Was Jesus crucified naked?

Wikipedia's article on crucifixion says > While a crucifixion was an execution, it was also a humiliation, by > making the condemned as vulnerable as possible. Although artists have > traditionally depicted the figure on a cross with a loin cloth or a > covering of the genitals, the person being crucified was usually > stripped naked. Is there a scholarly consensus that Jesus was also crucified naked? How have Christian traditions and scholars explained this?