A Hypothetical form of Broadcast Encryption

I have pursued the mental exercise, of supposing that a group of (n) people might exist, who are to receive a broadcast, encrypted message, but in such a way that two of those recipients’ credentials are required, to decrypt that message. The assumed author of the message is a secure party, entrusted to keep all the encryption details of the system.

The basis of my exercise is, that RSA encryption and hybrid encryption may be used, with the twist, that as long as the modulus is the same for two transactions, a symmetrical key can be encrypted twice, in order to be decrypted twice. A formalized way to write this could be:

C = (T ^ E1) ^ E2 mod (p)(q)

T = (C ^ D2) ^ D1 mod (p)(q)

Where (p) and (q) are random 1024-bit prime numbers, (T) stands for the symmetrical encryption key, and (C) stands for the encrypted form of that key. Clearly, (p) and (q) would be filtered by the central party, such that neither (p-1) nor (q-1) are divisible by either (E1) or (E2), which are, 65537 and 32771 respectively.

My concept continues, that the central party associates a single prime number with each distributed recipient for the long term, and that the recipient is not allowed to know their own prime number. For any pair of recipients, a modulus (p)(q) follows, which the recipients store, for each other recipient, that the current recipient may eventually want to combine his key with.

(Corrected 09/22/2018, 18h00 … )

(As of 09/21/2018, 23h40 : )

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