MAC 和密钥派生

Message authentication codes (MAC), HMAC (hash-based message authentication code) and KDF (key derivation functions) play important role in cryptography. Let's explain when we need MAC, how to calculate HMAC and how it is related to key derivation functions.

消息认证码（MAC），HMAC（基于哈希的消息认证码）和 KDF（密钥派生功能，key derivation functions）在加密中起着重要的作用。让我们解释一下何时需要 MAC，如何计算 HMAC 以及其与密钥派生函数的关系。

消息认证码（MAC）

Message Authentication Code (MAC) is cryptographic code, calculated by given key and given message:

消息认证码（Message Authentication Code，MAC）是由给定密钥和给定消息计算得出的密码：

auth_code = MAC(key, msg)

Typically, it behaves like a hash function: a minor change in the message or in the key results to totally different MAC value. It should be practically infeasible to change the key or the message and get the same MAC value. MAC codes, like hashes, are irreversible: it is impossible to recover the original message or the key from the MAC code. MAC algorithms are also known as "keyed hash functions", because they behave like a hash function with a key.

通常，它的行为类似于哈希函数：消息或密钥的微小变化将导致 MAC 值完全不同。更改密钥或消息并得出相同的 MAC 值实际上是不可行的。 MAC 值像哈希值一样是不可逆的：无法从 MAC 值中恢复原始消息或密钥。 MAC 算法也称为“键控哈希函数”，因为它们的行为类似于带有键值的哈希函数。

For example, the MAC code can be calculated by the HMAC-SHA256 algorithm like this:

例如，可以通过 HMAC-SHA256 算法计算 MAC 值，如下所示：

HMAC-SHA256('key', 'some msg') = 32885b49c8a1009e6d66662f8462e7dd5df769a7b725d1d546574e6d5d6e76ad

The above HMAC-SHA256 calculation can be coded in Python like this:

上述 HMAC-SHA256 计算可用 Python 编码如下：

import hashlib, hmac, binascii

mac = hmac.new(b'key', b'some msg', hashlib.sha256).digest()
print(binascii.hexlify(mac))

Run the above code example: https://repl.it/@nakov/HMAC-SHA256-in-Python.

运行上述的示例代码：https://repl.it/@nakov/HMAC-SHA256-in-Python。

The MAC code is digital authenticity code, like a digital signature, but with pre-shared key. We shall learn more about digital signing and digital signatures later.

MAC 值是数字认证码，类似于数字签名，但需要预共享密钥。稍后我们将学习更多关于数字签名的内容。

MAC 算法

Many algorithms for calculating message authentication codes (MAC) exist in modern cryptography. The most popular are based on hashing algorithms, like HMAC (Hash-based MAC, e.g. HMAC-SHA256) and KMAC (Keccak-based MAC). Others are based on symmetric ciphers, like CMAC (Cipher-based MAC), GMAC (Galois MAC) and Poly1305 (Bernstein's one-time authenticator). Other MAC algorithms include UMAC (based on universal hashing), VMAC (high-performance block cipher-based MAC) and SipHash (simple, fast, secure MAC).

现代密码学中存在许多计算消息认证码（MAC）的算法。最流行的是基于哈希算法的，比如 HMAC（基于哈希的 MAC，例如 HMAC-sha256）和 KMAC（基于 Keccak 的 MAC）。其他一些基于对称加密，如 CMAC（基于密码的 MAC）、GMAC（Galois MAC）和 Poly1305（Bernstein 的一次性身份验证器)。其他的 MAC 算法包括 UMAC（基于通用哈希）、VMAC（基于高性能块密码的 MAC）和 SipHash （简单、快速、安全的 MAC）。

什么时候需要 MAC 值?

A sample scenario for using MAC codes is like this:

使用MAC代码的场景示例如下：

Two parties exchange somehow a certain secret MAC key (pre-shared key).
双方以某种方式交换保密的 MAC 密钥（预共享密钥）。
We receive a msg + auth_code from somewhere (e.g. from Internet, from the blockchain, or from email message).
我们从某个地方（例如从互联网、区块链或电子邮件）接收到一个消息和验证码。
We want to be sure that the msg is not tampered, which means that both the key and msg are correct and match the MAC code.
我们想确认消息没有被篡改，即密钥和消息都是正确的，并且与 MAC 码匹配。
In case of tampered message, the MAC code will be incorrect.
如果消息被篡改，MAC 码将不正确。

认证加密：使用 MAC 加密/解密消息

Another scenario to use MAC codes is for authenticated encryption: when we encrypt a message and we want to be sure the decryption password is correct and the decrypted message is the same like the original message before encryption.

使用 MAC 码的另一个场景是用于认证加密：我们加密一条消息时，我们想确保有正确的解密密码，并且解密后的消息与加密前的原始消息相同。

First, we derive a key from the password. We can use this key for the MAC calculation algorithm (directly or hashed for better security).
首先，我们从密码中得到一个派生密钥。我们可以将此密钥用于 MAC 计算算法（直接使用或使用哈希以获得更好的安全性）。
Next, we encrypt the message using the derived key and store the ciphertext in the output.
接下来，我们使用派生密钥加密消息并将密文存储在输出中。
Finally, we calculate the MAC code using the derived key and the original message and we append it to the output.
最后，我们使用派生密钥和原始消息来计算 MAC码，并将其附加到输出中。

When we decrypt the encrypted message (ciphertext + MAC), we proceed as follows:

当我们解密加密的消息（密文+MAC）时，我们按如下步骤进行：

First, we derive a key from the password, entered by the user. It might be the correct password or wrong. We shall find out later.
首先，我们从用户输入的密码中得到派生密钥。密码可能是正确的，也可能是错误的。我们稍后可以确认。
Next, we decrypt the message using the derived key. It might be the original message or incorrect message (depends on the password entered).
接下来，我们使用派生密钥解密消息。它可能是原始消息，也可能是错误消息（这取决于输入的密码）。
Finally, we calculate a MAC code using the derived key + the decrypted message.
最后，我们使用派生密钥和解密的消息计算 MAC 码。
- If the calculated MAC code matches the MAC code in the encrypted message, the password is correct.
- 如果计算出的 MAC 码与加密消息中的 MAC 码匹配，则密码正确。
- Otherwise, it will be proven that the decrypted message is not the original message and this means that the password is incorrect
- 否则，将证明解密后的消息不是原始消息，这意味着密码不正确。

Some authenticated encryption algorithms (such as AES-GCM and ChaCha20-Poly1305) integrate the MAC calculation into the encryption algorithm and the MAC verification into the decryption algorithm. We shall learn more about these algorithms later.

一些认证加密算法（如 AES-GCM 和 ChaCha20-Poly1305）将 MAC 计算集成到加密算法中，将MAC 验证集成到解密算法中。我们稍后将进一步了解这些算法。

The MAC is stored along with the ciphertext and it does not reveal the password or the original message. Storing the MAC code, visible to anyone is safe, and after decryption, we know whether the message is the original one or not (wrong password).

MAC 与密文一起存储不会揭示密码或原始消息。存储任何人都能看到的 MAC 码是安全的，解密后，我们可以知道消息是否是原始消息（密码是否正确）。

基于 MAC 的伪随机发生器

Another application of MAC codes is for pseudo-random generator functions. We can start from certain salt (constant number or the current date and time or some other randomness) and some seed number (last random number generated, e.g. 0). We can calculate the next_seed as follows:

MAC 码的另一个应用是用于伪随机发生器函数。我们可以从某个盐（常数或当前日期和时间或其他一些随机数）和某个种子数（最近生成的随机数，例如 0）开始。我们可以如下计算下一个种子：

next_seed = MAC(salt, seed)

This next pseudo-random number is "randomly changed" after each calculation of the above formula and we can use it to generate the next random number in certain range. We shall demonstrated a fully working example in the "Secure Random Generators" chapter.

在上述公式每次计算之后，该下一个伪随机数将“随机更改”，我们可以使用它来生成特定范围内的下一个随机数。我们将在“安全随机生成器”一章中演示一个完整的示例。

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