Chameleon　Signature　(CS)　is　an　ideal　designated　verifier　signature,　it　realizes　non-transferability　by　using　chameleon　hash　function,　makes　any　third　party　distrust　the　content　disclosed　by　a　designated　verifier,　and　avoids　the　shortcoming　of　online　interactive　verification　of　undeniable　signature.　In　addition　to　non-transferability,　CS　also　should　satisfy　unforgeability,　deniability,　non-repudiation　for　the　signer,　and　so　on.　To　solve　the　problems　that　cryptosystems　based　on　the　number　theory　problems　such　as　integer　factorization　or　discrete　logarithm　cannot　resist　quantum　computing　attacks　and　users　rely　on　digital　certificates,　an　Identity-Based　Chameleon　Signature　(IBCS)　over　lattices　is　proposed,　the　new　scheme　avoids　the　security　vulnerability　that　the　signer　cannot　reject　the　forged　signature　of　the　designated　verifier　in　the　existing　schemes,　and　reduces　the　transmission　cost　of　the　final　signature　from　square　to　linear;　Furthermore,　to　solve　the　failure　problem　of　non-transferability　in　the　arbitration　phase,　an　IBCS　scheme　with　exposure-freeness　over　lattices　is　proposed,　the　new　scheme　enables　the　signer　to　reject　a　forged　signature　of　any　adversary　without　exposing　the　real　message.　Particularly,　based　on　the　hardness　of　the　small　integer　solution　problem,　both　schemes　can　be　proved　secure　in　the　random　oracle　model.　©　2024　Science　Press.　All　rights　reserved.