Test the P256 curve with ATECC508A

fastecdsa test with P256

start with a public key generated in:
https://github.com/sparkfun/SparkFun_ATECCX08a_Arduino_Library/blob/master/examples/Example1_Configuration/Example1_Configuration.ino

uint8_t publicKeyExternal[64] = {
0xF9, 0xC3, 0x6F, 0x89, 0x64, 0x62, 0x33, 0x78, 0xBD, 0xC0, 0x68, 0xD4, 0xBC, 0xE0, 0x7E, 0xD1, 
0x7C, 0x8F, 0xA4, 0x86, 0xF9, 0xAC, 0x0C, 0x26, 0x13, 0xCA, 0x3C, 0x8C, 0x30, 0x6D, 0x7B, 0xB6, 
0x1C, 0xD3, 0x67, 0x17, 0xB8, 0xAC, 0x5E, 0x4F, 0xEA, 0x8A, 0xD2, 0x3D, 0xC8, 0xD0, 0x78, 0x3C, 
0x23, 0x18, 0xEE, 0x4A, 0xD7, 0xA8, 0x0D, 0xB6, 0xE0, 0x02, 0x6A, 0xD0, 0xB0, 0x72, 0xA2, 0x4F
};

===> compress and split into 32 bit parts.
['f9c36f8964623378bdc068d4bce07ed17c8fa486f9acc2613ca3c8c306d7bb6', '1cd36717b8ac5e4fea8ad23dc8d0783c2318ee4ad7a8db6e026ad0b072a24f']
=== > convert to int

----------------- the int x,y --------------
7060700267049620596356235336501166570879242195065472674169415375238145604534
50930765665627190067685409014485724477345323970126409943904502612080370255

==> feed points into the fastecdsa library to create an encoded public key
----------------------

import fastecdsa as fec
import binascii

from binascii import hexlify, unhexlify

from fastecdsa.curve import P256 
from fastecdsa.encoding.sec1 import InvalidSEC1PublicKey, SEC1Encoder
from fastecdsa.point import Point

SEC1Encoder.encode_public_key(Point(7060700267049620596356235336501166570879242195065472674169415375238145604534,50930765665627190067685409014485724477345323970126409943904502612080370255,curve=P256),True)
-------
output:
-------
python3 testecdsa6.py

Traceback (most recent call last):
  File "testecdsa6.py", line 17, in <module>
    SEC1Encoder.encode_public_key(Point(7060700267049620596356235336501166570879242195065472674169415375238145604534,50930765665627190067685409014485724477345323970126409943904502612080370255,curve=P256),True)
  File "/home/ubuntu/.local/lib/python3.6/site-packages/fastecdsa/point.py", line 34, in __init__
    'coordinates are not on curve <{}>\n\tx={:x}\n\ty={:x}'.format(curve.name, x, y))
ValueError: coordinates are not on curve <P256>
        x=f9c36f8964623378bdc068d4bce07ed17c8fa486f9acc2613ca3c8c306d7bb6
        y=1cd36717b8ac5e4fea8ad23dc8d0783c2318ee4ad7a8db6e026ad0b072a24f

-----------
About the curves:
<! Actually it seems the same>
<!-- curve uses a different seed and the wieserstrauss curve:>
https://nvlpubs.nist.gov/nistpubs/SpecialPublications/NIST.SP.800-186-draft.pdf   (page 13)

<compare to>
https://csrc.nist.gov/csrc/media/publications/fips/186/3/archive/2009-06-25/documents/fips_186-3.pdf
====================

For each Weierstrass curve,  505 E :  y2≡x3 +ax +b (modp)

----------


        The check is done by evaluating the curve equation :math:`y^2 \equiv x^3 + ax + b \pmod{p}`
        at the given point :math:`(x,y)` with this curve's domain parameters :math:`(a, b, p)`. If
        the congruence holds, then the point lies on this curve.

note: I also tried other public keys:
(from the other crypto chip)
uint8_t publicKey[64] = {
0x39, 0xE6, 0x20, 0xFF, 0xF1, 0x5E, 0x20, 0xD6, 0x75, 0x2D, 0xEA, 0x9F, 0xFB, 0xA1, 0xD0, 0x6C,
0x07, 0x3A, 0x9F, 0x7F, 0xC8, 0xA5, 0xC0, 0x5A, 0x33, 0xA8, 0x61, 0x19, 0x5B, 0x32, 0xAD, 0xF1,
0x8D, 0xAC, 0x82, 0x91, 0x04, 0x0B, 0x72, 0x95, 0xE7, 0xFE, 0x23, 0xF3, 0x0F, 0x06, 0xE2, 0xAD,
0x47, 0x9F, 0x4E, 0xC6, 0x65, 0xC1, 0xD4, 0xC7, 0x5A, 0x58, 0x30, 0x5A, 0x81, 0x65, 0x03, 0xDD
};

(from the SparkFun Example)
https://learn.sparkfun.com/tutorials/cryptographic-co-processor-atecc508a-qwiic-hookup-guide/example-3-verify

The public key here works:
https://stackoverflow.com/a/30455259
Maybe the cryptographic authentication chip is producing public keys that are not on the curve. Why?

replicating writeup from fastecdsa (AntonKueltz/fastecdsa#57):

"This involves importing a public key from the cryptographic chip ATECC508A into the library. I found I had a public key that was generated using the p-256 according to the chip documentation, yet the fastecdsa library tells me that the point is not on the curve.

I created a gist to describe my procedure:
https://gist.github.com/bshambaugh/6f0fe5a63f96b0e0a95b404cc103e9c4

As well as my broader (newbie) exploration:
https://raptorlicious.blogspot.com/2020/07/bringing-together-last-3-cryptography.html

If this is out of scope, is there a better place for this question? Thanks for your time."

Here is a github issue for a library called cryptoauthlib which is made by the manufacturer of the ATECC508A. It talks about the format of the public key. Maybe I could use the public keys mentioned in here to get something that might work:
(MicrochipTech/cryptoauthlib#11)

Solved:
https://forum.sparkfun.com/viewtopic.php?f=102&t=53408&p=217284#p217284