According to this paper entitled "Using Commutative Encryption to Share a Secret" they define their modulus to be a large prime p, which is public. Both exponents are private in this case.
According to the wikipedia article on RSA link the modulus has to be a product of two primes, and " p, q, and φ(n) must also be kept secret because they can be used to calculate d.", and the exponent can be public.
In the paper both the modulus (p) and φ(p) are known. How is the algorithm in the paper secure? Is it because both keys are private?
Is there a secure way for the same modulus to be used across all parties, and $a_i$ are public for each user?