Is there a administrator key that can decrypt all ciphertexts encrypted with different keys by different persons in a group?

Question

here is the scenario:

• $A, B, C, \ldots, Z$ are in a group with a administrator $Admin$,
• each of the users in the group has his own key $Key_A, Key_B$, and so on...
• everyone encrypt his own information with his own key,

but would it be possible to have a key such as the Admin would have the possibility to decrypt all the ciphertexts of all the users?

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I had a simple idea:

1. the Admin share a master key with all the members in the group,
2. all users register his identity at the Admin,
3. the Admin generate every user's secret key for every user,
4. the Admin share keys with all the users.

but in this way the Admin will know all the users' keys, this is insecure.

Answer 1

Another solution (cf to @Raoul722 comment) is the following:

It is easily feasible with a mix of symmetric and asymmetric encryption.

Assume each user $k$ have a key pair: $(K_{pub}^k,K_{priv}^k)$.
The admin also have his key pair: $(K_{pub}^{admin},K_{priv}^{admin})$ where $K_{pub}^{admin}$ is known by all.

Encryption scheme for a user $k$:

1. generate a random key $K_{sym}$.
2. Encrypt your file with an asymmetric encryption devices such as AES with $K_{sym}$.
3. Encrypt $K_{sym}$ with asymmetric encryption (RSA, ECC...) with the $K_{pub}^k$, let's call it $K_k$.
4. Encrypt $K_{sym}$ with asymmetric encryption (RSA, ECC...) with the $K_{pub}^{admin}$ let's call it $K_{admin}$.

Decryption scheme for a user $k$:

1. Decrypt $K_k$ with his private key ($K_{priv}^k$), he will get $K_{sym}$.
2. Decrypt the file with $K_{sym}$.

Decryption scheme for a user $admin$:

1. Decrypt $K_{admin}$ with his private key ($K_{priv}^{admin}$), he will get $K_{sym}$.
2. Decrypt the file with $K_{sym}$.

The sole problem is where do you store the encrypted keys: $K_{k}$ and $K_{admin}$ (maybe in the meta-data of the encrypted files? :) )

About the key privacy: In this scheme, having an asymmetric scheme prevents the admin to know each user's private key.

Note: this kind of scheme is useful in the company in the following scenario. Assume that everybody encrypts his files. One happens to have a lethal accident (R.I.P.), how do you retrieve his work? The problem that will arise is the safe storage of the master key (usually off-line and sealed to prevent malicious usage).