An openjdk-6 security update has been released for Debian 6 LTS

Package : openjdk-6
Version : 6b34-1.13.6-1~deb6u1
CVE ID : CVE-2014-3566 CVE-2014-6585 CVE-2014-6587 CVE-2014-6591
CVE-2014-6593 CVE-2014-6601 CVE-2015-0383 CVE-2015-0395
CVE-2015-0407 CVE-2015-0408 CVE-2015-0410 CVE-2015-0412

Several vulnerabilities have been discovered in OpenJDK, an
implementation of the Oracle Java platform, resulting in the execution
of arbitrary code, information disclosure or denial of service.