A group oriented cryptosystem for the vector space access structure was proposed. This cryptosystem adopts self-certified public keys. It allows the participants of an authorized subset to cooperatively access an en crypted message. All data delivered in the cryptosystem are public. Therefore it does not need a partial decrypting results combiner and any secure communication channel. The security of the group oriented cryptosystem is based on the intractability of the discrete log problem and difficulty of factoring large integers. The suspected attacks can not break it.