The invention provides a key agreement method and an encryption / decryption method and a signature / verification method. The key agreement method comprises the following steps: step 1. an A(x) shared by a user group is prearranged, wherein the user group comprises at least two users; the A(x) is a nonlinear function group from n vector x to n vector y=(y1,ellipsis, yn)=A(x)=(A1(x1,ellipsis,xn),ellipsis, An(x1,ellipsis,xn), wherein n is more than 1; and the A(x) meets the conditions that when the s layer iterative A<(s)>(x) of the A(x) is compared with the A(x), the number and type of the subsections with non-zero x coefficient are kept unchanged, and s is an integer; if B(x) is equal to A(A(x)), A(B(x)) is equal to B(A(x)); step 2: the users in the user group exchange the intermediate results related to the integer layer iteratives of the A(x); and the step 3: the users respectively adopt the received intermediate results to calculate the key K which is shared by the user group. The method has the advantages of unique coding style, strong attack resistance, enhanced scale and complexity of the cryptographic algorithm, and improved space and safety of the algorithm.