Sensitive biometric data can be compromised.

• Variability: Environmental factors or physical changes can affect accuracy.

Best Practices:

• Secure Storage: Ensure biometric data is stored securely and encrypted.

• Combine with Other Methods: Use biometrics as part of multi-factor authentication for enhanced security.

Mathematical Improvement:

• Biometric Security: While exact mathematical quantification is complex, biometrics are generally considered highly secure due to their unique nature and difficulty to replicate.

Security Ranking from Weakest to Highest:

1. PIN

2. Patterns

3. Username and Password

4. Biometrics