How does your authenticator app generate a fresh code every 30 seconds with no network call? Pure math — and fewer than 15 lines of Python.

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Table of Contents

1. Background — Why One-Time Passwords?
2. The Standards: HOTP and TOTP
3. Step 1 — The Shared Secret
4. Step 2 — The Time Counter
5. Step 3 — HMAC-SHA1
6. Step 4 — Dynamic Truncation
7. Step 5 — The Final Code
8. Putting It All Together in Python
9. Building a Terminal Authenticator
10. Security Considerations
11. Takeaways

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1. Background — Why One-Time Passwords?

Passwords are broken. They get phished, leaked in data breaches, brute-forced, and reused across dozens of services. The answer the industry landed on is a second factor — something that proves you have a physical device in addition to knowing a password.

The most common form of software-based 2FA is TOTP: a 6-digit code that rotates every 30 seconds. You’ve seen it in Google Authenticator, Authy, Bitwarden, 1Password, and countless others. You scan a QR code once, and your authenticator app produces a fresh code every half-minute, in sync with the server, without ever making a network request.

The magic is that both sides — your phone and the server — are computing the same code independently, from a shared secret and the current time. There’s no communication, no challenge/response, just math.

That math is entirely public. It’s specified in RFC 6238 and fits in fewer than 15 lines of Python.

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2. The Standards: HOTP and TOTP

TOTP is built on top of an older standard — HOTP (HMAC-based One-Time Password, RFC 4226).

HOTP generates a code from a shared secret and an incrementing counter. Each time you generate a code, the counter ticks up. The problem: if the client and server counters drift, codes stop working.

TOTP solves this elegantly. Instead of a persistent counter, it derives the counter from the current Unix time:

$\text{counter} = \left\lfloor \frac{T_{\text{now}}}{T_{\text{step}}} \right\rfloor$

Where $T_{\text{step}}$ is 30 seconds by default. Both sides floor the Unix timestamp to the same 30-second window and get the same counter — no synchronization needed. The only requirement is that clocks are reasonably accurate, which is trivially guaranteed by NTP.

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3. Step 1 — The Shared Secret

When you scan a QR code to set up 2FA, you’re importing a shared secret — a random byte sequence known only to you and the server. It’s stored as a Base32-encoded string, which looks like:

JBSWY3DPEHPK3PXP

Base32 uses only uppercase letters A–Z and digits 2–7. It’s URL-safe, easy to type manually, and avoids ambiguous characters.

In Python, decoding it is one line:

import base64

secret = "JBSWY3DPEHPK3PXP"
secret_bytes = base64.b32decode(secret, casefold=True)
# b'Hello!\xde\xad\xbe\xef'

The casefold=True parameter accepts lowercase input too, which matters for secrets copied from apps or entered by hand.

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4. Step 2 — The Time Counter

With the secret decoded, we need the counter — a 64-bit big-endian integer representing which 30-second window we’re in:

import time

time_step = 30
current_time = int(time.time())      # Unix timestamp in seconds
counter = current_time // time_step  # Floor divide to get the window index
counter_bytes = counter.to_bytes(8, byteorder='big')  # 8-byte big-endian

For example, at 2026-04-17 12:00:00 UTC (Unix: 1776081600):

$\text{counter} = \left\lfloor \frac{1776081600}{30} \right\rfloor = 59202720$

Both the server and the authenticator app perform this same calculation. As long as their clocks agree to within a few seconds, they land in the same window and produce the same code.

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5. Step 3 — HMAC-SHA1

This is the cryptographic core. We compute an HMAC-SHA1 of the counter bytes, using the shared secret as the key:

import hmac
import hashlib

hmac_hash = hmac.new(secret_bytes, counter_bytes, hashlib.sha1).digest()
# 20-byte result

HMAC (Hash-based Message Authentication Code) takes a key and a message and produces a fixed-length tag. Unlike a raw hash, it’s resistant to length-extension attacks, and its security depends on the key being secret.

SHA-1 produces 20 bytes (160 bits). While SHA-1 is broken for collision resistance (think forged certificates), that vulnerability is irrelevant here — we’re not comparing hashes, we’re using HMAC as a PRF (Pseudo-Random Function). HMAC-SHA1 remains cryptographically sound for this use case, which is why RFC 4226 specifies it.

The result is a 20-byte array that looks like random noise. Next, we extract a 6-digit number from it.

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6. Step 4 — Dynamic Truncation

We can’t use all 20 bytes — that’d be a 40-character hex code, not a 6-digit number. RFC 4226 defines Dynamic Truncation to extract 4 bytes from the hash in a deterministic but unpredictable way:

1. Take the last byte of the HMAC output.
2. Mask it with 0x0F to get a value from 0 to 15. This is the offset.
3. Extract 4 bytes starting at that offset.
4. Mask the result with 0x7FFFFFFF to clear the sign bit (ensuring a positive integer).

offset = hmac_hash[-1] & 0x0F
truncated_hash = hmac_hash[offset : offset + 4]
code = int.from_bytes(truncated_hash, byteorder='big') & 0x7FFFFFFF

The offset is derived from the hash itself, so it varies with every counter value. This is what makes the truncation “dynamic” — an attacker observing outputs can’t predict which bytes will be extracted next.

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7. Step 5 — The Final Code

The last step is simple: take the 31-bit integer and produce a 6-digit code by taking it modulo $10^6$, then zero-padding to ensure exactly 6 digits:

digits = 6
totp_code = str(code % (10 ** digits)).zfill(digits)
# e.g. "048271"

The modulo discards all but the last 6 decimal digits. zfill(6) pads with leading zeros so codes like 48271 become 048271 — important because 048271 and 48271 are different 6-character strings.

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8. Putting It All Together in Python

Here’s the complete TOTP function — no third-party library, just the Python standard library:

import time
import hmac
import hashlib
import base64

def totp(secret, time_step=30, digits=6, hash_algorithm=hashlib.sha1):
    """Generates a Time-based One-Time Password (TOTP) per RFC 6238."""
    try:
        secret_bytes = base64.b32decode(secret, casefold=True)
    except base64.binascii.Error:
        raise ValueError("Invalid secret key. Must be base32 encoded.")

    current_time = int(time.time())
    counter = current_time // time_step
    counter_bytes = counter.to_bytes(8, byteorder='big')

    hmac_hash = hmac.new(secret_bytes, counter_bytes, hash_algorithm).digest()

    offset = hmac_hash[-1] & 0x0F
    truncated_hash = hmac_hash[offset : offset + 4]
    code = int.from_bytes(truncated_hash, byteorder='big') & 0x7FFFFFFF

    return str(code % (10 ** digits)).zfill(digits)

That’s the entire algorithm. 15 lines. You can verify it produces the same output as Google Authenticator or Authy for the same secret — they all implement the same RFC.

You can also swap in hashlib.sha256 or hashlib.sha512 for stronger hash algorithms. Some services (like Steam) use a different number of digits or a different time step; those are just parameters.

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9. Building a Terminal Authenticator

Having the totp() function is useful, but to make it practical you need:

• A loop that refreshes every second.
• A visual timer showing when the current code expires.
• A table of multiple accounts.

The main loop only redraws when the 30-second window changes (avoiding flicker), and remaining_time = time_step - (current_time % time_step) drives a progress bar that counts down to the next rotation. The table uses Unicode box-drawing characters for a clean look in any modern terminal. Here’s the complete script:

Here’s the full script — a self-contained terminal authenticator with no TOTP library dependency:

#!/usr/bin/env python
import time
import hmac
import hashlib
import base64
import os
import shutil
from colorama import Fore, Style, init

# Initialize colorama
init()

tOTP_ART = f"""
{Fore.RED}▗ {Fore.GREEN}▄▖{Fore.YELLOW}▄▖{Fore.BLUE}▄▖{Style.RESET_ALL}
{Fore.MAGENTA}▜▘{Fore.CYAN}▌▌{Fore.RED}▐ {Fore.GREEN}▙▌{Style.RESET_ALL}
{Fore.YELLOW}▐▖{Fore.BLUE}▙▌{Fore.MAGENTA}▐ {Fore.CYAN}▌{Style.RESET_ALL}
"""

def totp(secret, time_step=30, digits=6, hash_algorithm=hashlib.sha1):
    """Generates a Time-based One-Time Password (TOTP)."""
    try:
        secret_bytes = base64.b32decode(secret, casefold=True)
    except base64.binascii.Error:
        raise ValueError("Invalid secret key. Must be base32 encoded.")

    current_time = int(time.time())
    counter = current_time // time_step
    counter_bytes = counter.to_bytes(8, byteorder='big')
    hmac_hash = hmac.new(secret_bytes, counter_bytes, hash_algorithm).digest()
    offset = hmac_hash[-1] & 0x0F
    truncated_hash = hmac_hash[offset:offset + 4]
    code = int.from_bytes(truncated_hash, byteorder='big') & 0x7FFFFFFF
    return str(code % (10 ** digits)).zfill(digits)

def print_progress_bar(remaining_time, total, length=40):
    """Prints a progress bar with remaining time."""
    progress = total - remaining_time
    percent = ("{0:.1f}").format(100 * (progress / float(total)))
    remaining_percent = ("{0:.1f}").format(100 - float(percent))
    filled_length = int(length * progress // total)
    remaining_bar = '█' * (length - filled_length) + '░' * filled_length
    print(f'{Fore.BLUE}Remaining: {remaining_bar} {remaining_percent}% {Fore.YELLOW}Time until next update: {remaining_time} seconds{Style.RESET_ALL}', end='\r')

def display_otp_table(secrets):
    """Displays the OTPs in a formatted table with ASCII borders."""
    max_service_len = max(len(secret[1]) for secret in secrets)
    service_width = min(max_service_len + 4, 34)

    top_border    = f"{Fore.BLUE}╔{'═' * (service_width + 2)}╦{'═' * 10}╗{Style.RESET_ALL}"
    header_div    = f"{Fore.BLUE}╠{'═' * (service_width + 2)}╬{'═' * 10}╣{Style.RESET_ALL}"
    row_divider   = f"{Fore.BLUE}╟{'─' * (service_width + 2)}╫{'─' * 10}╢{Style.RESET_ALL}"
    bottom_border = f"{Fore.BLUE}╚{'═' * (service_width + 2)}╩{'═' * 10}╝{Style.RESET_ALL}"

    print(f"\n{top_border}")
    print(f"{Fore.BLUE}║ {Fore.GREEN}{'SERVICE':^{service_width}} {Fore.BLUE}║ {Fore.CYAN}{'OTP':^8} {Fore.BLUE}║{Style.RESET_ALL}")
    print(header_div)

    for i, secret in enumerate(secrets):
        if i > 0:
            print(row_divider)

        service = secret[1][:service_width-2]
        otp = totp(secret[0])
        display_service = (service + '..') if len(secret[1]) > service_width-2 else service

        print(
            f"{Fore.BLUE}║ {Fore.YELLOW}{display_service:<{service_width}} {Fore.BLUE}║ "
            f"{Fore.MAGENTA}{otp:^8} {Fore.BLUE}║{Style.RESET_ALL}"
        )

    print(bottom_border)

if __name__ == "__main__":
    secrets = [
        ['JBSWY3DPEHPK3PXP', 'Gmail Personal'],
        ['MFRGGZDFMZTWQ2LK', 'Gmail Work'],
        ['GEZDGNBVGY3TQOJQ', 'ORG1'],
    ]

    time_step = 30
    last_counter = -1
    terminal_width = shutil.get_terminal_size().columns

    try:
        while True:
            current_time = int(time.time())
            current_counter = current_time // time_step

            if current_counter != last_counter:
                os.system('cls' if os.name == 'nt' else 'clear')
                print(tOTP_ART)
                display_otp_table(secrets)
                last_counter = current_counter

            remaining_time = time_step - (current_time % time_step)
            print_progress_bar(remaining_time, time_step, min(terminal_width - 20, 50))
            time.sleep(min(1, remaining_time))

    except KeyboardInterrupt:
        print(f"\n{Fore.RED}Exiting...{Style.RESET_ALL}")

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10. Security Considerations

Secrets are sensitive. The Base32 secret is equivalent to your password. Anyone who obtains it can generate valid codes forever. Don’t hardcode secrets in scripts you commit to version control — use a secrets manager, an encrypted store, or at minimum environment variables.

TOTP doesn’t prevent phishing. A real-time phishing proxy can relay your code to the target site before it expires. TOTP protects against static password theft, not active relay attacks. Passkeys / FIDO2 hardware tokens solve this by binding authentication to the origin domain.

Clock skew matters. Most servers accept codes from the previous and next window (±30 seconds) to handle small clock differences. If your clock is off by more than a minute, codes will fail. NTP keeps this trivially in check.

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11. Takeaways

TOTP is a beautiful piece of applied cryptography: simple enough to fit in 15 lines of Python, yet secure enough to protect millions of accounts. The key insight is replacing a stateful counter with a stateless time window — both sides independently compute the same value with no communication.

The algorithm in order:

Step	Operation	Output
1	Base32-decode the shared secret	Raw bytes
2	Floor-divide Unix timestamp by 30	64-bit counter
3	HMAC-SHA1(secret, counter)	20-byte hash
4	Dynamic truncation (offset from last byte)	4-byte slice
5	Mask with 0x7FFFFFFF, mod $10^6$, zero-pad	6-digit code

Next time you open your authenticator app, you’re looking at the output of five simple operations on a shared secret and the current time. No magic, no network call — just math.