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If you prefer not to use Bouncy Castle for SCrypt and want to rely on the standard Java libraries, you can use the `javax.crypto.SecretKeyFactory` with the `PBKDF2WithHmacSHA256` algorithm for the KDF, and then use `java.security.MessageDigest` for SHA-256 hashing. Here's an example:

```java
import javax.crypto.SecretKeyFactory;
import javax.crypto.spec.PBEKeySpec;
import java.security.MessageDigest;
import java.security.NoSuchAlgorithmException;
import java.security.spec.InvalidKeySpecException;
import java.security.spec.KeySpec;
import java.util.Arrays;

public class KDFWithPBKDF2AndSHA256Example {

    public static void main(String[] args) throws NoSuchAlgorithmException, InvalidKeySpecException {
        // Replace with your secret key (derived from ECDH or any other source)
        byte[] secretKeyBytes = hexStringToByteArray("yourSecretKeyInHex");

        // Salt for PBKDF2
        byte[] salt = generateSalt();

        // PBKDF2 parameters
        int iterationCount = 10000; // You can adjust this based on your security requirements
        int keyLength = 32; // for a 256-bit key

        // Use PBKDF2 to derive a key
        SecretKeyFactory factory = SecretKeyFactory.getInstance("PBKDF2WithHmacSHA256");
        KeySpec spec = new PBEKeySpec(byteArrayToCharArray(secretKeyBytes), salt, iterationCount, keyLength * 8);
        byte[] derivedKey = factory.generateSecret(spec).getEncoded();

        // Hash the derived key with SHA-256
        byte[] hashedKey = hashWithSHA256(derivedKey);

        // Print the final key
        System.out.println("Final Key: " + byteArrayToHexString(hashedKey));
    }

    private static byte[] generateSalt() {
        // Replace this with a secure method of generating salt
        // For example, you can use SecureRandom:
        // SecureRandom random = new SecureRandom();
        // byte[] salt = new byte[16];
        // random.nextBytes(salt);
        // return salt;
        return hexStringToByteArray("yourSaltInHex");
    }

    private static byte[] hashWithSHA256(byte[] input) throws NoSuchAlgorithmException {
        MessageDigest digest = MessageDigest.getInstance("SHA-256");
        return digest.digest(input);
    }

    private static byte[] hexStringToByteArray(String hex) {
        int len = hex.length();
        byte[] data = new byte[len / 2];
        for (int i = 0; i < len; i += 2) {
            data[i / 2] = (byte) ((Character.digit(hex.charAt(i), 16) << 4)
                    + Character.digit(hex.charAt(i + 1), 16));
        }
        return data;
    }

    private static char[] byteArrayToCharArray(byte[] byteArray) {
        char[] charArray = new char[byteArray.length];
        for (int i = 0; i < byteArray.length; i++) {
            charArray[i] = (char) (byteArray[i] & 0xFF);
        }
        return charArray;
    }

    private static String byteArrayToHexString(byte[] byteArray) {
        StringBuilder result = new StringBuilder();
        for (byte b : byteArray) {
            result.append(String.format("%02X", b));
        }
        return result.toString();
    }
}
```

This example uses the PBKDF2 algorithm with HMAC-SHA-256 for key derivation and SHA-256 for hashing without relying on Bouncy Castle. Remember to replace "yourSecretKeyInHex" and "yourSaltInHex" with the actual secret key and salt in hexadecimal form. Handle exceptions and errors appropriately in a production environment.