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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A Note On Playing Back Commercially-Recorded Blu-rays

Just as it was with DVDs, when movies first started to be distributed in that format, commercially-recorded Blu-ray disks today use an encryption system, which is sometimes referred to as ‘content scrambling’, to prevent people from making unauthorized copies. It’s actually named ‘aacs’.

Experts already know about this, but I’m putting this in layman’s terms for anybody who might not.

Basically, Blu-ray playback-devices have a hidden store of public keys, which the users are not allowed to access, and this time, the company is able to update that store of keys via the Internet, because most Blu-ray players today are also online devices.

Unlike how it is with Blu-rays, the content-scrambling system of DVDs was famously hacked. This means that Linux computers are well-able to play back Movie-DVDs. OTOH, the ability to play back commercial Blu-rays, is mainly unsuccessful on Linux computers, or on any other unauthorized devices, because the content-scrambling which gets used – was never hacked. As long as the encryption continues to work, Linux users and pirates will not be able to play back or rip Blu-rays.

As it stands, the company is able to revoke public keys which it was once using.

This is a shame, because some Linux users might only be wanting to view Blu-ray movies which they purchased and paid for. But the main fear of the industry remains, that as a platform, a Linux computer is more susceptible to an unauthorized copy being made of anything, which that Linux computer would also be able to perform authorized playback of.

Therefore, when I gave instructions on how people can record Blu-rays privately, my assumption was that we would not be using any encryption. I don’t see encryption as being important in any way, for home-movies which people might shoot. But, the Blu-ray folder must nevertheless contain a sub-folder named ‘CERTIFICATES’. In the example I wrote about, this sub-folder will simply remain empty.

Further, the mere use of the Blu-ray (single-layer) disk, as a step-up from DVD+Rs, where a Blu-ray can store up to 25GB of pure data instead of 4.7GB, is unfettered for Linux users to use as they wish. All we need is an external Blu-ray burner, and we’re all set to burn pure data. But as soon as we want to burn something using ‘UDF’, which is the approved file-system of Blu-ray players, the level of difficulty already increases, even though no encryption has been used yet.

(Updated 09/19/2017 : )

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