What schemes support atomic decryption+reencryption What encryption schemes support this workflow?
Vendor encrypts and publishes information for the client

Client generates public and private key
Vendor encrypts private information
Vendor publishes that

ENCRYPT(PRIVATE_INFORMATION, CLIENT_PUBLIC_KEY) --&gt; Publish

Client re-encrypts for benefit of a third party

Client generates re-encryptor using its own private key and third party's public key
Client publishes that

CREATE_REENCRYPTOR(CLIENT_PRIVATE_KEY, THIRD_PARTY_PUBLIC_KEY) --&gt; Publish

Third-party decrypts data

The third-party decrypts the data

Other people

Nobody can decrypt PRIVATE_INFORMATION unless they have the THIRD_PARTY_PRIVATE_KEY or CLIENT_PUBLIC_KEY.


I know that the asymmetric scheme supports most of this workflow. However, it violates requirement 7. Is there another scheme that fully supports this workflow?
The blockchain network Nucypher offers something like that, through their cryptographic scheme, with a help of semi-trusted proxies. The scheme is secure as long as proxies don't cooperate, enough proxies don't reveal the secret and enough proxies stay online. They have papers on their website.