The Congress of ThéOùÇa enacted that civilian use of any public-key encryption system is authorized on the territory of ThéOùÇa, subject to meeting certain security requirements published by the Ministry of Defense. The essence of these is:
..must operate per the internationally recognized RSAES-OAEP algorithm and relevant requirements in PKCS#1 V2.2, with a 2048-bit public modulus $n$ product of two primes $p$ and $q$. In order to ensure separation of key domains with the Pailler cryptosystem used for national defense purposes, the key generator shall be such that $p$ and $q$ also meet the requirement $\gcd(pq, (p-1)(q-1))\ne 1$. Demonstration of conformance to that requirement shall be by submitting the mathematical description of the key generation method to the Ministry of Defense of ThéOùÇa.
Can a public-key encryption system lawfully usable by civilians on the territory of ThéOùÇa be secure? If yes, give a possible submission to the Ministry of Defense (English is spoken in ThéOùÇa). In either case, make a cryptographically convincing argument.
Thanks to Poncho for spotting a big mistake in my transcription of the Official Journal of ThéOùÇa, now fixed.
This is not homework. If you wonder, inspiration was that recent question.