What are TOTP and HOTP? The Principles Behind One-Time Password Algorithms | TOTP、HOTP 究竟係啲咩？ —— 一次性密碼認證算法背後嘅原理
Background: Why Did OTP Appear?
Traditional login relies on “passwords”—something only you know. But as we discussed in the previous article, passwords are vulnerable to leaks, guesses, and theft. Is there a way to make passwords that become useless after just one use?
This is the concept of OTP (One-Time Password)—a fresh, single-use password for every login. But how does it work?
HOTP: Where It All Begins
HOTP (HMAC-based One-Time Password) was standardized by IETF in 2005 (RFC 4226), and it’s the foundation of all modern 2FA algorithms.
Core Concept
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HOTP = Truncate(HMAC-SHA-1(key, counter))
Flow Diagram
Mathematical Details
- HMAC-SHA-1: Compute HMAC with key K and counter C, output 160-bit (20 bytes) hash
- Dynamic Truncation: Take last 4 bits as offset, extract 32 bits as integer
- Modulo: Apply modulo 1,000,000 to get a 6-digit number
TOTP: The Time-Driven Evolution
TOTP (Time-based One-Time Password) is HOTP’s improved version, standardized in 2008 (RFC 6238). The key change: using “time” instead of “counter”.
Core Formula
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T = floor(Unix_time / 30)
TOTP = Truncate(HMAC-SHA-1(key, T))
Flow Diagram
Why 30 Seconds?
Real-World Use Cases
TOTP Common Examples
- Google Authenticator, Microsoft Authenticator
- Bank app login
- Password manager’s secondary authentication
HOTP Common Examples
- Traditional bank security tokens (generate on press)
- Some smart card systems
Summary
| Feature | HOTP | TOTP |
|---|---|---|
| Base | HMAC-SHA-1 | HMAC-SHA-1 |
| Input | Counter (C) | Time (T) |
| Validity | Until verified | 30-second window |
| Advantage | No time sync needed | No counter sync needed |
| Drawback | Counter may drift | Clock must be synced |
Whether HOTP or TOTP, the core is key + one-way function, ensuring that even if someone intercepts an OTP, they can’t reuse it or predict the next one—simple math that protects your account.
背景：點解會出現一次性密碼？
傳統嘅登入方式靠「密碼」呢樣唔係所有人都知嘅嘢。但正如之前篇文講，密碼好易洩露、猜測、甚至被竊取。有咩方法可以做到「我用咗呢個密碼之後，呢個密碼就唔可以再用」？
呢個就係 OTP (One-Time Password) 嘅概念——每 次登入都用一個全新、一次性嘅密碼。咁即係點運作嘅呢？
HOTP：一切嘅起點
HOTP (HMAC-based One-Time Password) 係 2005 年由 IETF 標準化嘅算法（RFC 4226），係所有現代 2FA 算法嘅根源。
核心概念
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HOTP = Truncate(HMAC-SHA-1(密鑰, 計數器))
流程圖
數學細節
- HMAC-SHA-1：用密鑰 K 對計數器 C 做 HMAC 運算，輸出 160-bit（20 bytes）雜湊值
- Dynamic Truncation：取最後 4 bits 決定 offset，然後取 32 bits 作為整數
- Modulo：對 1,000,000 取模，得到 6 位數字
TOTP：時間驅動嘅進化
TOTP (Time-based One-Time Password) 係 HOTP 嘅改良版，2008 年標準化（RFC 6238）。最大嘅改變係：用「時間」取代「計數器」。
核心公式
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T = floor(Unix時間 / 30)
TOTP = Truncate(HMAC-SHA-1(密鑰, T))
流程圖
點解要用 30 秒？
實際應用場景
TOTP 常見用例
- Google Authenticator、Microsoft Authenticator
- 銀行 App 登入
- 密碼管理器嘅二次認證
HOTP 常見用例
- 傳統嘅銀行實體 security token（按一次生成一次）
- 某些 Smart Card 系統
總結
| 特性 | HOTP | TOTP |
|---|---|---|
| 基礎 | HMAC-SHA-1 | HMAC-SHA-1 |
| 輸入 | 計數器 (C) | 時間 (T) |
| 有效期 | 直至成功驗證 | 30 秒窗口 |
| 優點 | 無需同步時間 | 無需同步計數器 |
| 缺點 | 計數器可能 drift | 時鐘需同步 |
無論 HOTP 定 TOTP，核心都係用 密鑰 + 單向函數，確保即使有人截獲咗某次嘅 OTP，都唔可以重用或者推算下一次嘅密碼—— 就係咁簡單嘅數學原理，保障到你嘅帳戶安全。