Tuesday, 17 November 2015

public-key or the wedding-planner

Mathematician and cryptographer Alan Turing’s machines predated anything we’d recognise as a computer—these processors being a pure figment of his imagination in carrying brute applications out to their natural consequence, but the incredulous brilliance of this mental exercise does belie user-interface, reliance and ubiquity but rather in puzzling out the limitations of computation and programming. Given proper a proper set of instructions, an algorithm to solve a given computational problem, one of Turing’s Machines will tease out the answer eventually—though perhaps not to human-scale regardless of how these questions might be framed in mortal and approachable terms.Faced with finding the optimal seating arrangement for a small wedding party with the protocol that no guest ought to be seated next to one another whom would detest their neighbours and ruin the celebration might be easy enough—even for a human to juggle, an as yet hypothetical computer could reach the layout in a reasonable time, too, by running linearly through every possible permutation. While unconscionable teraflops make this seem instantaneous, Turing realised that for a grander matrimony with particularly prickly relations grows exponentially in complexity and computers can only work with the facts that they are given—with no capacity for compromise or good enough. Suppose one’s guests were to be the general assembly of the United Nations and then the number of possibilities that the computer must assay becomes greater than the number of atoms in the known Universe. The computer would cycle again and again for several billion years but would eventually produce a solution. The inability to provide a quick and comprehensive answer Turing recognised was a limitation and a liability, but at the same time Turing realised that this shortcoming was enduring and exploitable. Sometimes the numbers can be crunched forever. Perhaps there is no overseer, Evil Genius out there that knows where all the bodies are buried and the dirty little secrets that might make for a convivial setting, but there are also woefully multi-generational problems that can be solved with a clue. Data-encryption on one end delivers incredibly, increasingly long strings of numbers that are the product of multiplying two other numbers together on the other end, and hackers are not able to identify one or both figures—without some sort of clue. Just decades on, it seems too soon to descend into the realm of the practical from this elegant formulation, but having this limitation enables the security of on-line encryption and passing code. On the other hand, knowing how to solve logistics problems—given that finding a solution to one challenge presupposes eliminating the other as well—will serve up amazingly efficient systems of delivery. Both economic models are inseparable, it seems.