A group signature scheme in which signers are able to designate openers by specifying access structures over openers' attributes was introduced at CANDAR 2021, which is called GSdT. In this paper, we present a construction of GSdT from only symmetric-key primitives; pseudorandom functions, hash functions and commitments. Due to the features, our GSdT is expected to be secure against computational power of quantum computers. We first introduce syntax and security definitions in the static group model. Then, in our construction, the key ingredient is a non-interactive zero-knowledge proof of knowledge system that is constructed from the primitives in the "MPC-in-the-head" paradigm, owing the technique that was developed by Katz, Kolesnikov and Wang (ACM-CCS 2018). Our approach starts with their group signature scheme, but non-trivially extends the Merkle tree so that signers can treat (all-AND) boolean formulas as the access structures. According to our estimation, the signing time is less than 3.0 sec and the signature size is less than 0.5 MB in a scenario that the numbers of group members and attributes are 2^7 and 2^3, respectively, and security to be attained is 128 bit quantum security.