The volume of data transferred is constantly increasing, but the absolute
security of these exchanges cannot be guaranteed, as shown by cases of
hacking frequently reported in the news. To counter hacking, a team from the
University of Geneva (UNIGE), Switzerland, has developed a new system based
on the concept of zero-knowledge proofs, the security of which is based on
the physical principle of relativity: information cannot travel faster than
the speed of light. Thus, one of the fundamental principles of modern
physics allows for secure data transfer. This system allows users to
identify themselves in complete confidentiality without disclosing any
personal information, promising applications in the field of
cryptocurrencies and blockchain. These results can be read in the journal
Nature.

When a person—the so called "prover"—wants to confirm their identity, for
example when they want to withdraw money from an ATM, they must provide
their personal data to the verifier, in our example the bank, which
processes this information (e.g. the identification number and the pin
code). As long as only the prover and the verifier know this data,
confidentiality is guaranteed. If others get hold of this information, for
example by hacking into the bank's server, security is compromised.

### Zero-knowledge proof as a solution

To counter this problem, the prover should ideally be able to confirm their
identity, without revealing any information at all about their personal
data. But is this even possible? Surprisingly the answer is yes, via the
concept of a zero-knowledge proof. "Imagine I want to prove a mathematical
theorem to a colleague. If I show them the steps of the proof, they will be
convinced, but then have access to all the information and could easily
reproduce the proof," explains Nicolas Brunner, a professor in the
Department of Applied Physics at the UNIGE Faculty of Science. "On the
contrary, with a zero-knowledge proof, I will be able to convince them that
I know the proof, without giving away any information about it, thus
preventing any possible data recovery."

The principle of zero-knowledge proof, invented in the mid-1980s, has been
put into practice in recent years, notably for cryptocurrencies. However,
these implementations suffer from a weakness, as they are based on a
mathematical assumption (that a specific encoding function is difficult to
decode). If this assumption is disproved—which cannot be ruled out
today—security is compromised because the data would become accessible.

Today, the Geneva team is demonstrating a radically different system in
practice: a relativistic zero-knowledge proof. Security is based here on a
physics concept, the principle of relativity, rather than on a mathematical
hypothesis. The principle of relativity—that information does not travel
faster than light—is a pillar of modern physics, unlikely to be ever
challenged. The Geneva researchers' protocol therefore offers perfect
security and is guaranteed over the long term.

### Dual verification based on a three-colorability problem

Implementing a relativistic zero-knowledge proof involves two distant
verifier/prover pairs and a challenging mathematical problem. "We use a
three-colorability problem. This type of problem consists of a graph made up
of a set of nodes connected or not by links," explains Hugo Zbinden,
professor in the Department of Applied Physics at the UNIGE. Each node is
given one out of three possible colors—green, blue or red—and two nodes that
are linked together must be of different colors. These three-coloring
problems, here featuring 5,000 nodes and 10,000 links, are in practice
impossible to solve, as all possibilities must be tried. So why do we need
two pairs of checker/prover?

"To confirm their identity, the provers will no longer have to provide a
code, but demonstrate to the verifier that they know a way to three-color a
certain graph," says Nicolas Brunner. To be sure, the verifiers will
randomly choose a large number of pairs of nodes on the graph connected by a
link, then ask their respective prover what color the node is. Since this
verification is done almost simultaneously, the provers cannot communicate
with each other during the test, and therefore cannot cheat. Thus, if the
two colors announced are always different, the verifiers are convinced of
the identity of the provers, because they actually know a three-coloring of
this graph.

"It's like when the police interrogates two criminals at the same time in
separate offices: it's a matter of checking that their answers match,
without allowing them to communicate with each other," says Hugo Zbinden. In
this case, the questions are almost simultaneous, so the provers cannot
communicate with each other, as this information would have to travel faster
than light, which is of course impossible. Finally, to prevent the verifiers
from reproducing the graph, the two provers constantly change the color code
in a correlated manner: what was green becomes blue, blue becomes red, etc.
"In this way, the proof is made and verified, without revealing any
information about it," says the Geneva-based physicist.

### A reliable and ultra-fast system

In practice, this verification is carried out more than three million times,
all in less than three seconds. "The idea would be to assign a graph to each
person or client," says Nicolas Brunner. In the Geneva researchers'
experiment, the two prover/verifier pairs are 60 meters apart, to ensure
that they cannot communicate. "But this system can already be used, for
example, between two branches of a bank and does not require complex or
expensive technology," he says. However, the research team believes that in
the very near future this distance can be reduced to one meter. Whenever a
data transfer has to be made, this relativistic zero-knowledge proof system
would guarantee absolute security of data processing and could not be
hacked. "In a few seconds, we would guarantee absolute confidentiality,"
concludes Hugo Zbinden.

## Reference:

SÃ©bastien Designolle, Experimental relativistic zero-knowledge proofs,
Nature (2021).
DOI: 10.1038/s41586-021-03998-y.