"An unknown error occurred while processing the certificate"

Here's the log output for an attempted login:

2018-04-25 10:34:27.5761 | DEBUG |   ServerCollectionManager | 18 | Adding server connection. Type:jenkins, InstanceId:d570783b-bc07-405d-90e6-fe980f5c663f 
2018-04-25 10:34:27.5761 | DEBUG |               ServiceBase | 18 | Staring ServerManager 
2018-04-25 10:34:27.5761 | DEBUG |             ServerManager | 18 | d570 | Starting server manager for jenkins 
2018-04-25 10:34:27.5761 | DEBUG |               ServiceBase | 18 | Staring ServerAdapterPoller 
2018-04-25 10:34:27.5761 | DEBUG |      ConfigurationManager | 18 | Saving settings: Web.Services.ServerCollectionManager+ServerCollectionManagerSettings 
2018-04-25 10:34:27.5761 | DEBUG |          DashboardManager | 18 | Server list changed. Dashboard revision: 10 
2018-04-25 10:34:27.5761 |  INFO |               EventLogger | 18 | {"e":"App.AddNewModule","p":{"Type":"jenkins"}} 
2018-04-25 10:34:27.5761 | DEBUG |       NotificationManager | 34 | VM changed. Old: Web.ViewModels.DashboardViewModel , New: Web.ViewModels.DashboardViewModel 
2018-04-25 10:34:27.5919 |  INFO |               EventLogger | 58 | {"e":"Jenkins.EditConnectionSettings","p":null} 
2018-04-25 10:34:29.4508 | DEBUG |      ConfigurationManager | 55 | Web proxy not configured. 
2018-04-25 10:34:46.5024 |  INFO |               EventLogger | 54 | {"e":"Jenkins.UpdatingSettings","p":{"CredentialsType":"Password"}} 
2018-04-25 10:34:47.1702 |  WARN |         JenkinsController | 18 | Cannot save settings System.Net.Http.HttpRequestException: An error occurred while sending the request. ---> System.Net.Http.WinHttpException: An unknown error occurred while processing the certificate
   at System.Runtime.ExceptionServices.ExceptionDispatchInfo.Throw()
   at System.Threading.Tasks.RendezvousAwaitable`1.GetResult()
   at System.Net.Http.WinHttpHandler.<StartRequest>d__105.MoveNext()
   --- End of inner exception stack trace ---
   at System.Runtime.ExceptionServices.ExceptionDispatchInfo.Throw()
   at System.Runtime.CompilerServices.TaskAwaiter.ThrowForNonSuccess(Task task)
   at System.Runtime.CompilerServices.TaskAwaiter.HandleNonSuccessAndDebuggerNotification(Task task)
   at Web.Services.HttpLoggingHandler.<SendAsync>d__10.MoveNext() in C:\build\1\_work\2\s\Desktop\LocalWeb\Services\HttpLoggingHandler.cs:line 95
--- End of stack trace from previous location where exception was thrown ---
   at System.Runtime.ExceptionServices.ExceptionDispatchInfo.Throw()
   at System.Runtime.CompilerServices.TaskAwaiter.ThrowForNonSuccess(Task task)
   at System.Runtime.CompilerServices.TaskAwaiter.HandleNonSuccessAndDebuggerNotification(Task task)
   at System.Runtime.CompilerServices.ConfiguredTaskAwaitable`1.ConfiguredTaskAwaiter.GetResult()
   at System.Net.Http.HttpClient.<FinishSendAsyncBuffered>d__58.MoveNext()
--- End of stack trace from previous location where exception was thrown ---
   at System.Runtime.ExceptionServices.ExceptionDispatchInfo.Throw()
   at System.Runtime.CompilerServices.TaskAwaiter.ThrowForNonSuccess(Task task)
   at System.Runtime.CompilerServices.TaskAwaiter.HandleNonSuccessAndDebuggerNotification(Task task)
   at Web.Services.Jenkins.JenkinsAdapter.<ApiGet>d__55`1.MoveNext() in C:\build\1\_work\2\s\Desktop\LocalWeb\Services\Jenkins\JenkinsAdapter.cs:line 809
--- End of stack trace from previous location where exception was thrown ---
   at System.Runtime.ExceptionServices.ExceptionDispatchInfo.Throw()
   at System.Runtime.CompilerServices.TaskAwaiter.ThrowForNonSuccess(Task task)
   at System.Runtime.CompilerServices.TaskAwaiter.HandleNonSuccessAndDebuggerNotification(Task task)
   at Web.Services.Jenkins.JenkinsAdapter.<VerifyConnectionSettings>d__13.MoveNext() in C:\build\1\_work\2\s\Desktop\LocalWeb\Services\Jenkins\JenkinsAdapter.cs:line 73
--- End of stack trace from previous location where exception was thrown ---
   at System.Runtime.ExceptionServices.ExceptionDispatchInfo.Throw()
   at System.Runtime.CompilerServices.TaskAwaiter.ThrowForNonSuccess(Task task)
   at System.Runtime.CompilerServices.TaskAwaiter.HandleNonSuccessAndDebuggerNotification(Task task)
   at Web.Services.ServerManager.<SetConnectionSettings>d__23.MoveNext() in C:\build\1\_work\2\s\Desktop\LocalWeb\Services\ServerManager.cs:line 89
--- End of stack trace from previous location where exception was thrown ---
   at System.Runtime.ExceptionServices.ExceptionDispatchInfo.Throw()
   at System.Runtime.CompilerServices.TaskAwaiter.ThrowForNonSuccess(Task task)
   at System.Runtime.CompilerServices.TaskAwaiter.HandleNonSuccessAndDebuggerNotification(Task task)
   at Web.Controllers.JenkinsController.<UpdateConnectionSettings>d__4.MoveNext() in C:\build\1\_work\2\s\Desktop\LocalWeb\Controllers\JenkinsController.cs:line 77
2018-04-25 10:34:47.1702 |  INFO |               EventLogger | 18 | {"e":"Jenkins.FailedToUpdateSettings","p":{"Message":"An unknown error occurred while processing the certificate"}} 

This can happen if Jenkins, or proxy server in front of it, is configured to use obsolete security protocols (e.g. SSL3, TLS1.0). 

You can check if this is the case by opening the web page in Chrome and checking the security protocol as described here: https://security.stackexchange.com/a/169418/40423 

If everything is configured properly, it should show TLS1.2, but if it shows SSL, then this can be the problem.

The connection is established directly.