The Subversion server uses both client certificate and username+password. I've configured authentication as described in JENKINS-3912. I've also tried using a fresh .subversion dir, as described in JENKINS-4037 although that bug has a different NPE than this.

The client certificate part probably goes well, because after adding my cert and its password I get the authentication error details saying "401 Authentication Required":

Attempting an SSL client certificate authentcation
Passing user name null and password you entered
Failed to authenticate: org.tmatesoft.svn.core.SVNErrorMessage: svn: OPTIONS of /svn/project/trunk: 401 Authorization

But when adding login username and password I get:

Attempting an SSL client certificate authentcation
FAILED: org.tmatesoft.svn.core.SVNErrorMessage: svn: OPTIONS /svn/project/trunk failed

org.tmatesoft.svn.core.SVNException: svn: OPTIONS /svn/project/trunk failed
at org.tmatesoft.svn.core.internal.io.dav.http.HTTPConnection.request(HTTPConnection.java:291)
at org.tmatesoft.svn.core.internal.io.dav.http.HTTPConnection.request(HTTPConnection.java:276)
at org.tmatesoft.svn.core.internal.io.dav.http.HTTPConnection.request(HTTPConnection.java:264)
at org.tmatesoft.svn.core.internal.io.dav.DAVConnection.exchangeCapabilities(DAVConnection.java:516)
at org.tmatesoft.svn.core.internal.io.dav.DAVConnection.open(DAVConnection.java:98)
at org.tmatesoft.svn.core.internal.io.dav.DAVRepository.openConnection(DAVRepository.java:1001)
at org.tmatesoft.svn.core.internal.io.dav.DAVRepository.testConnection(DAVRepository.java:97)
at hudson.scm.SubversionSCM$DescriptorImpl.postCredential(SubversionSCM.java:1857)
at hudson.scm.SubversionSCM$DescriptorImpl.doPostCredential(SubversionSCM.java:1802)
at sun.reflect.NativeMethodAccessorImpl.invoke0(Native Method)
at sun.reflect.NativeMethodAccessorImpl.invoke(NativeMethodAccessorImpl.java:57)
at sun.reflect.DelegatingMethodAccessorImpl.invoke(DelegatingMethodAccessorImpl.java:43)
at java.lang.reflect.Method.invoke(Method.java:616)
at org.kohsuke.stapler.Function$InstanceFunction.invoke(Function.java:282)
at org.kohsuke.stapler.Function.bindAndInvoke(Function.java:149)
at org.kohsuke.stapler.Function.bindAndInvokeAndServeResponse(Function.java:88)
at org.kohsuke.stapler.MetaClass$1.doDispatch(MetaClass.java:104)
at org.kohsuke.stapler.NameBasedDispatcher.dispatch(NameBasedDispatcher.java:53)
at org.kohsuke.stapler.Stapler.tryInvoke(Stapler.java:561)
at org.kohsuke.stapler.Stapler.invoke(Stapler.java:646)
at org.kohsuke.stapler.MetaClass$6.doDispatch(MetaClass.java:234)
at org.kohsuke.stapler.NameBasedDispatcher.dispatch(NameBasedDispatcher.java:53)
at org.kohsuke.stapler.Stapler.tryInvoke(Stapler.java:561)
at org.kohsuke.stapler.Stapler.invoke(Stapler.java:646)
at org.kohsuke.stapler.MetaClass$6.doDispatch(MetaClass.java:234)
at org.kohsuke.stapler.NameBasedDispatcher.dispatch(NameBasedDispatcher.java:53)
at org.kohsuke.stapler.Stapler.tryInvoke(Stapler.java:561)
at org.kohsuke.stapler.Stapler.invoke(Stapler.java:646)
at org.kohsuke.stapler.Stapler.invoke(Stapler.java:477)
at org.kohsuke.stapler.Stapler.service(Stapler.java:159)
at javax.servlet.http.HttpServlet.service(HttpServlet.java:45)
at winstone.ServletConfiguration.execute(ServletConfiguration.java:249)
at winstone.RequestDispatcher.forward(RequestDispatcher.java:335)
at winstone.RequestDispatcher.doFilter(RequestDispatcher.java:378)
at hudson.util.PluginServletFilter$1.doFilter(PluginServletFilter.java:94)
at hudson.util.PluginServletFilter.doFilter(PluginServletFilter.java:86)
at winstone.FilterConfiguration.execute(FilterConfiguration.java:195)
at winstone.RequestDispatcher.doFilter(RequestDispatcher.java:368)
at hudson.security.csrf.CrumbFilter.doFilter(CrumbFilter.java:47)
at winstone.FilterConfiguration.execute(FilterConfiguration.java:195)
at winstone.RequestDispatcher.doFilter(RequestDispatcher.java:368)
at hudson.security.ChainedServletFilter$1.doFilter(ChainedServletFilter.java:84)
at hudson.security.ChainedServletFilter.doFilter(ChainedServletFilter.java:76)
at hudson.security.HudsonFilter.doFilter(HudsonFilter.java:164)
at winstone.FilterConfiguration.execute(FilterConfiguration.java:195)
at winstone.RequestDispatcher.doFilter(RequestDispatcher.java:368)
at hudson.util.CharacterEncodingFilter.doFilter(CharacterEncodingFilter.java:81)
at winstone.FilterConfiguration.execute(FilterConfiguration.java:195)
at winstone.RequestDispatcher.doFilter(RequestDispatcher.java:368)
at winstone.RequestDispatcher.forward(RequestDispatcher.java:333)
at winstone.RequestHandlerThread.processRequest(RequestHandlerThread.java:244)
at winstone.RequestHandlerThread.run(RequestHandlerThread.java:150)
at java.lang.Thread.run(Thread.java:636)
Caused by: org.tmatesoft.svn.core.SVNErrorMessage: svn: OPTIONS /svn/modules/cms-item/trunk failed
at org.tmatesoft.svn.core.SVNErrorMessage.create(SVNErrorMessage.java:200)
at org.tmatesoft.svn.core.SVNErrorMessage.create(SVNErrorMessage.java:146)
at org.tmatesoft.svn.core.SVNErrorMessage.create(SVNErrorMessage.java:89)
... 53 more
Caused by: org.tmatesoft.svn.core.SVNException: svn: Unknown error
at org.tmatesoft.svn.core.internal.io.dav.http.HTTPSSLKeyManager.acknowledgeAndClearAuthentication(HTTPSSLKeyManager.java:295)
at org.tmatesoft.svn.core.internal.io.dav.http.HTTPConnection._request(HTTPConnection.java:387)
at org.tmatesoft.svn.core.internal.io.dav.http.HTTPConnection.request(HTTPConnection.java:285)
... 52 more
Caused by: org.tmatesoft.svn.core.SVNErrorMessage: svn: Unknown error
at org.tmatesoft.svn.core.SVNErrorMessage.create(SVNErrorMessage.java:101)
... 55 more
Caused by: java.lang.NullPointerException
at org.apache.commons.io.FileUtils.openInputStream(FileUtils.java:129)
at org.apache.commons.io.FileUtils.readFileToByteArray(FileUtils.java:1135)
at hudson.scm.SubversionSCM$DescriptorImpl$SslClientCertificateCredential.<init>(SubversionSCM.java:1556)
at hudson.scm.UserProvidedCredential$AuthenticationManagerImpl.getFirstAuthentication(UserProvidedCredential.java:204)
at org.tmatesoft.svn.core.internal.io.dav.http.HTTPSSLKeyManager.initialize(HTTPSSLKeyManager.java:319)
at org.tmatesoft.svn.core.internal.io.dav.http.HTTPSSLKeyManager.initializeNoException(HTTPSSLKeyManager.java:301)
at org.tmatesoft.svn.core.internal.io.dav.http.HTTPSSLKeyManager.chooseClientAlias(HTTPSSLKeyManager.java:196)
at sun.security.ssl.AbstractWrapper.chooseClientAlias(SSLContextImpl.java:282)
at sun.security.ssl.ClientHandshaker.serverHelloDone(ClientHandshaker.java:629)
at sun.security.ssl.ClientHandshaker.processMessage(ClientHandshaker.java:228)
at sun.security.ssl.Handshaker.processLoop(Handshaker.java:610)
at sun.security.ssl.Handshaker.process_record(Handshaker.java:546)
at sun.security.ssl.SSLSocketImpl.readRecord(SSLSocketImpl.java:913)
at sun.security.ssl.SSLSocketImpl.performInitialHandshake(SSLSocketImpl.java:1158)
at sun.security.ssl.SSLSocketImpl.writeRecord(SSLSocketImpl.java:652)
at sun.security.ssl.AppOutputStream.write(AppOutputStream.java:78)
at java.io.BufferedOutputStream.flushBuffer(BufferedOutputStream.java:82)
at java.io.BufferedOutputStream.flush(BufferedOutputStream.java:140)
at org.tmatesoft.svn.core.internal.io.dav.http.HTTPConnection.sendData(HTTPConnection.java:229)
at org.tmatesoft.svn.core.internal.io.dav.http.HTTPRequest.dispatch(HTTPRequest.java:166)
at org.tmatesoft.svn.core.internal.io.dav.http.HTTPConnection._request(HTTPConnection.java:364)
... 53 more

In 1.373 I managed to get working authentication by caching credentials on the command line using svnkit-cli:

sudo -u hudson ./jsvn --config-dir /var/lib/hudson/.subversion/ info https://our-sever/svn/

However this produced the same NPE as above with latest Jenkins. I also tried using the patched Svnkit-1.3.4 from the Jenkins Subversion plugin distribution, but with that one the jsvn command fails to authenticate.