Guaiacum uses, including as lumber, for medicinal purposes, and as ornamentals. The trade of all species of "Guaiacum" is controlled under CITES Appendix II. "Guaiacum officinale" is the national flower of Jamaica, while "Guaiacum sanctum" is the national tree of the Bahamas. The genus is famous as the supplier of lignum vitae, which is the heartwood of several species in the genus. It is the fourth-hardest variety of wood as measured by the Janka hardness test, requiring a force of to embed a steel ball in diameter half that distance into the wood. The Spanish encountered guaiacum wood when they conquered
Computational hardness assumption an average-case hardness assumption is stronger than a worst-case hardness assumption for the same problem. Furthermore, even for incomparable problems, an assumption like the Exponential Time Hypothesis is often considered preferable to an average-case assumption like the planted clique conjecture. Note, however, that in most cryptographic applications, knowing that a problem has some hard instance (i.e. a problem is hard on the worst-case) is useless because it does not provide us with a way of generating hard instances. Fortunately, many average-case assumptions used in cryptography (including RSA, discrete log, and some lattice problems) can be based on worst-case assumptions via