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 of Understanding for medical equipment in Supplement No. 3 to Part 774 of the EAR can be accessed at Electronic Code of Federal Regulations site. Please visit the Question #15 in the FAQ section of the encryption page for sample items BIS has listed that can claim Note 4 exemptions.
(ii) your app uses, accesses, implements or incorporates encryption for authentication only
(iii) your app uses, accesses, implements or incorporates encryption with key lengths not exceeding 56 bits symmetric, 512 bits asymmetric and/or 112 bit elliptic curve
(iv) your app is a mass market product with key lengths not exceeding 64 bits symmetric, or if no symmetric algorithms, not exceeding 768 bits asymmetric and/or 128 bits elliptic curve.
Please review Note 3 in Category 5 Part 2 to understand the criteria for mass market definition.
(v) your app is specially designed and limited for banking use or ‘money transactions.’ The term ‘money transactions’ includes the collection and settlement of fares or credit functions.
(vi) the source code of your app is “publicly available”, your app distributed at free of cost to general public, and you have met the notification requirements provided under 740.13.(e).
Please visit encryption web page in case you need further help in determining if your app qualifies for any exemptions.
If you believe that your app qualifies for an exemption, please answer “YES” to the question."
Best Answer
Submitting a new binary stops the review process of the "old" binary anyway - so putting the information, Apple needs to properly test your app in the "Review notes" field in the meta data of your new binary will be sufficient.