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M.Z. avatar Crypto

multi-user deterministic symmetric encryption

er flag
M.Z.

I was wondering whether there exists a symmetric encryption scheme such that

  1. there is 1 sender and n receivers. Each receiver has 1 random and independent symmetric key. The sender knows the symmetric keys of all receivers in advance.
  2. the sender can encrypt one message using the above n keys and produce a ciphertext. Each receiver can decrypt the ciphertext using his own symmetric key to recover the message.
  3. the above n keys are used only for encrypting/decrypting 1 message.
  4. the encryption is deterministic. This excludes some trivial constructions such that sampling one shared key that is used for encrypting the message, followed by respectively encrypting the shared key using n symmetric keys.
  5. the scheme achieves somewhat one-time-CPA security. Of course, compared to the standard notion, the difference is that we need to consider n keys instead of 1 key.

Motivation: Now I am facing one problem that a large file needs to be sent to multiple users (only once) under the condition that the randomness generator of the sender is broken (or unreliable).

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Steffen Ullrich avatar
kp flag
Steffen Ullrich
I'm not sure what all the requirement you list have to do with the problem you mention as motivation. Anyway, this kind of question is more on-topic at [crypto.se].
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foreverska avatar Crypto
cn flag
foreverska

Not sure there's anything out of the box.

A trivial construction might be to encrypt the file with a symmetric key and then encrypt the symmetric key n times with receiver symmetric keys and prepend that to the ciphertext. The downsides are obvious.

A broken randomness is going to be a major downside for any symmetric cipher that uses an IV (all the good ones).

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