The black box groups are a group G whose elements are encoded by bit strings of length N and were introduced by Babai and Szemerdi in 1984 as a formalism for (constructive) group recognition and property testing.
In computational group theory, a black box group (black-box group) is a group G whose elements are encoded by bit strings of length N, and group operations are performed by an oracle (the "black box"). The black box groups were introduced by Babai and Szemeredi in 1984. They were used as a formalism for (constructive) group recognition and property testing. 
