A Detailed Guide to the ECDSA Algorithm with Java Spring Boot and Bouncy Castle
Kāshān Asim
Sr. Software Developer: SpringBoot || Angular || ApacheSpark || Scala || PKI || eSignature
Introduction to ECDSA
Elliptic Curve Digital Signature Algorithm (ECDSA) is a cryptographic algorithm used for digital signatures. It is a variant of the Digital Signature Algorithm (DSA) that uses elliptic curve cryptography (ECC). ECDSA is widely used in various security protocols such as TLS, SSL, and blockchain technologies like Bitcoin and Ethereum due to its strong security with relatively small key sizes, making it efficient in terms of performance and resource usage.
How ECDSA Works
ECDSA involves three primary steps:
1. Key Generation:
- A private key is randomly selected from a large set of possible keys.
- A public key is then generated from the private key using elliptic curve point multiplication.
2. Signing:
- The signing process involves creating a digital signature using the private key. The message to be signed is first hashed using a cryptographic hash function (e.g., SHA-256). The hash value is then combined with the private key and a random number to produce the signature.
3. Verification:
- The verification process involves checking the signature against the message and the signer's public key. If the signature is valid, it confirms that the message has not been tampered with and was indeed signed by the holder of the corresponding private key.
The Math Behind ECDSA
1. Key Generation:
- Select a random integer d, where \(1 \leq d \leq n-1\), where n is the order of the elliptic curve.
- Calculate the public key Q as \(Q = d \times G\), where G is the base point on the curve.
2. Signing:
- Compute \(z = \text{HASH}(m)\), where m is the message.
- Select a random integer k, where \(1 \leq k \leq n-1\).
- Compute the point \(R = k \times G\), where R is a point on the elliptic curve.
- Compute \(r = R_x \mod n\), where \(R_x\) is the x-coordinate of point R.
- Compute \(s = k^{-1}(z + r \times d) \mod n\).
- The signature is the pair \((r, s)\).
3. Verification:
- Compute \(z = \text{HASH}(m)\).
- Compute \(w = s^{-1} \mod n\).
- Compute \(u_1 = z \times w \mod n\) and \(u_2 = r \times w \mod n\).
- Compute the point \(P = u_1 \times G + u_2 \times Q\).
- Compute \(v = P_x \mod n\).
- The signature is valid if \(v = r\).
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Using ECDSA with Java Spring Boot and Bouncy Castle
To implement ECDSA in a Java Spring Boot application, we can use the Bouncy Castle library, which provides comprehensive support for cryptographic operations, including ECDSA.
Step 1: Setting Up Bouncy Castle
Add the Bouncy Castle dependency to your pom.xml:
<dependency>
<groupId>org.bouncycastle</groupId>
<artifactId>bcprov-jdk15on</artifactId>
<version>1.70</version>
</dependency>
Step 2: Generating ECDSA Keys
import org.bouncycastle.jce.provider.BouncyCastleProvider;
import java.security.KeyPair;
import java.security.KeyPairGenerator;
import java.security.Security;
import java.security.spec.ECGenParameterSpec;
public class ECDSAKeyGenerator {
static {
Security.addProvider(new BouncyCastleProvider());
}
public static KeyPair generateECDSAKeyPair() throws Exception {
KeyPairGenerator keyPairGenerator = KeyPairGenerator.getInstance("ECDSA", "BC");
ECGenParameterSpec ecSpec = new ECGenParameterSpec("secp256r1");
keyPairGenerator.initialize(ecSpec);
return keyPairGenerator.generateKeyPair();
}
public static void main(String[] args) throws Exception {
KeyPair keyPair = generateECDSAKeyPair();
System.out.println("Private Key: " + keyPair.getPrivate());
System.out.println("Public Key: " + keyPair.getPublic());
}
}
Step 3: Signing a Message
import org.bouncycastle.jce.provider.BouncyCastleProvider;
import java.security.PrivateKey;
import java.security.Signature;
import java.security.Security;
import java.util.Base64;
public class ECDSASignature {
static {
Security.addProvider(new BouncyCastleProvider());
}
public static String signMessage(String message, PrivateKey privateKey) throws Exception {
Signature signature = Signature.getInstance("SHA256withECDSA", "BC");
signature.initSign(privateKey);
signature.update(message.getBytes());
byte[] signatureBytes = signature.sign();
return Base64.getEncoder().encodeToString(signatureBytes);
}
}
Step 4: Verifying a Signature
import org.bouncycastle.jce.provider.BouncyCastleProvider;
import java.security.PublicKey;
import java.security.Signature;
import java.security.Security;
import java.util.Base64;
public class ECDSAVerification {
static {
Security.addProvider(new BouncyCastleProvider());
}
public static boolean verifySignature(String message, String signatureStr, PublicKey publicKey) throws Exception {
Signature signature = Signature.getInstance("SHA256withECDSA", "BC");
signature.initVerify(publicKey);
signature.update(message.getBytes());
byte[] signatureBytes = Base64.getDecoder().decode(signatureStr);
return signature.verify(signatureBytes);
}
}
Step 5: Integrating with Spring Boot
You can easily integrate these ECDSA operations into your Spring Boot application. For example, you can create a REST controller to handle signing and verifying messages:
import org.springframework.web.bind.annotation.*;
@RestController
@RequestMapping("/ecdsa")
public class ECDSAController {
private final KeyPair keyPair;
public ECDSAController() throws Exception {
this.keyPair = ECDSAKeyGenerator.generateECDSAKeyPair();
}
@PostMapping("/sign")
public String signMessage(@RequestBody String message) throws Exception {
return ECDSASignature.signMessage(message, keyPair.getPrivate());
}
@PostMapping("/verify")
public boolean verifySignature(@RequestBody SignatureRequest request) throws Exception {
return ECDSAVerification.verifySignature(request.getMessage(), request.getSignature(), keyPair.getPublic());
}
public static class SignatureRequest {
private String message;
private String signature;
// Getters and setters omitted for brevity
}
}
Understanding the Bouncy Castle Provider
Bouncy Castle is an open-source cryptography library that provides a wide range of cryptographic operations, including support for elliptic curve algorithms like ECDSA. The Bouncy Castle provider is used in Java to enhance the standard JCA (Java Cryptography Architecture) with additional algorithms and features. It is highly regarded for its comprehensive support, strong security practices, and regular updates.
To use Bouncy Castle as a provider, you typically need to add it to the list of security providers in your Java environment:
Security.addProvider(new BouncyCastleProvider());
This ensures that Bouncy Castle is used for cryptographic operations like key generation, signing, and verification.
Conclusion
ECDSA is a powerful and efficient algorithm for digital signatures, especially suitable for systems requiring strong security with limited computational resources. By leveraging the Bouncy Castle library in a Java Spring Boot application, you can easily implement ECDSA for secure message signing and verification. This guide provides a foundation for working with ECDSA in Java, allowing you to build more secure and robust applications.