Self signed X509 Certificate with Bouncy Castle in Java

Using Bouncycastle latest version – 1.55 1.66

Update to the answer by @Bewusstsein. The bouncycastle classes are deprecated in the latest version as of this answer (5/11/2017). If you are using version 1.55 or later:

public static Certificate selfSign(KeyPair keyPair, String subjectDN) throws OperatorCreationException, CertificateException, IOException
{
    Provider bcProvider = new BouncyCastleProvider();
    Security.addProvider(bcProvider);

    long now = System.currentTimeMillis();
    Date startDate = new Date(now);

    X500Name dnName = new X500Name(subjectDN);
    BigInteger certSerialNumber = new BigInteger(Long.toString(now)); // <-- Using the current timestamp as the certificate serial number

    Calendar calendar = Calendar.getInstance();
    calendar.setTime(startDate);
    calendar.add(Calendar.YEAR, 1); // <-- 1 Yr validity

    Date endDate = calendar.getTime();

    String signatureAlgorithm = "SHA256WithRSA"; // <-- Use appropriate signature algorithm based on your keyPair algorithm.

    ContentSigner contentSigner = new JcaContentSignerBuilder(signatureAlgorithm).build(keyPair.getPrivate());

    JcaX509v3CertificateBuilder certBuilder = new JcaX509v3CertificateBuilder(dnName, certSerialNumber, startDate, endDate, dnName, keyPair.getPublic());

    // Extensions --------------------------

    // Basic Constraints
    BasicConstraints basicConstraints = new BasicConstraints(true); // <-- true for CA, false for EndEntity

    certBuilder.addExtension(new ASN1ObjectIdentifier("2.5.29.19"), true, basicConstraints); // Basic Constraints is usually marked as critical.

    // -------------------------------------

    return new JcaX509CertificateConverter().setProvider(bcProvider).getCertificate(certBuilder.build(contentSigner));
}