The　minimum　travel　distance　of　task　participants　is　one　of　the　significant　optimization　objectives　of　privacy-preserving　task　assignment　in　mobile　crowdsensing　(MCS).　However,　when　the　travel　distance　is　minimized,　most　of　the　previous　schemes　only　focus　on　the　task　participant　privacy　and　disregard　the　task　requester　privacy.　Moreover,　existing　solutions　usually　only　support　the　constraint　of　a　single　type,　such　as　equality　constraints　or　range　constraints.　In　this　paper,　we　propose　a　bilateral　privacy-preserving　Task　Assignment　mechanism　for　MCS　(iTAM),　which　protects　not　only　the　task　participants　privacy　but　also　the　task　requesters　privacy　and　can　minimize　the　travel　distance.　Furthermore,　iTAM　provides　both　equality　and　range　constraints　of　task　assignment　by　utilizing　the　Paillier　cryptosystem.　To　accommodate　the　multiple　relations　between　the　task　participants　and　the　task,　we　propose　the　single/multiple　task　participants　selection　problems　for　a　task　requiring　task　participants　to　compete　and　cooperate.　Experimental　evaluations　over　synthetic　and　real-world　data　illustrate　that　iTAM　is　feasible　and　effective.　Compared　with　the　state-of-the-art,　iTAM　positively　solves　the　optimal　problem　of　travel　distance.　The　complexities　of　iTAM　are　$\mathcal　{O}(n)$O(n)　and　$\mathcal　{O}(n\log　n)$O(nlogn)　for　a　single　and　multiple　task　participants　selection　problems,　respectively.　©　2002-2012　IEEE.