Secure non-transferable proxy re-encryption for group membership and non-membership

In proxy re-encrytpion (PRE) scheme, the message is sent by a delegator to a delegatee with a help of the trusted third party proxy without knowing the existing plaintext. PRE schemes are widely used in various applications. However, the standard PRE scheme has some proxy problems called private key generator (PKG) despotism problem. This means that PKG can make re-encryption key without permission from delegator. And also, if someone can attack PKG in a PRE scheme, they can decrypt both the original ciphertext and the re-encrypted ciphertext which means the key-escrow problem. A solution for these two problems is to use non-transferable PRE scheme. Non-transferable PRE scheme solved the above PKG despotism problem and key-escrow problem. We would like to introduce our PRE scheme with a new approach. In our scheme, there are three sub-processes, which are based on a non-transferable PRE scheme and group signature. Our scheme will provide the security for delegator i, delegatee j (who is in the same group with delegator i), and delegatee k (who is in a different group with delegator i).