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   Phantasm (phnt@fluffytail.org)'s status on Tuesday, 04-Mar-2025 06:56:22 JST Phantasm

   • meso
   @meso It depends on your scale and how smooth you want the plot to look like. The more values you throw at the equation in your wanted interval, the more "smooth" the resulting chart will be. The reason why Bézier curves look smooth on a screen is because the software throws a lot points at it. A linear Bézier curve is literally a linear line.
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     Phantasm (phnt@fluffytail.org)'s status on Tuesday, 04-Mar-2025 07:08:26 JST Phantasm

     in reply to

     • meso
     @meso A plotted curve is a result of an equation in 2D or 3D space and of the points on the x or y axis you plug into the equation.
     
     Of course the elliptic curves I was talking about in relation to Diffie-Hellman are standardized (usually Curve25519; If you look at the Matlab, you can see that I stole the equation for that, because I thought it would plot into something nice to look at. But it just looks like a parabola).
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     meso (meso@new.asbestos.cafe)'s status on Tuesday, 04-Mar-2025 07:08:27 JST meso

     in reply to
     @phnt wait really? its not like a mathematically defined way of creating a curve? its just... points? what the fuck man
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     Phantasm (phnt@fluffytail.org)'s status on Tuesday, 04-Mar-2025 07:23:45 JST Phantasm

     in reply to

     • meso
     @meso
     
     from wiki:
     >Curve25519 is constructed such that it avoids many potential implementation pitfalls.
     
     There isn't really anything special about the equation itself, or the numbers. The numbers were chosen mostly at random with consideration for some properties as to not undermine the "security" behind the elliptic discrete log problem.
     
     https://en.wikipedia.org/wiki/Nothing-up-my-sleeve_number
     
     On a related note: The reason why the DUAL_EC_DRBG (Dual elliptic curve deterministic random bit generator) was a suspected backdoor by the NSA is specifically because the NSA didn't disclose how they got the number. For example the SHA hash algorithms also depend on these randomly selected variables (one of them is pi with some amount of decimal accuracy; there's also letters in the alphabet and stuff like that; something you wouldn't suspect was placed there to compromise the system). The ChaCha stream cipher also has a part of the table that is always at the beginning the same value. In the ChaCha case it literally describes what the algorithm does (expand 32-byte k)
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     meso (meso@new.asbestos.cafe)'s status on Tuesday, 04-Mar-2025 07:23:46 JST meso

     in reply to
     @phnt i know Curve25519 but i wonder why 25519 specifically
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     meso (meso@new.asbestos.cafe)'s status on Tuesday, 04-Mar-2025 07:23:46 JST meso

     in reply to

     • meso
     @phnt > 2^255 − 19
     ah, but why -19
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     Phantasm (phnt@fluffytail.org)'s status on Tuesday, 04-Mar-2025 07:48:23 JST Phantasm

     in reply to

     • meso
     @meso It's basically as you've said. Instead of a prime factor, there was a chance that the points P and Q for the curve chosen by the NSA had a secret relation with a number that only the NSA knew. And with that knowledge it was trivially simple to go back through the random bits and get into the state of the generator which would compromise all future random bits.
     
     Instead of a prime factor, it was a simple number (d) with which you would multiply Q and it would give you P. (dQ = P). The reason why this simple fact compromises the whole algorithm is somewhat complex, but Computerphile also made a video about that called the Elliptic Curve Back Door.
     
     https://www.youtube.com/watch?v=nybVFJVXbww
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     meso (meso@new.asbestos.cafe)'s status on Tuesday, 04-Mar-2025 07:48:25 JST meso

     in reply to
     @phnt >was a suspected backdoor by the NSA is specifically because the NSA didn't disclose how they got the number.
     Oh, I did wonder about that. so it's kind of similar to finding out the prime factor of a number in that sense. like NSA knowing a prime factor and not sharing it, people can't find it out but the NSA can (I am not entirely sure how this works so i think you'll correct me that it isn't a prime factor in stuff like RSA encryption and i'm confusing this for something else)
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     Phantasm (phnt@fluffytail.org)'s status on Tuesday, 04-Mar-2025 19:06:02 JST Phantasm

     in reply to

     • meso
     @meso Curiosity. Everything I know about computers and related subjects is self taught. The math behind it usually isn't that advanced as computers also can't calculate advanced math quickly enough. And most of it can be understood in an abstract way where you take the properties of the used math at face value while still understanding how the whole algorithm works. The very advanced part usually is the proof of why it works.
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     meso (meso@new.asbestos.cafe)'s status on Tuesday, 04-Mar-2025 19:06:03 JST meso

     in reply to
     @phnt how did you learn all this? I missed many many years of math on account of not going to school for years and dammit i wanna get good at it
     Phantasm likes this.