Is it possible to set permission on user, so that users can see only that issue that they are assigned to that users.
Well, you can set a default security level which includes assignee (Reporter and maybe some other roles should be contained as well). Then you have what you want.
See https://confluence.atlassian.com/display/JIRA/Configuring+Issue-level+Security
As long as you remember to set the security level (correctly) ;-)
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