CURVE object in Montgomery curves

[li0ard]

Is it possible to get the parameters of the montgomery curve through the CURVE property?

[paulmillr]

Not currently. Which params do you need and why?

[li0ard]

I need all the constants of the curve, because i'm developing a module to create birationally equivalent Weierstrass curves from Edwards and Montgomery curves

[paulmillr]

It would make sense to expose them if it was real curve methods.

We have very specific code for x25519 / x448. Generic Montgomery curves can't be constructed using it. Hence, this is a way of discouraging doing anything complex.

[li0ard]

You can see formulas here. Im just trying to port code from sage to noble

[paulmillr]

We only have two montgomery curves for now. Just hardcode the params. We won't have any generic methods for the near future, because there is no point to implement them. For example, there are no specs, no real-world usage, etc.

[li0ard]

Also possibly off topic, but how do I take a negative number to degree 2 (over x448 prime field)?

In sage i got:

p = 0xfffffffffffffffffffffffffffffffffffffffffffffffffffffffeffffffffffffffffffffffffffffffffffffffffffffffffffffffff
K = GF(p)
a = K(0x01)

print(-a^2)
# 726838724295606890549323807888004534353641360687318060281490199180612328166730772686396383698676545930088884461843637361053498018365438

in noble:

const f = Field(0x7fffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffedn)
const a = f.create(0x01)

console.log(f.pow(-a, 2n));
// 1n

[paulmillr]

I'm not sure what you're doing here. # 726838... is number which is just p - 1. It does not print the result.

The number is the same as f.create(-1n).