SciAm reports:
This demonstration of his recently discovered laws of perspective is said to have occurred sometime between 1415 and 1420, if his biographers are correct. The use of the laws of perspective amazed bystanders, altered the course of Western art for more than 450 years and, more recently, led to mathematical discoveries that enable elliptic curve cryptography. This is the security scheme that underpins Bitcoin and other cryptocurrencies and has become a fast-growing encryption method on other Internet platforms as well.The article explains how the above art inspired projective geometry, over the next few centuries.
You would think that Microsoft and Google would be able to quickly adapt to a superior software technology, but that has not happened.
Elliptic curve cryptography is a relative latecomer to the encryption game. The first suite of tools did not appear until 2004, far too late to become a standard for the Web but early enough to adopted by the inventors of Bitcoin, which launched in 2009.Current thinking is to abandon elliptic curve cryptography, and switch to new quantum-resistant protocols.Its status as the de facto standard for cryptocurrencies made people more familiar with it and more comfortable implementing it, although it still lags behind RSA encryption, the standard method in use today, by a wide margin.
Yet elliptic curve cryptography has distinct advantages over RSA cryptography: it provides stronger security per bit and is faster than RSA. An elliptic curve cryptographic key of just 256 bits is roughly as secure as a 3,072-bit RSA key and considerably more secure than the 2,048-bit keys that are commonly used.
The trouble is, if the industry could not switch from RSA to ECC, how will it switch to quantum-resistant?
ECC is superior to RSA in every respect, except compatibility with ancient systems. ECC is is faster, more secure, less error-prone, and smaller. The new quantum-resistant methods will be worse in all those things, except that it will supposedly resist some quantum computer that might be built in 50 years.
Most people think that non-euclidean geometry means curved manifolds, such as a sphere or hyperbolic space. But the original non-euclidean geometry was projective geometry. Projective geometry also indirectly led to the discovery of relativity.
Think of it this way. A geometry could be defined by the formula for the distance between two points. On a more elementary level, a geometry can be defined by what the lines are. In special relativity, the light rays are the lines of particular interest, and they are different from Euclidean geometry.