If I encrypt copyrighted data to which I have no right with a private key known only to me, am I infringing the copyright by holding only the encrypted version?
Mere possession of copyrighted material does not infringe any of the copyright holder's exclusive rights.1
This conclusion is echoed by Jay Dratler:
Nothing in copyright law prohibits the mere possession of an unauthorized copy of a copyrighted work.2
From the Fifth Circuit:
The copyright owners not only had no interest in the tangible video cassettes that contained copies of the works, but they did not have the exclusive right to possess or authorize possession of video cassettes containing copies of the works.3
From the Tenth Circuit:
The Copyright Act, however, says nothing about an exclusive right to possession of a copyrighted work.4
Possession may be used as evidence that you copied the work, though.
courts have held that when two works are so strikingly similar as to preclude any reasonable possibility that the defendant’s work was independently created, access may be presumed. Any circumstantial evidence of copying (i.e., proof of access and probative similarities, including the presumption of access created by striking similarities) can, however, be rebutted.5
The fact that your copy is encrypted doesn't change the copyright infringement analysis, but it may be an investigatory hurdle.
2. Jay Dratler, Cyberlaw: Intellectual Property in the Digital Millennium 2-83 (2000)
3. United States v. Smith 686 F.2d 234 (5th Cir. 1982)
4. Khandji v. Keystone Resorts Management Inc. 140 F.R.D. 697 (D. Col. 1992)
5. Jason E. Sloan, An Overview of the Elements of a Copyright Infringement Cause of Action - Part I: Introduction and Copying, American Bar Association (last visited Dec. 7, 2016).