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I'm looking for a process to create a material which has some easy to measure properties. These properties should be consistent over a long period. It should be very hard (expensive) to predict/reproduce a material which results in the same measurable properties. Every material product should generate an unique measurement result and impossible (or very expensive) to product a second product with the same measurement result.

What process, material and/or measurement could be used?

Some context: The goal would be block-chain backed physical cash currency. The process should result in a 'coin' (material product). The 'coin' can be 'read' (measurement of some over time consistent material properties) resulting in a 'coin-id' (measurement). The producer of the 'coin' reads the coin-id and adds a block to the chain which contains the 'coin-id' and his signature of the 'coin-id' and spends some (crypto) currency value. The physical coin represents the spend (crypto) currency value. For ease of use the signature could be attached to the coin (bar or qr-code). The blockchain also contains the certificates of the coin producers. The coins can be exchanged in the physical world without changes on the blockchain. A receiver of a coin can read (measure) the unique coin-id and scan the signature. A receiver knows the certificates of the coin producers. A receiver can check the veracity by checking if the coin-id is signed by a known coin producer certificate.

Addendum

Let the cost to produce a coin be c. Let the probability of a duplicate measurement be p. Let the value represented by the coin be v.

Because the represented value should be a lot bigger than the cost of a coin. The value should be a factor f bigger than the cost.

$v=cf$

The minimal value to make forgery too expensive:

$v=\frac{c}{p}$

The maximal p should be:

$p=\frac{c}{v}$

So given a $c=0.1$\$ and $v=100$\$

then the maximum $p=\frac{0.1}{100}=0.001$

Or put otherway around: given a more realistic forgery probability of $p=10^{-10}$

Maximum $f=\frac{1}{p}$, $f=10^{10}$

So a coin given $c=0.1$\$ could have a maximum value of $v=0.1*10^{10}=1.000.000.000$\$

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    $\begingroup$ Such material could be reverse engineered and reproduced. $\endgroup$
    – Poutnik
    Dec 23, 2021 at 8:27
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    $\begingroup$ @Poutnik Of course it could be reverse engineered. Likewise, md5 can be broken, given enough effort. The question (as always) is "Where is the money". If breaking a thing costs too much, it is effectively unbreakable. $\endgroup$ Dec 23, 2021 at 11:03
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    $\begingroup$ @IvanNeretin I have meant it in context of a single, not structured, reproducibly managed material, as I have not at the time thought about heterogenous structured options. $\endgroup$
    – Poutnik
    Dec 23, 2021 at 11:06
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    $\begingroup$ A good red wine. Everyone knows that it is good, but it is impossible to make another bottle just like it. Measuring would be easy - just send me the bottle. $\endgroup$
    – Karsten
    Dec 23, 2021 at 14:07
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    $\begingroup$ Process to create: sexual reproduction; resulting material: fingerprints of the offspring (or retina patterns). $\endgroup$
    – Karsten
    Dec 23, 2021 at 14:11

3 Answers 3

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Impossible for a homogeneous material, however ...

basically every nonhomogeneous material fits your description. Say the pattern of microphase separation in a copolymer. Or the arrangement of filler particles in a composite.

You just have to think of something that is not only easy to make, but also easy to measure, i.e. take a digital photo of (microscopes and MRT or µCT scanners are out, I guess):

Pour resin of say four colours into a round bin, so you have four differently-coloured pie pieces. Now take a fork and run it through the bin a few times, perhaps in a "random" fashion (rotation, speed, direction, duration).

Let resin set, and you get a disk ("coin") with a pattern that is impossible to regenerate, even if someone stole the random number, which you delete immediately after use, that initialised the fork movement. They'd get something that looks somewhat similar, but clearly distinguishable. If they tried ten thousand times, they might get one or two that look similar enough to fool your algorithm, but that forgery is uneconomic, so you're safe.

Of course someone could forge those coins by printing a photographed pattern onto a coin, just like you can photocopy a dollar note.

The bigger problem I see is to make sure the "measurement" never creates a false negative (negative==forged) outcome, and that it doesn't require you to save a multi-megabyte dataset for every single coin.

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    $\begingroup$ I thought about the pattern of crystals formed by cooling of a liquid metal (zinc?) $\endgroup$ Dec 23, 2021 at 10:23
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    $\begingroup$ Good idea. They would keep the database of patterns of all released coins and any non-genuine coin would not match. $\endgroup$
    – Poutnik
    Dec 23, 2021 at 10:29
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    $\begingroup$ @Hubert A hash doesn't work, where any tiny difference (a scratch or sth.) makes the comparison fail, and you don't know why. You want a compression algorithm for the actual pattern, so you can quantify the difference between the thing on the blockchain and the picture of the coin in your hand. $\endgroup$
    – Karl
    Dec 23, 2021 at 20:28
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    $\begingroup$ I believe the nuclear weapons monitor folk have used glitter in epoxy as parts of seals before (with photographs). You could combine that with illumina-style coloured-dot imaging. $\endgroup$ Dec 24, 2021 at 16:28
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    $\begingroup$ Like your answer but concerned about robustness of the material. As such, I provided my alternate suggestion. $\endgroup$
    – AJKOER
    Dec 25, 2021 at 2:46
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The OP asks: What process, material and/or measurement could be used?

Answer: Snowflake maker, dihydrogen monoxide, photograph (with metric ruler included). "Snowflake maker" is a vapor condenser from steam onto a cooler surface or simply from the vapor.

enter image description here

It is well-known that no two snowflakes are alike. The unscientific media (Ref 1) propose the opposite, but the scientific consensus is that the probability of finding two identical snowflakes is zero (Ref 2).

An advantage of Snowflake Bitcoin is that it requires a physical repository (a bank, but not a snowbank) with a temperature low enough to prohibit melting and sublimation (which would allow the snowflakes to grow or diminish). Antarctica might not be cold enough; the actual snowflakes might have to be stored in outer space, but that cost could be prohibitive. An alternate bank could be physical storage of the actual photographs, or digital images with a very high resolution.

Ref 1. https://www.nbcnews.com/id/wbna16759121

Ref 2. https://www.loc.gov/everyday-mysteries/meteorology-climatology/item/is-it-true-that-no-two-snow-crystals-are-alike/

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  • $\begingroup$ Very seasonal, but the idea was that you cannot copy them, that excludes photographs, on paper or digital. And a currency that you cannot remove from the back does not need be represented as physical objects. $\endgroup$
    – Karl
    Dec 23, 2021 at 16:05
  • $\begingroup$ The photos are only the proof of ownership; the snowflakes are the product and cannot be duplicated, but are stored in the (very cold) bank. The snowflakes can be stored at great expense - for a time. The measurements are unique and irreproducible; the metric ruler can be augmented with another at 90 degrees, and various angles can be specified, as well as opacities and reflectance. Trust in the bank grows over time; the numbered photos serve as the substitute coin and are traded. Like serially numbered dollar bills vs gold in Fort Knox. No counterfeiting possible! $\endgroup$ Dec 23, 2021 at 16:37
  • $\begingroup$ Serially numbered bills have been counterfeited for centuries. If the copy is perfect, there is no way of knowing if a specific note is original. Even if you have a second one with the same number, you only know that you have a problem, but no solution. A picture that has no representative in the bank would obviously be a fake, but for that you can also store a copy of the photo, or a hash of the digital picture. No need to keep the snowflake. $\endgroup$
    – Karl
    Dec 23, 2021 at 16:48
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    $\begingroup$ Gotta combine the snowflakes with NFTs! $\endgroup$
    – Ed V
    Dec 23, 2021 at 16:52
  • $\begingroup$ The cold temperature would make handeling and exchanging the coin difficult. Is there an other crystallisation process that results in room temperature crystall-flakes? $\endgroup$
    – Hubert
    Dec 23, 2021 at 19:44
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As to what process, material and/or measurement could be used, the same that exists for minting metal alloy coins.

The material could be composed of said four (or more) alloys with the coin displaying an ID. The latter can be a mathematical function of associated chemical and electrical properties of said coin.

For example, an alloy of Ni, Sn, Fe and Zn may work based on the there actual (or predicted) respective variations in an anodic index (see this Table).

So, a simple chemical (like density) and electrochemical measurements (electrical resistance) may provide in conjunction with engraved ID an authenticity check.

This concept differs from government issued coins in the respect they are crafted for corrosion resistance (to increase circulation life span) while these coins are minted for identification purposes primarily,

Coins are known historically to be robust instrument for currency, and said coins can also be made completely virtual by mathematical fitting algorithms (applied to a provided data string) based on actual coins with specified varying compositions, from which the ID is generated.

Note: this answer complies with the need to be measured consistently over time at a low cost.

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  • $\begingroup$ Very clever to ingrave the ID so it will be a part of the material properties. $\endgroup$
    – Hubert
    Dec 26, 2021 at 18:10
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    $\begingroup$ What now stops me from reproducing a single coin with the same ID and alloy composition? Also highly accurate density measurements are expensive, and accurately measuring the electrical resistance of a coin is basically impossible. $\endgroup$
    – Karl
    Jan 3, 2022 at 13:05
  • $\begingroup$ Karl: Alas, experimenting with actual produced coins will likely suggests needed specifics. By the way, how does a vending machine (accepting coins for payment) actually determine a fake coin? Idea: Take advantage of existing technology! $\endgroup$
    – AJKOER
    Jan 4, 2022 at 0:29

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