1. HMAC (Hash-based MAC) — Most Common

Formula:

HMAC(K, m) = H((K' ⊕ opad) || H((K' ⊕ ipad) || m))

• H = hash function (e.g., SHA-256)
• K = secret key
• K' = key padded/truncated to block size
• opad = 0x5c5c5c... (outer padding)
• ipad = 0x363636... (inner padding)
• || = concatenation
• ⊕ = XOR

Step-by-step:

1. If key length > block size → hash the key first
2. Pad key with zeros to block size → K'
3. XOR K' with ipad → inner key
4. Concatenate inner key + message, hash it → inner hash
5. XOR K' with opad → outer key
6. Concatenate outer key + inner hash, hash again → HMAC

Python example:

import hmac
import hashlib

key = b'secret-key'
message = b'Hello, World!'

mac = hmac.new(key, message, hashlib.sha256).hexdigest()
print(mac)

2. CMAC (Cipher-based MAC)

Steps:

1. Generate two subkeys K1, K2 from the cipher key
2. Split message into blocks
3. XOR the last block with K1 (or K2 if padding needed)
4. CBC-encrypt all blocks; the final ciphertext block = MAC

from Crypto.Hash import CMAC
from Crypto.Cipher import AES

key = b'0123456789abcdef'  # 16-byte AES key
message = b'Hello, World!'

cobj = CMAC.new(key, ciphermod=AES)
cobj.update(message)
print(cobj.hexdigest())

3. CBC-MAC

1. Pad message to a multiple of the block size
2. Encrypt message blocks in CBC mode with IV = 0
3. The final ciphertext block is the MAC

MAC = E_K(m_n ⊕ E_K(m_{n-1} ⊕ ... ⊕ E_K(m_1 ⊕ 0)))

⚠️ CBC-MAC is insecure for variable-length messages — prefer CMAC or HMAC.

4. GMAC (Galois/MAC — part of AES-GCM)

Quick Comparison

What is MAC?

• It is analogous to the ED₅₀ for intravenous drugs
• It reflects the partial pressure of the anesthetic in the brain (since alveolar partial pressure equilibrates with brain partial pressure)
• The lower the MAC, the more potent the agent

MAC Values of Common Inhaled Anesthetics

Values are for 30–55-year-old subjects at 1 atmosphere. Expressed as volume % of the inspired gas mixture.

How MAC is "Calculated" / Determined

1. Administering a steady-state concentration of the inhaled agent to a subject
2. Applying a standardized noxious stimulus (typically surgical skin incision)
3. Observing whether the patient moves or does not move
4. The concentration at which 50% of subjects do not move = 1 MAC

Clinically Useful MAC Multiples

MAC is Additive

0.5 MAC nitrous oxide + 0.5 MAC isoflurane = 1.0 MAC equivalent effect on movement suppression

Factors That Alter MAC

• Older age (↓ 6% per decade)
• Hypothermia
• Pregnancy (↓ ~1/3 at 8 weeks gestation)
• Opioids, benzodiazepines, barbiturates, ketamine
• Hypoxia (PaO₂ < 40 mmHg)
• Hypercarbia (PaCO₂ > 95 mmHg)
• Hypotension (MAP < 40 mmHg)
• Acute alcohol intoxication
• Hyponatremia, hypocalcemia

• Young age
• Hyperthermia (> 42°C)
• Chronic alcohol abuse
• Hypernatremia
• Increased CNS neurotransmitters (cocaine, amphetamines, MAOIs, levodopa)

• Sex
• Duration of anesthesia
• Thyroid status (hyper or hypothyroid)
• Species

Key Takeaway