studying – Inconsistent habits testing Taproot Workshop – Part: 0.2 Elliptic Curve Math

Workshop hyperlink: https://github.com/bitcoinops/taproot-workshop/

Within the part 0.2.4 Programming Train: Distributivity of scalar operations we implement the next code:

a_key = ECKey().set(a)

b = random.randrange(1, SECP256K1_ORDER)
b_key = ECKey().set(b)

c = random.randrange(1, SECP256K1_ORDER)
c_key = ECKey().set(c)

# Left: Compute a - b as ints (modulo the sepc256k1 group order)
a_minus_b =  (a - b) % SECP256K1_ORDER# TODO: implement

# Left: Compute (a - b) * c as ints (modulo the sepc256k1 group order)
left =  (a_minus_b * c) % SECP256K1_ORDER# TODO: implement

# Proper: Compute a * c - b * c as ECKeys
proper = (a * c % SECP256K1_ORDER) - (b * c % SECP256K1_ORDER) # TODO: implement 
#when you dont modulo curve order in each parenthesis your quantity (in all probability) turns into too giant for the curve
#subsequently calling .secret on it is not going to work even when you forged it to ECKey Object (so the assertion can not even occur on this case)
#you'd solely be capable to name .secret on a price throughout the curve order

print("Left: {}".format(left))
print("Proper: {}".format(proper))


proper = ECKey().set(proper)
# Left/Proper: Assert equality
assert left == proper.secret
print("nSuccess!")

Word that the traces with #TODO: implement are the one ones I’ve modified.

When making an attempt this code block a number of instances I seen that it fails sometimes with:

Left: 84229569338898829804715923445734053841060795723920762893503652295039608159004
Proper: -31562519898417365618855061562953854011776768555154141489101510846478553335333
---------------------------------------------------------------------------
AttributeError                            Traceback (most up-to-date name final)
Cell In[32], line 28
     26 proper = ECKey().set(proper)
     27 # Left/Proper: Assert equality
---> 28 assert left == proper.secret
     29 print("nSuccess!")

AttributeError: 'ECKey' object has no attribute 'secret'

The attribute error means that the generated secret is outdoors the curve order and was not correctly was the ECKey

However for a minimum of 50% of the time it returns one thing like:

Left: 51082417157028894624564857296082907029625179491897309339882235219613900809295
Proper: 51082417157028894624564857296082907029625179491897309339882235219613900809295

Success!

What’s inflicting this inconsistency?