The key to establish an encrypted language to preserve the privacy of millions of internet data and that has proved to be vulnerable to hackers would lie in the Lo Shu magic square, the legendary mathematical formula which emerged in China.
According to history, after a great flood, the inhabitants of a remote town began to offer sacrifices, without success, to calm the Lou River, until a turtle emerged from its waters with a magic pattern where the vertical, horizontal and diagonal sum of the numbers 1 through 9 written on its shell would always be 15. This number determined the exact amount that would calm the Gods.
“As in this era Arabic writing did not exist, numbers were represented by dots and this was the most adequate manner to teach mathematics,” said Universidad Nacional de Colombia (UNal) Department of Mathematics Professor Agustín Moreno Cañadas, from whom the Lo Shu magic square has a scientific interpretation and may be decoded.
Moreno and a group of researchers have used the adapted formula to send encrypted messages with information on his work says the encryption system based on the magic square is so simple that they only need to substitute the possible combinations with letters of the alphabet to transmit a message.
The “Steps of Yu” are three established forms to interpret the Lo Shu magic square stemming from three fundamental beliefs, part of a religion based on the Big Dipper.
“The dance of the magic square is performed following the bearing of the stars of this constellation and is usually carried out by three priests,” says Moreno, for whom this is a coincidence which had not been seen before, despite the mystic importance of the figure for many followers of this philosophic thinking.
Paraphrasing Sun Tzu, a military strategist and author of the Art of War, Moreno says that as in music, the magic square makes possible to compose unimaginable melodies, it would also be possible to develop an infinite number of codes.
A graphic comprised of dots, vertices (or meeting points) and edges (or intersection lines) all connected, which could be directed in a way that point one is directed towards the other and vice versa. Although the procedure is simple it is necessary to decode the magic square so that all the nine symbols acquire significance.
In the case of the Lu Shu magic square, the number 5 is in the center, with a vertex connecting to the rest, equal to what is known as the star with the least possible amount of energy.
As the bearing of the graphic corresponding to the number 9 has the maximum energy among all the numbers that comprises the square, to decode the square it is necessary to work your way from the center to the outside.
As there is the possibility of multiplying the trajectories according to the bearing between them, the Lo Shu square allows building words on what Moreno deems as the best of languages, as they use symbols devoid of any association to cultural or ideological particularities.
After establishing that only numbers from 1 to 5 would be used to produce the remaining amounts in the square, they discovered it was the same as the “tree of life” and that superimposing an equivalent method, –the ying-yang symbol– they could establish the trajectories and determine which was the most adequate for the corresponding calculations or what in mathematics is known as path algebra.
The category is an algebraic structure which provides sense to integers and in what in cryptography is one of the links to decipher a code, stemming from a theorem in which only two numbers are enough to produce the rest of the matrix.
As substituting numbers for letters would provide each combination a value and specific equivalence, the magic squares would allow establishing an encrypted language –similar to the one used by masons to encrypt their messages– coming from trajectories and calculating graphics which could inclusively result in an image.
Former UNal rector and mathematician Professor Ignacio Mantilla contradicts this saying, “The squares do not have anything special that excel over numeric properties which seem magical and being placed to the reach of all are elevated to a category they do not possess.”
According to Mantilla, using algorithms based on number properties such as prime numbers –a natural number greater than 1 that cannot be formed by multiplying two smaller natural numbers– is the most appropriate to be implemented in machines and processes.
“The procedure which normally is carried out to achieve encryption scientifically corresponds to algorithms which have been very useful in backing security and the internet, and definitely their sole objective is to propose that they can be used by specialized firms or mathematicians to develop other theories using these principles,” he added.
Having a system that only adds and subtracts would not only preserve the privacy of relevant but also would avoid using cyphering codes whose interpretation would not be accessible to anybody.
It is good to remember that in May of last year, the FBI released a world alert suggesting rebooting all routers, as a consequence of a cyberattack coming from Russia which could insert a virus through these domestic devices to access personal data of users and/or companies.
A vulnerable code
Although quantum cryptography is a considered a secure cyphering method, as its sends two photons simultaneously in different directions and at both ends of the connection to alert of any sign of possible interference, researchers of the Universities of Linköping and Stockholm (Sweden) demonstrated that it is possible to replace the light source and intercept the message if the source of the photons is substituted by a source of traditional light.
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