In an increasingly interconnected and computerised world, with more powerful and capable computers and more advanced artificial intelligence algorithms, the protection of sensitive information has become a critical issue. Today, the most important and most widely used encryption tools are one-way functions: in essence, mathematical functions that are relatively easy to perform but almost impossible to reverse from the end result. At least for now, because security experts are sounding the alarm about the imminent emergence of quantum computers and their potential to breach one-way encryption systems. Some experts estimate that this could happen in as little as ten years.
Against this backdrop, efforts have turned to the development of physical functions (or systems) that are unclonable, i.e. physical systems that spontaneously generate randomness. And this, which may sound rather ambiguous or complex, is easy to visualise when we think of systems such as, for example, the arrangement of water droplets on the windscreen of our car every time it rains; it is completely random. This type of unclonable physical function would be the 2.0 version of one-way functions, because each generation process would be irreproducible and impossible to replicate and reverse. Every time it rains, the drops fall unpredictably on that front windscreen.
With this in mind, researchers at ETH Zurich have proposed a new physically unclonable system designed primarily to verify the authenticity of a work of art.
Brainteaser 1: Deconstructing compositions in red, yellow, blue and black
Which of the following reproductions of Piet Mondrian’s 1921 Composition in Red, Yellow, Blue and Black is the authentic one? What telltale differences do each of the fake reproductions have?
In reality, however, we should speak of a (bio)chemically unclonable system, since it is based on the randomness of DNA sequences that are generated in a culture medium. In very simplified terms, the new system involves converting a numerical value into a DNA primer (a small piece of DNA). The primer is fed into a reservoir in which trillions of different DNA strands have been randomly created (to be more precise, millions of different patterns have been created, each of which is repeated hundreds of times). The idea is that this primer, which encodes the key, will bind to a particular strand pattern of all those present, based on the complementarity of the nitrogenous bases.
A necessary aside: DNA is a code written with four nitrogenous bases: adenine (A), guanine (G), thymine (T) and cytosine (C). DNA molecules are made up of two complementary strands. This complementarity is provided by the complementarity of the nitrogenous bases, which are paired two by two: A binds to G and C to T.
Therefore, if the primer were A-G-A-T, it would only bind to a strand that has the complementary sequence C-T-C-G at some point in its structure.
The next step is to add the enzyme DNA polymerase into the medium, which adds complementary bases to a single strand. However, it only works from a point where two complementary fragments already exist. In other words, it will only complete the chain (all existing copies of that template) to which the primer has been attached. The result is a two-stranded DNA molecule in an ocean of DNA strands. This makes it possible to separate it from the rest and obtain a sequence of nitrogenous bases much longer than the original and random one, which is the key or output value. And because the pool of DNA strands is randomly generated each time, it is irreproducible.
Brainteaser 2: Searching for complementary DNA strands
If our primer is GATTACA, which of the following DNA strands from our pool will it bind to?
1) CCGTAGACCTCTATTCACGCGCGTATATAGC
2) GTGTACACCAGGTTCTCAGTAATAA
3) TCAGCGCGCGAGCCGTGTGTCATTCATTTAAGC
4) CGGCGTTAATACCGAGTTGATGGAT
To make this clearer, let’s look at how the technique could be applied in practice: let’s imagine that the owner of an artwork decides to lend it for an exhibition. In order to guarantee the authenticity of the artwork when it is returned to him, before handing it over, a reservoir of DNA molecules is created and divided in two (as mentioned above, each model chain generated appears hundreds of times, which guarantees that both reservoirs will contain all the models). One of the reservoirs is kept by the owner, and the other is somehow introduced into the artwork (injected somewhere). When the artwork is returned, the owner generates a key that is converted into the primer, which is inserted into the stored reservoir and the reservoir retrieved from the artwork. If the output keys are identical in both cases (the DNA strands obtained at the end of the process), then the owner can be sure that it is the authentic artwork and not a forgery. The only way to forge the artwork would be to physically steal the reservoir of DNA molecules from the piece. But of course that would no longer be a computer security problem, because it could not be done by any computer no matter how quantum, nor by a hacker; such a crime could only be perpetrated by a white-collar criminal.
Brainteaser 3: The genetic key to its authenticity
At the end of the loan period to a museum for exhibition, the owner of the artwork obtains the following key (DNA sequence) from the reservoir of DNA strands that he generated at the time of the loan and a copy of which he inserted into the work:
GTGAATATTGTCTTCTTGTTATGGTGAATATTGCTTTTTCATTATG
Which of these three reproductions is the authentic one?
Solutions
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