Busqué varias publicaciones relacionadas aquí y en otros lugares, pero ninguna de ellas resolvió mi problema. Tengo un programa que envía correos electrónicos a un conjunto de personas que usan "API de javamail". Funcionó bien una vez. Hoy volví a necesitarlo, pero no puedo enviar ningún correo electrónico ... Mi método de envío de correo electrónico es el siguiente:

public void sendEmail(String userName, String password, String toAddress, 
       String subject, String message, String[] attachFiles) 
       throws AddressException, MessagingException {

     // sets SMTP properties
    Properties properties = new Properties();
    properties.put("mail.smtp.host", "smtp.gmail.com");
    properties.put("mail.smtp.port", "587");
    properties.put("mail.smtp.auth", "true");
    properties.put("mail.smtp.starttls.enable", "true");
    properties.put("mail.user", userName);
    properties.put("mail.password", password);

    // creates a new session with an authenticator
    Authenticator auth = new SMTPAuthenticator(userName, password);
    Session session = Session.getInstance(properties, auth);

    // creates a new e-mail message
    MimeMessage msg = new MimeMessage(session);

    try {
        msg.setFrom(new InternetAddress(userName, "My name"));
    } catch (UnsupportedEncodingException e) {
        e.printStackTrace();
    }
    InternetAddress[] toAddresses = {new InternetAddress(toAddress)};        
    msg.setRecipients(Message.RecipientType.TO, toAddresses);
    msg.setSubject(subject);
    msg.setSentDate(new Date());

    // creates message part
    MimeBodyPart messageBodyPart = new MimeBodyPart();
    messageBodyPart.setContent(message, "text/html");

    // creates multi-part
    Multipart multipart = new MimeMultipart();
    multipart.addBodyPart(messageBodyPart);       

    // adds attachments
    if (attachFiles != null && attachFiles.length > 0) {
        for (String filePath : attachFiles) {
            addAttachment(multipart, filePath);
        }
    }

    // sets the multi-part as e-mail's content
    msg.setContent(multipart);

    // sends the e-mail
    Transport.send(msg);

}

Entonces, ahora el intento de llamar a este método recibí el siguiente error (estoy usando jdk 1.7.0_21):

Sending email Failed...

javax.mail.MessagingException: Could not convert socket to TLS;
  nested exception is:
    javax.net.ssl.SSLHandshakeException: sun.security.validator.ValidatorException: PKIX path building failed: sun.security.provider.certpath.SunCertPathBuilderException: unable to find valid certification path to requested target
    at com.sun.mail.smtp.SMTPTransport.startTLS(SMTPTransport.java:1907)
    at com.sun.mail.smtp.SMTPTransport.protocolConnect(SMTPTransport.java:666)
    at javax.mail.Service.connect(Service.java:367)
    at javax.mail.Service.connect(Service.java:226)
    at javax.mail.Service.connect(Service.java:175)
    at javax.mail.Transport.send0(Transport.java:253)
    at javax.mail.Transport.send(Transport.java:124)
    at EmailSender.sendEmail(EmailSender.java:86)
    at CFP_LaWasp_EmailSender.sendCFPLaWasp(CFP_LaWasp_EmailSender.java:178)
    at CFP_LaWasp_EmailSender.main(CFP_LaWasp_EmailSender.java:220)
Caused by: javax.net.ssl.SSLHandshakeException: sun.security.validator.ValidatorException: PKIX path building failed: sun.security.provider.certpath.SunCertPathBuilderException: unable to find valid certification path to requested target
    at sun.security.ssl.Alerts.getSSLException(Alerts.java:192)
    at sun.security.ssl.SSLSocketImpl.fatal(SSLSocketImpl.java:1886)
    at sun.security.ssl.Handshaker.fatalSE(Handshaker.java:276)
    at sun.security.ssl.Handshaker.fatalSE(Handshaker.java:270)
    at sun.security.ssl.ClientHandshaker.serverCertificate(ClientHandshaker.java:1341)
    at sun.security.ssl.ClientHandshaker.processMessage(ClientHandshaker.java:153)
    at sun.security.ssl.Handshaker.processLoop(Handshaker.java:868)
    at sun.security.ssl.Handshaker.process_record(Handshaker.java:804)
    at sun.security.ssl.SSLSocketImpl.readRecord(SSLSocketImpl.java:1016)
    at sun.security.ssl.SSLSocketImpl.performInitialHandshake(SSLSocketImpl.java:1312)
    at sun.security.ssl.SSLSocketImpl.startHandshake(SSLSocketImpl.java:1339)
    at sun.security.ssl.SSLSocketImpl.startHandshake(SSLSocketImpl.java:1323)
    at com.sun.mail.util.SocketFetcher.configureSSLSocket(SocketFetcher.java:528)
    at com.sun.mail.util.SocketFetcher.startTLS(SocketFetcher.java:465)
    at com.sun.mail.smtp.SMTPTransport.startTLS(SMTPTransport.java:1902)
    ... 9 more
Caused by: sun.security.validator.ValidatorException: PKIX path building failed: sun.security.provider.certpath.SunCertPathBuilderException: unable to find valid certification path to requested target
    at sun.security.validator.PKIXValidator.doBuild(PKIXValidator.java:385)
    at sun.security.validator.PKIXValidator.engineValidate(PKIXValidator.java:292)
    at sun.security.validator.Validator.validate(Validator.java:260)
    at sun.security.ssl.X509TrustManagerImpl.validate(X509TrustManagerImpl.java:326)
    at sun.security.ssl.X509TrustManagerImpl.checkTrusted(X509TrustManagerImpl.java:231)
    at sun.security.ssl.X509TrustManagerImpl.checkServerTrusted(X509TrustManagerImpl.java:126)
    at sun.security.ssl.ClientHandshaker.serverCertificate(ClientHandshaker.java:1323)
    ... 19 more
Caused by: sun.security.provider.certpath.SunCertPathBuilderException: unable to find valid certification path to requested target
    at sun.security.provider.certpath.SunCertPathBuilder.engineBuild(SunCertPathBuilder.java:196)
    at java.security.cert.CertPathBuilder.build(CertPathBuilder.java:268)
    at sun.security.validator.PKIXValidator.doBuild(PKIXValidator.java:380)
    ... 25 more

No sé cómo resolver este problema, ya que solía funcionar antes ... Además, no sé si mi Gmail tiene algo que ver con esto (si bloqueó este acceso ...)

Aprecio cualquier ayuda.