A random polymer comprising: a unit represented by the following Chemical Formula 1; and a brancher derived from a compound represented by the following Chemical Formula 2 or a brancher represented by the following Chemical Formula 3: wherein, in Chemical Formulae 1 to 3, A is -SO 3 H, -SO 3 - M +, -COOH, -COO - M +, -PO 3 H 2, -PO 3 H - M +, -PO 3 2- 2M +, -O(CF 2) m SO 3 H, -O(CF 2) m SO 3 - M +, -O(CF 2) m COOH, -O(CF 2) m COO - M +,-O(CF 2) m PO 3 H 2, -O(CF 2) m PO 3 H - M + or -O(CF 2) m PO 3 2- 2M +; m is an integer of 2 to 6; M is a group 1 element; R1 and R2 are the same as or different from each other, and each independently a halogen group; n is an integer of 2 to 10, and structures in the 2 to 10 parentheses are the same as or different from each other; X is S; O; CO; SO; SO 2; NR; a hydrocarbon-based or fluorine-based assembly; l is an integer of 0 to 10; when l is 2 or greater, two or more Xs are the same as or different from each other; Y1 and Y2 are the same as or different from each other, and each independently NRR; an aromatic ring in which one, two or more are substituted with substituents selected from the group consisting of a hydroxyl group and a halogen group; or an aliphatic ring in which one, two or more are substituted with substituents selected from the group consisting of a hydroxyl group and a halogen group; R is an aromatic ring substituted with a halogen group; or an aliphatic ring substituted with a halogen group; and Z is a trivalent organic group. a unit represented by the following Chemical Formula 1; and a brancher derived from a compound represented by the following Chemical Formula 2 or a brancher represented by the following Chemical Formula 3: wherein, in Chemical Formulae 1 to 3, A is -SO 3 H, -SO 3 - M +, -COOH, -COO - M +, -PO 3 H 2, -PO 3 H - M +, -PO 3 2- 2M +, -O(CF 2) m SO 3 H, -O(CF 2) m SO 3 - M +, -O(CF 2) m COOH, -O(CF 2) m COO - M +,-O(CF 2) m PO 3 H 2, -O(CF 2) m PO 3 H - M + or -O(CF 2) m PO 3 2- 2M +; m is an integer of 2 to 6; M is a group 1 element; R1 and R2 are the same as or different from each other, and each independently a halogen group; n is an integer of 2 to 10, and structures in the 2 to 10 parentheses are the same as or different from each other; X is S; O; CO; SO; SO 2; NR; a hydrocarbon-based or fluorine-based assembly; l is an integer of 0 to 10; when l is 2 or greater, two or more Xs are the same as or different from each other; Y1 and Y2 are the same as or different from each other, and each independently NRR; an aromatic ring in which one, two or more are substituted with substituents selected from the group consisting of a hydroxyl group and a halogen group; or an aliphatic ring in which one, two or more are substituted with substituents selected from the group consisting of a hydroxyl group and a halogen group; R is an aromatic ring substituted with a halogen group; or an aliphatic ring substituted with a halogen group; and Z is a trivalent organic group. A is -SO 3 H, -SO 3 - M +, -COOH, -COO - M +, -PO 3 H 2, -PO 3 H - M +, -PO 3 2- 2M +, -O(CF 2) m SO 3 H, -O(CF 2) m SO 3 - M +, -O(CF 2) m COOH, -O(CF 2) m COO - M +,-O(CF 2) m PO 3 H 2, -O(CF 2) m PO 3 H - M + or -O(CF 2) m PO 3 2- 2M +; m is an integer of 2 to 6; M is a group 1 element; R1 and R2 are the same as or different from each other, and each independently a halogen group; n is an integer of 2 to 10, and structures in the 2 to 10 parentheses are the same as or different from each other; X is S; O; CO; SO; SO 2; NR; a hydrocarbon-based or fluorine-based assembly; l is an integer of 0 to 10; when l is 2 or greater, two or more Xs are the same as or different from each other; Y1 and Y2 are the same as or different from each other, and each independently NRR; an aromatic ring in which one, two or more are substituted with substituents selected from the group consisting of a hydroxyl group and a halogen group; or an aliphatic ring in which one, two or more are substituted with substituents selected from the group consisting of a hydroxyl group and a halogen group; R is an aromatic ring substituted with a halogen group; or an aliphatic ring substituted with a halogen group; and Z is a trivalent organic group.