The problem appears to be the server. This is from the log of a 1.643 instance, which worked properly until today (or maybe yesterday):
[SNIP]
Jenkins is fully up and running
Jan 26, 2016 9:40:40 PM SEVERE hudson.model.UpdateSite updateData
ERROR: Signature verification failed in update site 'default' <a href='#' class='showDetails'>(show details)</a><pre style='display:none'>java.security.cert.CertPathValidatorException: Algorithm constraints check failed: MD5withRSA<br> at sun.security.provider.certpath.PKIXMasterCertPathValidator.validate(PKIXMasterCertPathValidator.java:135)<br> at sun.security.provider.certpath.PKIXCertPathValidator.validate(PKIXCertPathValidator.java:219)<br> at sun.security.provider.certpath.PKIXCertPathValidator.validate(PKIXCertPathValidator.java:140)<br> at sun.security.provider.certpath.PKIXCertPathValidator.engineValidate(PKIXCertPathValidator.java:79)<br> at java.security.cert.CertPathValidator.validate(CertPathValidator.java:292)<br> at org.jvnet.hudson.crypto.CertificateUtil.validatePath(CertificateUtil.java:93)<br> at jenkins.util.JSONSignatureValidator.verifySignature(JSONSignatureValidator.java:76)<br> at hudson.model.UpdateSite.verifySignature(UpdateSite.java:219)<br> at hudson.model.UpdateSite.updateData(UpdateSite.java:198)<br> at hudson.model.UpdateSite.updateDirectlyNow(UpdateSite.java:170)<br> at hudson.PluginManager.doCheckUpdatesServer(PluginManager.java:891)<br> at jenkins.model.DownloadSettings$DailyCheck.execute(DownloadSettings.java:118)<br> at hudson.model.AsyncPeriodicWork$1.run(AsyncPeriodicWork.java:53)<br> at java.lang.Thread.run(Thread.java:745)<br></pre>
Jan 26, 2016 9:40:40 PM INFO hudson.model.AsyncPeriodicWork$1 run
Finished Download metadata. 1,642 ms
[/SNIP]
I am investigating the cert on https://updates.jenkins-ci.org
wait one - this now appears to be pilot error. Still investigating...