One file encryption, multiple user decryption?

I need a system such that a given message can be encrypted once and every member of the recipient group can decrypt it independently of all others. This will work for a broadcast scheme.
LizaMolyAsked:
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Russ SuterSenior Software DeveloperCommented:
You could use RSA encryption. Encrypt the file using a private key then make sure you only distribute the public key to the members you want to be able to decrypt.

Alternatively you could set up a key exchange system but that would be a lot more work.
LizaMolyAuthor Commented:
I mean, the distribution will be  for a subset of users "n"  from main group "N". Each time the subset  "n" changed, no one out of "n"  can decrypt the file.
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LizaMolyAuthor Commented:
Dear ozo , what you mentioned is secret sharing scheme or  secret splitting like Shamir's secret sharing. These schemes need the users to corporate to reconstruct the secret. But in my situation no communication between the subset users accrue after cipher broadcast. This is an offline file sharing.
ozoCommented:
Maybe we are misunderstanding the question.  Can you clarify how your situation differs from trivial (1,n) secret sharing?
LizaMolyAuthor Commented:
My situation is that i have N group of users can share secret once "the first time",then the it turned to offline. One user needs to encrypt message for (n,N) users. The other users have no right to read that message, just the subset n. No cob-oration between those n users done to reconstruct the key. Each should be able to decrypt the message.
Note: in threshold schemes users must cob-orate for constructing the key, in my situation this not allowed due to offline communication.
ozoCommented:
Can you clarify why is this not solved by the trivial (1,n) secret sharing method of giving a password to the subset of n users?
Dave HoweSoftware and Hardware EngineerCommented:
Sounds *exactly* like the problem the hybrid scheme of pgp (or gnupg) was designed to solve. encrypt the file *once* to a symmetric key, then append a block with the symmetric key encrypted to the public key(s) of the recipients. any recipient in the keyblock can decrypt the symmetric key, and hence the file.

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Encryption

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