It is not possible to run slaves anymore using IBM Java.

This is due to the new encrypted communication introduced in Jenkins 1.653, where the handshake is done using "AES/CTR/PKCS5Padding".
I couldn't find what ciphers IBM Java does or doesn't support (maybe nothing else than the default ones), but I created a quick test to check (see below).

Would it be possible to switch to a cipher supported by IBM Java?

Test:
import java.security.NoSuchAlgorithmException;
import javax.crypto.Cipher;
import javax.crypto.NoSuchPaddingException;
public class PaddingIssue {
private static final String CIPHER = "AES/CTR/PKCS5Padding";
public static void main(String[] args) throws NoSuchAlgorithmException, NoSuchPaddingException

{ Cipher encryptCipher = Cipher.getInstance(CIPHER); System.out.println("Fine!"); }

}

Executions:
IBM JAVA 1.6
/usr/lib/j2re1.6-ibm/jre/bin/java PaddingIssue
Exception in thread "main" java.security.NoSuchAlgorithmException: Cannot find any provider supporting AES/CTR/PKCS5Padding
at javax.crypto.Cipher.getInstance(Unknown Source)
at PaddingIssue.main(PaddingIssue.java:10)
Caused by: javax.crypto.NoSuchPaddingException: CTR mode must be used with ISO10126Padding or NoPadding
at com.ibm.crypto.provider.AESCipher.engineSetPadding(Unknown Source)
at javax.crypto.Cipher$a.a(Unknown Source)
... 2 more

IBM JAVA 1.7
/usr/lib/j2re1.7-ibm/jre/bin/java PaddingIssue
Exception in thread "main" java.security.NoSuchAlgorithmException: Cannot find any provider supporting AES/CTR/PKCS5Padding
at javax.crypto.Cipher.getInstance(Unknown Source)
at PaddingIssue.main(PaddingIssue.java:10)
Caused by: javax.crypto.NoSuchPaddingException: CTR mode must be used with ISO10126Padding or NoPadding
at com.ibm.crypto.provider.AESCipher.engineSetPadding(Unknown Source)
at javax.crypto.Cipher$a.a(Unknown Source)
... 2 more

IBM JAVA 1.8
/usr/lib/jvm/java-ibm-x86_64-80/jre/bin/java PaddingIssue
Exception in thread "main" java.security.NoSuchAlgorithmException: Cannot find any provider supporting AES/CTR/PKCS5Padding
at javax.crypto.Cipher.getInstance(Unknown Source)
at PaddingIssue.main(PaddingIssue.java:10)
Caused by: javax.crypto.NoSuchPaddingException: CTR mode must be used with ISO10126Padding or NoPadding
at com.ibm.crypto.provider.AbstractBufferingCipher.engineSetPadding(Unknown Source)
at javax.crypto.Cipher$a.a(Unknown Source)
... 2 more

OpenJDK 7
/usr/lib/jvm/java-7-openjdk-amd64/jre/bin/java PaddingIssue
Fine!

Full stacktrace:
Mar 22, 2016 3:54:13 PM hudson.remoting.jnlp.Main$CuiListener status
INFO: Trying protocol: JNLP3-connect
Mar 22, 2016 3:54:14 PM hudson.remoting.jnlp.Main$CuiListener error
SEVERE: Failed to create handshake ciphers
java.lang.AssertionError: Failed to create handshake ciphers
at org.jenkinsci.remoting.engine.HandshakeCiphers.create(HandshakeCiphers.java:116)
at org.jenkinsci.remoting.engine.JnlpProtocol3.performHandshake(JnlpProtocol3.java:138)
at org.jenkinsci.remoting.engine.JnlpProtocol.establishChannel(JnlpProtocol.java:77)
at hudson.remoting.Engine.run(Engine.java:308)
Caused by: java.security.NoSuchAlgorithmException: Cannot find any provider supporting AES/CTR/PKCS5Padding
at javax.crypto.Cipher.getInstance(Unknown Source)
at org.jenkinsci.remoting.engine.HandshakeCiphers.create(HandshakeCiphers.java:109)
... 3 more
Caused by: javax.crypto.NoSuchPaddingException: CTR mode must be used with ISO10
126Padding or NoPadding
at com.ibm.crypto.provider.AESCipher.engineSetPadding(Unknown Source)
at javax.crypto.Cipher$a_.a(Unknown Source)
... 5 more