I don't think there's really any overlap there. The overlap with the 4th would be less about secrecy and more if someone demanded full content from an account, since NSLs are not warrants (legality of procuring "metadata" without a warrant is the much larger issue there, but so far courts have been ok with it).
The secrecy part can be a violation of the 6th amendment (right to confront your accuser), but theoretically evidence procured under the NSL will be produced by trial time (except when shown to conflict with national security, which judges can sometimes accept too readily).
The real problem with secrecy is the first amendment, since you are forcing people to not divulge that they received an order to hand over information. Typically prior restraint like that is heavily circumscribed to protect an ongoing investigation but no further, which means that indefinite gag orders should have correspondingly extraordinary justification. Considering the hundreds of thousands of NSLs that have been issued, this seems unlikely to be the norm.
The first amendment approach has been successfully[1] argued by the EFF at the district court level. This has opened the way for more lawsuits, including an appeal of that case, which will hopefully make their way higher in the court system.
(read the linked EFF article if you're interested in more. It lays the case and the judge's ruling out in great detail)
The secrecy part can be a violation of the 6th amendment (right to confront your accuser), but theoretically evidence procured under the NSL will be produced by trial time (except when shown to conflict with national security, which judges can sometimes accept too readily).
The real problem with secrecy is the first amendment, since you are forcing people to not divulge that they received an order to hand over information. Typically prior restraint like that is heavily circumscribed to protect an ongoing investigation but no further, which means that indefinite gag orders should have correspondingly extraordinary justification. Considering the hundreds of thousands of NSLs that have been issued, this seems unlikely to be the norm.
The first amendment approach has been successfully[1] argued by the EFF at the district court level. This has opened the way for more lawsuits, including an appeal of that case, which will hopefully make their way higher in the court system.
(read the linked EFF article if you're interested in more. It lays the case and the judge's ruling out in great detail)
[1] https://www.eff.org/deeplinks/2013/03/depth-judge-illstons-r...