“…In 2002, Zeng and Keitel [ 12 ] proposed the first arbitrated quantum signature protocol based on the Green–Horne–Zeilinger (GHZ) state. Since then, various quantum signature protocols have been proposed, for example, arbitrated quantum signature [ 13 , 14 , 15 , 16 , 17 , 18 , 19 , 20 ], quantum blind signature [ 21 , 22 , 23 , 24 , 25 , 26 ], quantum proxy signature [ 27 , 28 ], and quantum group signature [ 29 ]. Inspired by the above quantum signature schemes [ 11 , 12 , 13 , 14 , 15 , 16 , 17 , 18 , 19 , 20 , 21 , 22 , 23 , 24 , 25 , 26 , 27 , 28 , 29 ], Zhao et al [ 30 ] proposed a signature scheme based on the concept of “bi-signature.” In Zhao et al’s quantum bi-signature protocol, two participants sign their signatures on the same message.…”