java secure socket without authentication?

Question

I have a trivial secure socket server-client program.
For the server certificates, I created a keystore using keytool.
When I try to connect to the server by my client I get these exceptions:
In server:

Exception in thread "main" javax.net.ssl.SSLHandshakeException: Received fatal alert: certificate_unknown

In client:

Exception in thread "main" 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.net.ssl.internal.ssl.Alerts.getSSLException(Unknown Source)

If my understanding is correct, these exceptions are caused due to the fact, that I am using certificates I created.
My question is the following:
If I set in the enabled cipher suites, both in server and in client, all the *_anon* cipher suites, shouldn't this solved the problem?
I mean If I enable the *_anon_* cipher suites then no authentication would be needed hence no exceptions.
Is this correct?
Because I still get exceptions. I tried having in the enabled cipher suites all the enabled+the _anon ones. No success. I tried setting only the anon ones and got a new exception:

Exception in thread "main" java.lang.IllegalArgumentException: Name must not be null

Could someone please explain why I get these exceptions, with the anon cipher suites?
Note:
If I set on the client the system property javax.net.ssl.trustStore pointing to the keystore I created and being used by my server, the communication is fine!
The program works with no exceptions and the data are send ok, from client to server.

---

UPDATE:
This is the snippet I use to enable the anon ciphers (I have done this for server and client part):

String[] supported = server.getSupportedCipherSuites();
String[] anonCipherSuitesSupported = new String[supported.length];
int count = 0;

for(int i = 0; i < supported.length; i++)
{
    if(supported[i].indexOf("_anon_") > 0)
    {
        anonCipherSuitesSupported[count++] = supported[i];
    }
}

String[] oldEnabled = server.getEnabledCipherSuites();
String[] newEnabled = new String[oldEnabled.length + count];
System.arraycopy(oldEnabled, 0, newEnabled, 0, oldEnabled.length);
System.arraycopy(anonCipherSuitesSupported, 0, newEnabled, oldEnabled.length, count);
server.setEnabledCipherSuites(newEnabled);

The stack trace is on client side:

Exception in thread "main" 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.net.ssl.internal.ssl.Alerts.getSSLException(Unknown Source)
    at com.sun.net.ssl.internal.ssl.SSLSocketImpl.fatal(Unknown Source)
    at com.sun.net.ssl.internal.ssl.Handshaker.fatalSE(Unknown Source)
    at com.sun.net.ssl.internal.ssl.Handshaker.fatalSE(Unknown Source)
    at com.sun.net.ssl.internal.ssl.ClientHandshaker.serverCertificate(Unknown Source)
    at com.sun.net.ssl.internal.ssl.ClientHandshaker.processMessage(Unknown Source)
    at com.sun.net.ssl.internal.ssl.Handshaker.processLoop(Unknown Source)
    at com.sun.net.ssl.internal.ssl.Handshaker.process_record(Unknown Source)
    at com.sun.net.ssl.internal.ssl.SSLSocketImpl.readRecord(Unknown Source)
    at com.sun.net.ssl.internal.ssl.SSLSocketImpl.performInitialHandshake(Unknown Source)
    at com.sun.net.ssl.internal.ssl.SSLSocketImpl.writeRecord(Unknown Source)
    at com.sun.net.ssl.internal.ssl.AppOutputStream.write(Unknown Source)
    at sun.nio.cs.StreamEncoder.writeBytes(Unknown Source)
    at sun.nio.cs.StreamEncoder.implFlushBuffer(Unknown Source)
    at sun.nio.cs.StreamEncoder.implFlush(Unknown Source)
    at sun.nio.cs.StreamEncoder.flush(Unknown Source)
    at java.io.OutputStreamWriter.flush(Unknown Source)
    at com.client.SSLClient1.main(SSLClient1.java:58)
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(Unknown Source)
    at sun.security.validator.PKIXValidator.engineValidate(Unknown Source)
    at sun.security.validator.Validator.validate(Unknown Source)
    at com.sun.net.ssl.internal.ssl.X509TrustManagerImpl.validate(Unknown Source)
    at com.sun.net.ssl.internal.ssl.X509TrustManagerImpl.checkServerTrusted(Unknown Source)
    at com.sun.net.ssl.internal.ssl.X509TrustManagerImpl.checkServerTrusted(Unknown Source)
    ... 14 more
Caused by: sun.security.provider.certpath.SunCertPathBuilderException: unable to find valid certification path to requested target
    at sun.security.provider.certpath.SunCertPathBuilder.engineBuild(Unknown Source)
    at java.security.cert.CertPathBuilder.build(Unknown Source)
    ... 20 more

and on server side:

Exception in thread "main" javax.net.ssl.SSLHandshakeException: Received fatal alert: certificate_unknown
    at com.sun.net.ssl.internal.ssl.Alerts.getSSLException(Unknown Source)
    at com.sun.net.ssl.internal.ssl.Alerts.getSSLException(Unknown Source)
    at com.sun.net.ssl.internal.ssl.SSLSocketImpl.recvAlert(Unknown Source)
    at com.sun.net.ssl.internal.ssl.SSLSocketImpl.readRecord(Unknown Source)
    at com.sun.net.ssl.internal.ssl.SSLSocketImpl.performInitialHandshake(Unknown Source)
    at com.sun.net.ssl.internal.ssl.SSLSocketImpl.readDataRecord(Unknown Source)
    at com.sun.net.ssl.internal.ssl.AppInputStream.read(Unknown Source)
    at com.sun.net.ssl.internal.ssl.AppInputStream.read(Unknown Source)
    at com.server.SecureOrderTaker.main(SecureOrderTaker.java:92) 

Now if I simply do:

server.setEnabledCipherSuites(anonCipherSuitesSupported);

So that only the anon cipher suites are enabled I get:

Exception in thread "main" java.lang.IllegalArgumentException: Name must not be null
    at com.sun.net.ssl.internal.ssl.CipherSuite.valueOf(Unknown Source)
    at com.sun.net.ssl.internal.ssl.CipherSuiteList.<init>(Unknown Source)
    at com.sun.net.ssl.internal.ssl.SSLServerSocketImpl.setEnabledCipherSuites(Unknown Source)
    at com.server.SecureOrderTaker.main(SecureOrderTaker.java:82)

Thank you