A novel group signature scheme without one way hash

Abstract

The group signatures scheme was introduced by Chaum and van Heijst which allow members of a group to sign messages anonymously on behalf of the whole group. Only a
designated Group Manager is able to trace the identify of the group member who issued a valid signature. The group members sign a message with their secret key gsk and produce
a signature that cannot be linked to the identities of the signers without the secret key of the manager. The group manager can open the signature to recover the identities of the signers in case of any legal dispute. Group signatures have been widely used in Electronic markets where the sellers are the group members, the buyers are the veriers and the market administrator is the group manager.
We aim to propose a group signature scheme that is devoid of any one-way hash function and is based upon the Integer Factorization Problem (IFP). The scheme uses the concept
of safe primes to further enhance the security of the scheme. The scheme supports message recovery and hence the overload of sending the message is avoided. The scheme satisfies security properties such as Anonymity (The verier cannot link a signature to the identity
of the signer), Traceability (The Group Manager can trace the identity of the signer of any
valid signature), Unforgeability (A valid signature cannot be produced without the group
secret keys), Exculpability (Neither the GM nor any member can produce a signature on
behalf of a group member).