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Comment by RcouF1uZ4gsC | Hacker News Reader

I think a big reason for the persistence of RSA keys is that they are easier to understand than eliptical curve.

Basically, every first year computer science student who has taken discrete math can write a (horribly broken, ineffecient) implementation of RSA encryption and decryption and have a pretty good intuitive understanding of what is going on.

In fact, I did that just for fun as a first year CS student.

With elliptical curves, I have read through the multiple websites and explanations and over several years and still feel I do not have an intuitive grasp of what is really going on.

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In my second year, I had to do this on paper, showing every step. The prime sizes were about 10 digits as to keep things within a few sheets of paper.

It seems my memory of it was traumatizing, one of the few assignments I had where I remember where I sat in the library computing this assignment on paper. Without electronic assistance.

At least you took the sound advice of always using a library to do cryptography.

lol

Golf clap.

I’m going disagree with this. Elliptic curves are just a scalar private key multiplied with a static point to make a public key. It’s very easy to make a naive implementation and there are far fewer gotchas.

> Elliptic curves are just a scalar private key multiplied with a static point to make a public key

To a lot of people, this will sound like

"Monads are just monoids in the category of endofunctors"

Basically, every high school student knows what prime numbers are, what factors are, what exponentiation is, what modulo (remainder) is. A scientific calculator will have all the functions for you to do RSA encryption by hand with small primes.

You need more math courses to understand what it means to multiply a point by a scalar along a curve.

elliptical curve crypto really is pretty simple when explained geometrically.

https://arstechnica.com/information-technology/2013/10/a-rel...

But the explanation is lacking.

>A more interesting property is that any non-vertical line will intersect the curve in at most three places.

If this is correct, that means a line could intersect at 1,2, or 3 places.

>Let's imagine this curve as the setting for a bizarre game of billiards. Take any two points on the curve and draw a line through them; the line will intersect the curve at exactly one more place.

No that is not correct. I can already see two points where a horizontal line would only intersect 2 points and not intersect another. Basically, you can draw a line tangent to the curve on the left and intersect only 2 points instead of three.

These geometric explanations strike me as simplifications, and as I imagine what it would look like in code, I get the feeling that there would be all sorts of special cases, boundary conditions, and asymptotes.

The other part of RSA is that mathematicians have been doing math on primes for millennia, prime factoring is likely as hard as we think it is, and RSA, despite being pretty old. hasn't had problems crop up. The only downsides are key length and quantum computing.

Implementations of RSA have suffered from all sorts of problems that have led to real world attacks irrespective of the hardness of factoring prime numbers. The intuition behind RSA being hard is alluring in its simplicity, but it's deceptive. https://blog.trailofbits.com/2019/07/08/fuck-rsa/

How many of these types of issues are unique to RSA? Does it being old help in that more of them have been discovered, and there are known implementations that are usually good?

Its stil based on a problem highly related to prime numbers.

Rsa fits on a tshirt, Export of cryptography from the United States - Wikipedia https://en.m.wikipedia.org/wiki/Export_of_cryptography_from_...

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