Permutation　polynomials　with　low　c-differential　uniformity　and　boomerang　uniformity　have　wide　applications　in　cryptography.　In　this　paper,　by　utilizing　the　Weil　sums　technique　and　solving　some　certain　equations　over　F2,　we　determine　the　c-differential　uniformity　and　boomerang　uniformity　of　these　permutation　polynomials:　(1)　f1(x)=x+Tr1n(x2+x3+x+ux),　where　n=2k+1,　u∈F2　with　Tr1n(u)=1;　(2)　f2(x)=x+Tr1n(x2+(x+1)2),　where　n=2k+1;　(3)　f3(x)=x−1+Tr1n((x−1+1)d+x−d),　where　n　is　even　and　d　is　a　positive　integer.　The　results　show　that　the　involutions　f1(x)　and　f2(x)　are　APcN　functions　for　c∈F2﹨{0,1}.　Moreover,　the　boomerang　uniformity　of　f1(x)　and　f2(x)　can　attain　2n.　Furthermore,　we　generalize　some　previous　works　and　derive　the　upper　bounds　on　the　c-differential　uniformity　and　boomerang　uniformity　of　f3(x).　©　2023　Elsevier　Inc.