for the purposes of known factoring algorithms. The existence of even one large factor would imply that the logarithm of a large number is missing, resulting in a very low intensity; because most numbers have this property, the device's output would tend to consist of stretches of low intensity output with brief bursts of high intensity output. In the above it is assumed that X is square-free, i.e. it is not divisible by the square of any prime. This is acceptable since the factoring algorithms only require "sufficiently many" smooth numbers, and the "yield" decreases only by a small constant factor due to the square-freeness assumption. There is also the problem of false positives due to the inaccuracy of the optoelectronic hardware, but this is easily solved by adding a PC-based post-processing step for verifying the smoothness of the numbers identified by TWINKLE. See also TWIRL, the successor to TWINKLE References Cryptanalytic devices Weizmann Institute of Science