# an asymmetric encryption scheme with multiple distinct private keys [duplicate]

This question already has an answer here:

Is there a asymmetric encryption scheme that allows for multiple private decryption keys?

where m= plaintext message and c= cyphertext message

c = Ek(m) where K is the public encryption key.

and

m = Dj(c) where J is the private decryption key.

nothing out of the ordinary here, RSA satisfies this basic scenario.

In addition I also want the message to be decrypted by any number of additional keys, ( Dj1 ... Djn ) such that:

eg.

m = Djn(c)

does such a scheme exist?

note: I am NOT referring to the way GPG/PGP broadcasts a message to many parties.

edit: looks to be similar to One Encryption, Many Decryption Keys

in particular see D.W.'s answer https://crypto.stackexchange.com/a/39403/29315

## marked as duplicate by e-sushiDec 2 '17 at 19:46

• If it is symmetric, then the holder of $k_1$ could also encrypt any message that the other $k, k_2, ..., k_n$ holders can decrypt. If this is what you're thinking about, then any symmetric cipher would satisfy this requirement where $k = k_x$ for $1\leq x \leq n$. What's the point of such a scheme? – Artjom B. Dec 2 '17 at 9:50