UPDATE: Using HTTPS is now exempt from the ERN as of late September, 2016
https://stackoverflow.com/a/40919650/4976373
Unfortunately, I believe that your app "contains encryption" in terms of US BIS even if you just use HTTPS (if your app is not an exception included in question 2).
Quote from FAQ on iTunes Connect:
"How do I know if I can follow the Exporter Registration and Reporting (ERN) process?
If your app uses, accesses, implements or incorporates industry standard encryption algorithms for purposes other than those listed as exemptions under question 2, you need to submit for an ERN authorization. Examples of standard encryption are: AES, SSL, https. This authorization requires that you submit an annual report to two U.S. Government agencies with information about your app every January.
"
"2nd Question: Does your product qualify for any exemptions provided under category 5 part 2?
There are several exemptions available in US export regulations under Category 5 Part 2 (Information Security & Encryption regulations) for applications and software that use, access, implement or incorporate encryption.
All liabilities associated with misinterpretation of the export regulations or claiming exemption inaccurately are borne by owners and developers of the apps.
You can answer “YES” to the question if you meet any of the following criteria:
(i) if you determine that your app is not classified under Category 5, Part 2 of the EAR based on the guidance provided by BIS at encryption question. The Statement
answered 2013-04-18T10:16:09.177