Token-based authentication (JWT) in IOT Protocols - Time & Space Complexity

Time Complexity: Token-based authentication (JWT)

O(n)

Understanding Time Complexity

We want to understand how the time to verify a JWT token changes as the token size or number of tokens grows.

How does the work needed to check tokens increase with input size?

Scenario Under Consideration

Analyze the time complexity of the following code snippet.

// Pseudocode for JWT verification
function verifyJWT(token) {
  header = decodeBase64(token.header)
  payload = decodeBase64(token.payload)
  signature = token.signature

  validSignature = verifySignature(header, payload, signature, secretKey)
  return validSignature
}
    

This code decodes parts of the token and checks the signature to confirm the token is valid.

Identify Repeating Operations

Identify the loops, recursion, array traversals that repeat.

• Primary operation: Decoding base64 strings and verifying the signature.
• How many times: Each token is processed once; inside verification, signature check may involve iterating over the token data bytes.

How Execution Grows With Input

As the token size grows, the decoding and signature verification take longer because they process more data.

Input Size (token length)	Approx. Operations
10 bytes	10 operations
100 bytes	100 operations
1000 bytes	1000 operations

Pattern observation: The work grows directly with the size of the token data.

Final Time Complexity

Time Complexity: O(n)

This means the time to verify a token grows in a straight line with the token size.

Common Mistake

[X] Wrong: "Verifying a token always takes the same time no matter how big it is."

[OK] Correct: Larger tokens have more data to decode and check, so they take more time.

Interview Connect

Understanding how token verification time grows helps you design systems that stay fast even with many or large tokens.

Self-Check

"What if we cached decoded tokens? How would the time complexity change when verifying repeated tokens?"

Practice

1. What is the main purpose of a JWT (JSON Web Token) in IoT device communication?

easy

A. To store large files securely on the device

B. To encrypt all data sent between devices

C. To prove the device's identity without sending passwords repeatedly

D. To replace the device's IP address

Solution

1. Step 1: Understand JWT role in authentication

   JWT tokens are used to prove identity securely without resending passwords each time.

2. Step 2: Compare options with JWT purpose

   Only To prove the device's identity without sending passwords repeatedly matches this purpose; others describe unrelated functions.

3. Final Answer:

   To prove the device's identity without sending passwords repeatedly -> Option C

4. Quick Check:

   JWT = Identity proof without password [OK]

Hint: JWTs prove identity without passwords [OK]

Common Mistakes:

• Thinking JWT encrypts all data
• Confusing JWT with file storage
• Assuming JWT replaces IP addresses

2. Which of the following is the correct structure of a JWT token?

easy

A. header.payload.signature

B. payload.header.signature

C. signature.payload.header

D. header.signature.payload

Solution

1. Step 1: Recall JWT token parts order

   A JWT consists of three parts separated by dots: header, payload, and signature in that order.

2. Step 2: Match options with correct order

   Only header.payload.signature shows header.payload.signature correctly.

3. Final Answer:

   header.payload.signature -> Option A

4. Quick Check:

   JWT format = header.payload.signature [OK]

Hint: JWT parts order: header, payload, signature [OK]

Common Mistakes:

• Mixing the order of parts
• Placing signature before payload
• Confusing payload and header positions

3. Given this JWT payload JSON: {"sub":"device123","exp":1700000000}, what does the "exp" field represent?

medium

A. The token's signature

B. The device's unique ID

C. The encryption algorithm used

D. The token's expiration time as a Unix timestamp

Solution

1. Step 1: Identify the meaning of 'exp' in JWT payload

   The 'exp' field stands for expiration time, given as a Unix timestamp.

2. Step 2: Match 'exp' meaning with options

   The token's expiration time as a Unix timestamp correctly states it is the token's expiration time; others are unrelated.

3. Final Answer:

   The token's expiration time as a Unix timestamp -> Option D

4. Quick Check:

   exp = expiration time [OK]

Hint: "exp" means token expiration time [OK]

Common Mistakes:

• Confusing 'exp' with device ID
• Thinking 'exp' is encryption info
• Mixing 'exp' with signature data

4. You receive this JWT token string: eyJhbGciOiJIUzI1NiJ9.eyJzdWIiOiJkZXZpY2UxMjMiLCJleHAiOjE3MDAwMDAwMDB9. When verifying, you get an error about the signature. What is the most likely cause?

medium

A. The token is missing the expiration field

B. The token's signature does not match because the secret key used is incorrect

C. The header is not base64 encoded

D. The payload is missing the device ID

Solution

1. Step 1: Understand signature verification in JWT

   Signature errors usually happen when the secret key used to verify does not match the one used to sign.

2. Step 2: Check other options for signature error cause

   Missing payload fields or encoding issues cause different errors, not signature mismatch.

3. Final Answer:

   The token's signature does not match because the secret key used is incorrect -> Option B

4. Quick Check:

   Signature error = wrong secret key [OK]

Hint: Signature errors usually mean wrong secret key [OK]

Common Mistakes:

• Assuming missing fields cause signature errors
• Ignoring base64 encoding correctness
• Thinking expiration absence causes signature failure

5. You want to limit IoT device access by making JWT tokens expire after 10 minutes. Which approach correctly sets this expiration in the token payload?

hard

A. Set the "exp" field to the current Unix timestamp plus 600 seconds

B. Set the "iat" field to 600

C. Set the "exp" field to the current date string

D. Omit the "exp" field to allow unlimited token life

Solution

1. Step 1: Understand JWT expiration setting

   The 'exp' field must be a Unix timestamp indicating when the token expires, so add 600 seconds (10 minutes) to current time.

2. Step 2: Evaluate other options

   'iat' is issued-at time, not expiration; date string is invalid format; omitting 'exp' disables expiration.

3. Final Answer:

   Set the "exp" field to the current Unix timestamp plus 600 seconds -> Option A

4. Quick Check:

   Use 'exp' with timestamp + 600 seconds [OK]

Hint: Use 'exp' = now + 600 seconds for 10-minute expiry [OK]

Common Mistakes:

• Using 'iat' instead of 'exp' for expiration
• Setting 'exp' as a date string
• Leaving out 'exp' to limit token life