Elliptikus görbék – a geometriától a titkos kommunikációig

"One cannot divide the cube into two cubes, nor the squared square into two squared squares, and in general, no power above the square up to infinity into two powers of the same number," says Fermat's conjecture in its original form, as it was phrased by the French mathematician of the seventeenth century. Although Fermat stated that he also knew a "quite amazing demonstration" of it, no such train of thought was left behind by him. No one managed to demonstrate the conjecture for 350 years. Therefore it was quite a sensation in the middle of the 1990s when mathematician Andrew Wiles from Britain succeeded. His demonstration is more or less based on the theory of elliptical curves. Apart from providing the key to a centuries-old enigma, elliptical curves can also be applied in encryption: they will probably have a role in the safe encryption of our credit cards in the future. Seemingly digressing from the subject a little bit, we also use the theory of elliptical curves to better understand the mysterious picture of the Dutch artist M. C. Escher called "Picture Gallery".