preface
Thanks to great mathematicians and cryptographers, our networks are in a relatively safe environment.
In a recent review of HTTPS, all the analysis in this article is based on TLS1.2.
WebTrust
WebTrust is a security audit standard jointly formulated by the world’s two famous CPA associations AICPA (American Institute of Certified Public Accountants) and CICA (Canadian Institute of Certified Public Accountants). It mainly examines and authenticates the security and confidentiality of Internet service providers’ system and business operation logic in a total of seven aspects. Only the root certificate authenticated by WebTrust can be pre-installed in mainstream browsers.
CA institution
CA mechanism Definition
Certificate Authority (CA) is an organization that issues digital certificates. It is the authority responsible for issuing and managing digital certificates, and as a trusted third party in e-commerce transactions, it undertakes the responsibility of verifying the validity of public keys in the public key system.
What CA organizations are there
At present, the mainstream CA organizations in the world include Comodo, Symantec, GeoTrust, DigiCert, Thawte, GlobalSign, RapidSSL, etc. Symantec and GeoTrust are both subsidiaries of DigiCert. At present, the mainstream SSL certificate brands in the market are Comodo certificate, Symantec certificate, GeoTrust certificate, Thawte certificate and RapidSSL certificate, and some unknown certificate bodies can also issue digital certificates.
The main CA institutions in China are CFCA, WoSign, GDCA and AnTruet, etc.
Symmetric encryption
define
In the encryption method of single-key cryptosystem, the same key can be used to encrypt and decrypt information at the same time. This encryption method is called symmetric encryption, also called single-key encryption.
Common encryption algorithms
DES, AES, RC2, RC4, and RC5
The sample
public class DES {
public static String encrypt(String content, String key) {
try {
byte[] encryptionBytes = content.getBytes("UTF-8");
SecureRandom random = new SecureRandom();
DESKeySpec desKey = new DESKeySpec(key.getBytes());
SecretKeyFactory keyFactory = SecretKeyFactory.getInstance("DES");
SecretKey secureKey = keyFactory.generateSecret(desKey);
Cipher cipher = Cipher.getInstance("DES");
cipher.init(Cipher.ENCRYPT_MODE, secureKey, random);
byte[] encryptionBase64Bytes = Base64.getEncoder().encode(cipher.doFinal(encryptionBytes));
return new String(encryptionBase64Bytes);
} catch (Exception e) {
e.printStackTrace();
}
return null;
}
public static String decrypt(String content, String key) {
try {
byte[] decryptionBytes = Base64.getDecoder().decode(content);
SecureRandom random = new SecureRandom();
DESKeySpec desKey = new DESKeySpec(key.getBytes());
SecretKeyFactory keyFactory = SecretKeyFactory.getInstance("DES");
SecretKey secureKey = keyFactory.generateSecret(desKey);
Cipher cipher = Cipher.getInstance("DES");
cipher.init(Cipher.DECRYPT_MODE, secureKey, random);
return new String(cipher.doFinal(decryptionBytes), "UTF-8");
} catch (Exception e) {
e.printStackTrace();
}
return null;
}
public static void main(String[] args) {
final String key = "this_is_key";
String content = "Leave at nine.";
String encryptStr = DES.encrypt(content, key);
System.out.println("Encrypt:" + encryptStr);
String decryptStr = DES.decrypt(encryptStr, key);
System.out.println("Decrypt:"+ decryptStr); }}Copy the code
1. Li Lei wants to send a message to Han Meimei, and they agree to use symmetric encryption to encrypt the message
Li Lei encrypts the message with the key and sends it to Han Meimei
3, Han Meimei decrypts with the same key, and then sees the message sent to her by Li Lei
As you can see, with the above approach, once the key is compromised, the message is easily cracked
Asymmetric encryption
define
Symmetric encryption algorithms use the same secret key for encryption and decryption, whereas asymmetric encryption algorithms require two keys for encryption and decryption: a public key and a private key.
Common encryption algorithms
RSA, ECC, etc
The sample
public class RSA {
private static Cipher cipher;
static {
try {
cipher = Cipher.getInstance("RSA");
} catch (NoSuchAlgorithmException e) {
e.printStackTrace();
} catch(NoSuchPaddingException e) { e.printStackTrace(); }}public static void generateKeyPair(a) {
try {
KeyPairGenerator keyPairGenerator = KeyPairGenerator.getInstance("RSA");
keyPairGenerator.initialize(2048);
KeyPair keyPair = keyPairGenerator.generateKeyPair();
PublicKey publicKey = keyPair.getPublic();
PrivateKey privateKey = keyPair.getPrivate();
String publicKeyStr = getKeyString(publicKey);
String privateKeyStr = getKeyString(privateKey);
System.out.println("publicKeyStr :" + publicKeyStr);
System.out.println("privateKeyStr :" + privateKeyStr);
} catch(Exception e) { e.printStackTrace(); }}public static PublicKey getPublicKey(String key) throws Exception {
byte[] keyBytes = Base64.decode(key);
X509EncodedKeySpec keySpec = new X509EncodedKeySpec(keyBytes);
KeyFactory keyFactory = KeyFactory.getInstance("RSA");
PublicKey publicKey = keyFactory.generatePublic(keySpec);
return publicKey;
}
public static PrivateKey getPrivateKey(String key) throws Exception {
byte[] keyBytes = Base64.decode(key);
PKCS8EncodedKeySpec keySpec = new PKCS8EncodedKeySpec(keyBytes);
KeyFactory keyFactory = KeyFactory.getInstance("RSA");
PrivateKey privateKey = keyFactory.generatePrivate(keySpec);
return privateKey;
}
public static String getKeyString(Key key) {
byte[] keyBytes = key.getEncoded();
return Base64.encode(keyBytes);
}
public static String encrypt(String publicKey, String content) {
try {
cipher.init(Cipher.ENCRYPT_MODE, getPublicKey(publicKey));
byte[] encryptBytes = cipher.doFinal(content.getBytes());
return Base64.encode(encryptBytes);
} catch (Exception e) {
e.printStackTrace();
}
return null;
}
public static String decrypt(String privateKey, String content) {
try {
cipher.init(Cipher.DECRYPT_MODE, getPrivateKey(privateKey));
byte[] decryptBytes = cipher.doFinal(Base64.decode(content));
return new String(decryptBytes);
} catch (Exception e) {
e.printStackTrace();
}
return null;
}
public static void main(String[] args) {
// generateKeyPair();
final String publicKey = "Generated using generateKeyPair";
final String privateKey = "Generated using generateKeyPair";
String content = "Leave at nine.";
String encryptStr = encrypt(publicKey, content);
System.out.println("Encrypt:" + encryptStr);
String decryptStr = decrypt(privateKey, encryptStr);
System.out.println("Decrypt:"+ decryptStr); }}Copy the code
1. Li Lei wants to send a message to Han Meimei, and they agree to use asymmetric encryption to encrypt the message
2, Li Lei first to get han Meimei’s public key
2. Li Lei encrypts the message with Han Meimei’s public key and sends it to Han Meimei
3, Han Meimei decrypts with her private key, and then sees the message sent to her by Li Lei
Han Meimei sends a message to Li Lei.
A digital signature
Digital Signature is a method of identifying Digital information that functions like ordinary signatures written on paper but uses public key cryptography. A set of digital signatures typically defines two complementary operations, one for signing and one for validation. Normally we use public key encryption and private key decryption. In digital signatures, we use private key encryption (equivalent to generating a signature) and public key decryption (equivalent to verifying a signature). The message can be signed directly (that is, encrypted with a private key for the purpose of signature, not secrecy), and the verifier decrypts the message correctly with the public key. If it matches the original message, the signature is verified successfully. But we usually sign the hash value of the message, because the hash value is usually much shorter than the original message, making the signature (asymmetric encryption) much more efficient. Note that calculating the hash value of the message is not a necessary step in digital signature.
The TLS and SSL
TLS (Transport Layer Security) and its predecessor SSL (Secure Sockets Layer) are Security protocols designed to ensure the Security and data integrity of Internet communications.
Let’s go to my blog democome.com/ and use WireShark to capture the TLS handshake.
WireShark TLS handshake for packet capture
TLS handshake includes RSA handshake and ECDH handshake. Through my packet capture analysis below, the ECDH handshake is used in the following example. The WireShark is used to filter IP addresses
DST == 185.199.109.153 or ip.src == 185.199.109.153
The TLS handshake process is shown as follows. For now, we only pay attention to the packet capture information with Protocol TLSv1.2:
According to the figure above, we can find that the TLS handshake process is mainly divided into the following steps.
- Client Hello
- Server Hello
- Certificate
- Server Key Exchange
- Client Key Exchange
Which involves symmetric encryption, asymmetric encryption and other algorithms, we will analyze each step.
Client Hello
The browser sends it to the server
We need to focus on the following:
- The TLS version: 1.2
- Random number: Radnom
- Cipher Suites supported by the browser
As you can see, there are 17 Cipher Suites supported by the browser, and the server chooses one of them. The random number is used in the final calculation of the master key, which is used for symmetric encryption.
Server Hello
The server sends it to the browser
- Random number: Radnom
- Cipher Suite for the server
The encryption suite selected by the server is TLS_ECDHE_RSA_WITH_AES_128_GCM_SHA256
Let’s look at what each part means
ECDHE: key negotiation algorithm
RSA: indicates the certificate public key encryption algorithm
AES_128: indicates the password length of the symmetric encryption algorithm and AES
GCM: AES encryption mode
SHA256: Message digest algorithm for validating messages (hash algorithm)
Certificate
The server sends it to the browser
The Server selects an encryption suite during Server Hello. The server delivers a certificate, which carries the CA certificate chain and the certificate public key. There is a root CA certificate at the top of the certificate chain, which is stored in the browser or operating system and trusted by the system.
Let’s look at the certificate chain in the browser as follows:
Then take a look at the macOS system root certificate and you can see that the uppermost certificate is trusted by the system.
The browser validates the server certificate by first finding the intermediate certificate Authority (Let’s Encrypt Authority X3) that found the Democome.com certificate, and then going up to the Root certificate (DST Root CA X3).
The digital signature is then verified from the root certificate down. In this example, DST Root CA X3’s public key is used to verify the digital signature of the Let’s Encrypt Authority X3 certificate. Verify the digital signature of the server certificate Democome.com using the public key of the Let’s Encrypt Authority X3 certificate. If any part of the validation process fails, the certificate is invalid.
The information for the Certificate step is as follows
The public key of the certificate is shown as follows:
The signature of the certificate is as follows:
A certificate’s signature is used to ensure that the certificate has not been tampered with.
Server Key Exchange
The server sends it to the browser
The selected encryption suite is as follows: TLS_ECDHE_RSA_WITH_AES_128_GCM_SHA256 Elliptic Curve Diffie Hellman Ephemeral (ECDHE) is used for key negotiation. Elliptic curve encryption is involved here. Elliptic Curve Cryptography (ECC) is a public key encryption algorithm based on Elliptic Curve mathematics. The main advantage of ECC is that in some cases it uses smaller keys than other algorithms (such as RSA encryption algorithms) and provides an equivalent or higher level of security.
Ecdiffie-hellman Server Params Named Curve X25519 Server Key Exchange Its principle can be simply understood as follows:
Li Lei and Han Meimei are still writing letters
1. Li Lei uses his own private key
2. Han Meimei uses her own private key
3. According to the calculation rules of elliptic curve, both parties jointly calculate it
This allows symmetric encryption, and the encrypted key has never been passed over the network. This is actually calculated
The Pubkey in the figure above can be understood as a point on an ellipse calculated by the server.
The following content is mainly about some mathematical principles of elliptic curve encryption algorithm. If you are not interested, you can ignore it and go directly to the Client Key Exchange step.
DH algorithm
Diffie-hellman Key Exchange (DH) Enables two parties to create a key through an insecure channel without any prior information about the other party. This key can be used as a symmetric key to encrypt communication content in subsequent communication.
To explain briefly, suppose the two sides of the correspondence are Li Lei and Han Meimei
Prerequisites:
It’s Li Lei’s private key,
It’s Han Meimei’s private key.
It’s a prime number. It’s public
是
Negotiation process:
Step 1: Li Lei according to his private key
Step 2: Li Leijiang
The third step: Han Meimei according to his private key
Step 4: Han Meimei puts her own public key
Step 5: Li Lei calculates the key of symmetric encryption
Step 6: Han Meimei calculates the key of symmetric encryption
From the derivation of the figure above, we know the final calculation
Specific examples:
Li Lei and Han Meimei agreement for use
You can see the key for symmetric encryption
ECC algorithm
Elliptic Curve Cryptography (ECC) is a public key encryption algorithm based on Elliptic Curve mathematics. The main advantage of ECC is that in some cases it uses smaller keys than other algorithms (such as RSA encryption algorithms) and provides an equivalent or higher level of security.
The equation of an elliptic curve is as follows:
The function graph of an elliptic curve is as follows:
You can see it’s symmetric about the X axis.
Elliptic curve operation
Points A and B on the curve intersect with the elliptic curve at point C, which is symmetric about axis A and intersects with the elliptic curve at point A+B.
So let’s take A special case of addition, if A is equal to B, if A (B) is the tangent point of the elliptic curve, and then we repeat this and we get A plus A is equal to 2A.
The point at which A is symmetric with respect to the X-axis is defined as minus A.
Here are two motion pictures that illustrate the process:
A+B = C
A+C = D
A+D = E
The overlap between A and B is shown as follows:
There are more than the
A finite field of elliptic curves
Elliptic curve encryption algorithm does not use real number field, but uses finite field, so we define elliptic curve on finite field.
with
Example: Add our curve is
point
So the point
So this is the discretized point. The process of using elliptic curve to encrypt communication is as follows (the reasoning process is presented here, which involves complex operation and requires more mathematical knowledge, and I am still studying) :
1. Li Lei chooses a curve
2. Li Lei selects a private key
3. Li Leiba
4. Han Meimei gets the above information and codes the plaintext to
5, Han Meimei calculation
6. Han Meimei
7. After Receiving the information, Li Lei calculated
because
Mathematical concept
Finite field
In mathematics, a finite field is a field containing a finite number of elements. Like any other field, a finite field is a set of well-defined operations that satisfy certain rules for addition, subtraction, multiplication and division. The most common example of a finite field is when
Group of
A group in mathematics is a set that defines a binary operation (which we call addition, denoted by the sign +). If I want to set the
1. Closure: if
2. Associative law
3. There is an identity element (note: in binary operations, the identity element refers to the element that does not change its value when operating with any element. Take real numbers as an example, the identity element of multiplication is 1 and that of addition is 0)
4. Every element has an inverse element, that is, for any element
If we add a fifth requirement:
5. Commutative law:
So this group is the Abelian group.
Curve25519
In cryptography, Curve25519 is an elliptic curve designed for use in the elliptic curve diffier-hermann (ECDH) key exchange method. It is one of the fastest ECC curves not covered by any known patent.
Curve25519 elliptic curve equation is:
ECDH
Taking Li Lei and Han Meimei as examples, the exchange content of DH is changed to the point on the curve
When Curve25519 is selected as an elliptic curve, the parameters are determined and so is G, so only the public keys of both sides can be exchanged.
Client Key Exchange
The browser sends it to the server
Similarly, Pubkey here can be interpreted as a point on an ellipse computed by the browser. This step is similar to Server Key Exchange in that it calculates the Key for symmetric encryption.
Symmetric encrypted communication
With this foundation, the browser can calculate a symmetric encryption key, and the server can calculate a symmetric encryption key, which is guaranteed to be the same even though the two keys are not transmitted over the network. Then you can use this key to encrypt and transfer it over the network.
The above is the basic process of TLS handshake, which ensures the security of data transmission over the network.
X.509
X.509 is the standard format for public key certificates in cryptography. X.509 certificates are used in many network protocols, including TLS/SSL, and in many off-line applications, such as electronic signature services. X.509 certificates contain public keys, identity information (such as network host names, organization names, or individual names), and signature information (either signed by the CA or self-signed). For a certificate that has been signed by a trusted certificate authority or that can be otherwise verified, the certificate owner can use the certificate and the corresponding private key to create secure communication and digitally sign the document.
tool
Online drawing tool
Refer to the article
SSL certificate CA authority
Digital Certificates and network security
What is a digital signature?
Elliptic curve encryption
Curve25519
A simple introduction to elliptic curve cryptography
TLS handshake process
Talk about the HTTPS
ECC elliptic curve encryption and decryption principle
ECC Elliptic curve encryption algorithm: Introduction
Beginner on the road: Elliptic curves and Group Theory on real numbers
Fundamentals of cryptography 2: Analysis of the principles of elliptic curve cryptography
HTTPS — key calculation in TLS
Finite field