Prime 256 is too long

[micchickenburger]

Prime Group 256 is defined here:

tssrp6a/src/parameters.ts

Line 32 in ec90b27

"125617018995153554710546479714086468244499594888726646874671447258204721048803",

I calculate this prime having a length of 264 bits instead of 256 bits. All the other primes are the correct length. (It is possible that I made an error in my code, though.)

[bufistov]

Hey @micchickenburger! I was eventually able to take a look into this thanks to the global day off on Friday :)

I think you are partially correct :) This particular number requieres 257 bits, 33 bytes to fit.
Here is a small check I tried:

$ python3
Python 3.12.7 (main, Oct  1 2024, 02:05:46) [Clang 15.0.0 (clang-1500.3.9.4)] on darwin
Type "help", "copyright", "credits" or "license" for more information.
>>> a=125617018995153554710546479714086468244499594888726646874671447258204721048803
>>> bin(a)
'0b10001010110111000101101101001001011100000111000000100010101101001001011001111001010000000101101000011011001110011010111000111011110100101101010011110100010101001111001111110110101010110110010010110010111111000011111011011010110110010101000101110110011100011'
>>> len(bin(a))
259
>>> len(bin(a))-2
257
>>>

I wanted to create a test that checks the size of all the numbers in the parameters, but this test actually already exists. Please take a look.

The same test also sends us to the related discussion about why the parameter is actually of 257 bits instead of 256 bits.
I understood that this is a known issue, but no-one care since such small prime numbers cannot be used in a real life application. We keep it only for testing purposes.