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All of the JDK security providers are supposed to have provider numbers updated for each release.  It's not always done.  
    protected SunJSSE() {
        super("SunJSSE", 1.7d, info);
These are all candidates.
sun.security.pkcs11.SunPKCS11
sun.security.provider.Sun
sun.security.rsa.SunRsaSign
sun.security.ec.SunEC
com.sun.net.ssl.internal.ssl.Provider
com.sun.crypto.provider.SunJCE
sun.security.jgss.SunProvider
com.sun.security.sasl.Provider
org.jcp.xml.dsig.internal.dom.XMLDSigRI  // maybe not this one.
sun.security.smartcardio.SunPCSC
sun.security.mscapi.SunMSCAPI
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