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| title = d65536 | | title = d65536 | ||
| image = d65536.png | | image = d65536.png | ||
− | | titletext = They're robust against quantum attacks because it's hard to make a quantum system that large | + | | titletext = They're robust against quantum attacks because it's hard to make a quantum system that large |
}} | }} | ||
==Explanation== | ==Explanation== | ||
− | In binary computing, 16 bit | + | {{incomplete|Created by a HEXAKISMYRIAPENTAKISCHILIAPENTAHECTATRIACONTAKAIHEXAHEDRON - The claim in the trivia that the numbers refer to a comic, should be substantiated with an explanation. If true interesting, if not... Do NOT delete this tag too soon.}} |
+ | In binary computing, 16 bit numbers range from 0 to 65535, for a total of 65536 unique numbers, a number which is hence well-known to software engineers. Generating large numbers in a manner that is truly random is a recurring problem in cryptography, required to send private messages to another party. People today still use dierolls to generate private random numbers. | ||
− | In role-playing games (and occasionally in other tabletop games), | + | In role-playing games (and occasionally in other tabletop games), dice are often referred to as d''n'' according to their number of faces. A traditional six-faced die would be a d6, and many popular pen-and-paper role-playing games use dice ranging between d4 and d20. While there are larger dice used in tabletop games (most commonly d100), these are usually split into multiple smaller ones to save the hassle of throwing large dice. For example, a d100 is often two d10s rolled together, with one die providing the first digit and the other die giving the second digit — the total number of possible combinations (100) is the product of the number of faces of the two dice (10 * 10). There are, however, "real" {{w|Zocchihedron|d100s}} and similar dice as well, but they are considered specialty dice and often nicknamed "golf balls" to emphasize how large and unwieldy they are. The Zocchihedron (d100) die is also biased because of geometry requiring different sized faces, the next unbiased die is a d120, it is very likely that [[Cueball|Cueball's]] d65536 die is also biased. |
− | Here, Cueball has constructed a d65536 for generating random 16 bit numbers. It may have solved the problem of generating large random numbers with fewer die rolls, but | + | Here, Cueball has constructed a d65536 for generating random 16 bit numbers, likely with a [https://www.shapeways.com/product/U9CN6MT6X/d256 3d printer] or other CAM tools. It may have solved the problem of generating large random numbers with fewer die rolls, but presents a new set of challenges from its sheer size, dwarfing an average human. While large in itself, a die that big could still be emulated by rolling multiple dice (e.g. 8 4-faced dice or 16 coin flips) and converting the result into binary before getting the desired number. Part of the humor stems from the the comic completely failing to mention another big problem with this die: Deciding which of the 65536 faces is up. This is another problem with a d100, as many sides appear to be up at once. Similarly horrible hilarity will ensue if such a massive die is cast with enough energy to be random while expect it to stop rolling in a short period of time let alone on a table top or even within a building (which raises the question of whether breaking through a wall or furniture is all part of the randomization or requiring a re-roll as per house rules). |
The closest regular shape similar to the depicted in the comic could be a {{w|Goldberg polyhedron}}. However, no such polyhedron exists with exactly 65536 hexagonal faces. The closest Goldberg Polyhedron has a mixture of 65520 hexagons and 12 pentagons, totaling 65532 faces. It is possible to construct a fair die without a matching regular shape by limiting the sides which it could land on and designing those sides to be fair (for instance, a prism with rectangular facets that extend its entire length, and rounded ends to ensure it doesn't balance on end). | The closest regular shape similar to the depicted in the comic could be a {{w|Goldberg polyhedron}}. However, no such polyhedron exists with exactly 65536 hexagonal faces. The closest Goldberg Polyhedron has a mixture of 65520 hexagons and 12 pentagons, totaling 65532 faces. It is possible to construct a fair die without a matching regular shape by limiting the sides which it could land on and designing those sides to be fair (for instance, a prism with rectangular facets that extend its entire length, and rounded ends to ensure it doesn't balance on end). | ||
− | The title text references how cryptographic systems (especially RSA and other factoring-is-hard based systems) are vulnerable to quantum attacks as quantum computing technology develops. The title text is essentially punning on the idea of a "large" quantum system. "Large" in the quantum computing sense would be on the order of 64 qubits each of which would be an atom or two at most. This would still be microscopic and will never be as large as the giant die the comic is centered on; but for a well-observed environment and human rolling without sufficient entropy (consider somebody obsessed with a certain number dropping the die on something soft), a conventional computer could predict some rolls. See also [[538]] for non-mathematical paths of cryptography | + | The title text references how many cryptographic systems (especially RSA and other factoring-is-hard based systems) are vulnerable to quantum attacks as quantum computing technology develops. The title text is essentially punning on the idea of a "large" quantum system. "Large" in the quantum computing sense would be on the order of 64 qubits each of which would be an atom or two at most. This would still be microscopic and will never be as large as the giant die the comic is centered on; but for a well-observed environment and human rolling without sufficient entropy (consider somebody obsessed with a certain number dropping the die on something soft), a conventional computer could predict some rolls. See also [[538]] for non-mathematical paths of cryptography. |
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==Transcript== | ==Transcript== | ||
− | :[A large sphere with a several lines, and in some places grids, are shown. Cueball, standing next to it, is dwarfed by its size, as it is at least seven times as tall as he is. The sphere has many lines following various great circles or parallel lesser circles around the curve of the sphere, and some patches of cross hatching to suggest further texturing along these lines hovering just below the degree of most of the illustrative detailing | + | :[A large sphere with a several lines, and in some places grids, are shown. Cueball, standing next to it, is dwarfed by its size, as it is at least seven times as tall as he is. The sphere has many lines following various great circles or parallel lesser circles around the curve of the sphere, and some patches of cross hatching to suggest further texturing along these lines hovering just below the degree of most of the illustrative detailing. In the top right part of the ball is a black circle. An arrow points to this circle, and the end of the arrow goes to a larger circle that partly obscures the rightmost part of the sphere. The circle shows a zoom in on the surface in the black circle on the sphere. The zoom shows a small portion of the spheres surface, showing that the grid comes along because the sphere is divided into elongated hexagonal faces with numbers up to at least five-digits. Seven numbers can be fully seen, but there are nine other faces partly shown, five of these with part of their numbers visible, one of these clearly only have four digits. One of the empty faces must also have a number with only 1-3 digits, as no numbers are visible although a significant part of the face is visible.] |
:[Here follows the numbers in the zoomed in part of the sphere, with "..." represents numbers being cut off. The numbers are read in lines left to right, even though the numbers are tilted from down towards the right, which could have suggested a different reading order.] | :[Here follows the numbers in the zoomed in part of the sphere, with "..." represents numbers being cut off. The numbers are read in lines left to right, even though the numbers are tilted from down towards the right, which could have suggested a different reading order.] | ||
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*If a real d65536 were constructed with each number having an equal area and each printed in 12 point font, the resulting die would be about 5 feet (1.5 meters) in diameter, which isn't several times the size of a person as the comic suggests, but is still large enough to be hilariously inconvenient. If it were made out of standard acrylic, and not hollow, it would weigh about 2 tons (1700kg). | *If a real d65536 were constructed with each number having an equal area and each printed in 12 point font, the resulting die would be about 5 feet (1.5 meters) in diameter, which isn't several times the size of a person as the comic suggests, but is still large enough to be hilariously inconvenient. If it were made out of standard acrylic, and not hollow, it would weigh about 2 tons (1700kg). | ||
*This die would have a 0.00001526 chance of rolling a natural one (or any other number). | *This die would have a 0.00001526 chance of rolling a natural one (or any other number). | ||
− | *There are seven 16-bit numbers fully visible in the picture: 30827, 25444, 11875, 28525, 12082, 13874 and 13359. | + | *There are seven 16-bit numbers fully visible in the picture: 30827, 25444, 11875, 28525, 12082, 13874 and 13359. They conceal a message. If these numbers are split big-endian into two 8-bit ASCII characters each, the result is <code>xkcd.com/2624/</code>{{citation needed}}. |
{{comic discussion}} | {{comic discussion}} | ||
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[[Category:Cryptography]] | [[Category:Cryptography]] | ||
[[Category:Comics featuring Cueball]] | [[Category:Comics featuring Cueball]] | ||
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