A diene rubber may give a crosslinked product or forming a rubber composition which has high levels of both ice grip performance and wet grip performance; a rubber composition may include the diene rubber; a tire member may be formed from the rubber composition or a crosslinked product thereof; and a tire may include the rubber composition or a crosslinked product thereof as at least a portion thereof. A resin modifier may include the diene rubber and give such a resin composition. A diene rubber may include butadiene units and an Mw of 5,000 to 50,000, and may satisfy (i) to (iii): (i) βcp>0; (ii) β12>40; and (iii) βcp/(β12−40)≤2, wherein β12 is the mol % of 1,2-bonded butadiene units, and βcp is the mol % of specific structural units, both with respect to all butadiene units present in the diene rubber.