In　recent　years,　Qu-Tan-Tan-Li　function,　Zha-Hu-Sun　function　and　Tang-Carlet-Tang　function　have　been　proposed　with　differential　uniformity　4　and　many　good　cryptographic　properties.　the　counting　problem　of　affine　equivalent　to　the　three　families　cryptographic　functions　was　investigated.　By　using　some　properties　of　finite　fields,　the　upper　and　lower　bound　of　the　number　of　affine　equivalent　to　the　Zha-Hu-Sun　function,　and　the　upper　bound　of　the　number　of　affine　equivalent　to　the　Qu-Tan-Tan-Li　function　and　Tang-Carlet-Tang　function　were　computed,　respectively.　Moreover,　a　conjecture　was　given　about　the　exact　number　of　affine　equivalent　to　the　Zha-Hu-Sun　function.　Results　show　that　there　are　at　least　[Formula　is　presented]　cryptographic　functions　of　affine　equivalent　to　the　Zha-Hu-Sun　function　over　finite　field　GF(28),　which　can　be　chosen　as　S-boxes　of　block　ciphers.　©　2017,　Editorial　Board　of　Journal　on　Communications.　All　right　reserved.