Update cryptography.adoc

[feltroidprime]

Description of the Changes

Add information about the curve order.

PR Preview URL

https://starknet-io.github.io/starknet-docs/pr-1625/architecture-and-concepts/cryptography/#the_stark_curve

Check List

• Changes made against main branch and PR does not conflict
• PR title is meaningful, e.g: minor typos fix in README
• Detailed description added under "Description of the Changes"
• Specific URL(s) added under "PR Preview URL"

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This change is 

[starknet-bot]

Oops, your pull request failed to pass the Typo tests stage :( . see the result:
error: DECALRE should be DECLARE
--> ./components/Starknet/modules/architecture-and-concepts/pages/network-architecture/starknet-state.adoc:52:21
|
52 | * stem:[$tx$] is a DECALRE transaction, and stem:[$S'$] contains the class hash and definition in the contract class's mapping
| ^^^^^^^
|

Please fix the typo, commit and push!

[starknet-bot]

Oops, your pull request failed to pass the Typo tests stage :( . see the result:
error: DECALRE should be DECLARE
--> ./components/Starknet/modules/architecture-and-concepts/pages/network-architecture/starknet-state.adoc:52:21
|
52 | * stem:[$tx$] is a DECALRE transaction, and stem:[$S'$] contains the class hash and definition in the contract class's mapping
| ^^^^^^^
|

Please fix the typo, commit and push!

[starknet-bot]

Oops, your pull request failed to pass the Typo tests stage :( . see the result:
error: DECALRE should be DECLARE
--> ./components/Starknet/modules/architecture-and-concepts/pages/network-architecture/starknet-state.adoc:52:21
|
52 | * stem:[$tx$] is a DECALRE transaction, and stem:[$S'$] contains the class hash and definition in the contract class's mapping
| ^^^^^^^
|

Please fix the typo, commit and push!

[starknet-bot]

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[starknet-bot]

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[starknet-bot]

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[LandauRaz]

Hey @feltroidprime, thanks for the contribution 🙏
The typo has been fixed, but regarding the info about the number of points on the STARK curve:

1. Can you add more information on how you got to it?
2. Why did you feel adding this info was necessary in the first place?

[feltroidprime]

Hey @feltroidprime, thanks for the contribution 🙏 The typo has been fixed, but regarding the info about the number of points on the STARK curve:

1. Can you add more information on how you got to it?

2. Why did you feel adding this info was necessary in the first place?

1 . It can be verified by pasting this SageMath snippet ( https://sagecell.sagemath.org/ ) :

a = 1
b = 3141592653589793238462643383279502884197169399375105820974944592307816406665
p = 2^251 + 17*2^192 +1

E = EllipticCurve(GF(p), [0,0,0,a,b])
print(E)
n=E.order()
print(f"order = {n}")
print(f"      = {hex(n)}")
print(f"order is prime: {n.is_prime()}")

output:

Elliptic Curve defined by y^2 = x^3 + x + 3141592653589793238462643383279502884197169399375105820974944592307816406665 over Finite Field of size 3618502788666131213697322783095070105623107215331596699973092056135872020481
order = 3618502788666131213697322783095070105526743751716087489154079457884512865583
      = 0x800000000000010ffffffffffffffffb781126dcae7b2321e66a241adc64d2f
order is prime: True

2. Short answer : because I was looking for it, so other might too.

The order of an elliptic is a standard information, for most (if not all) algorithms using an elliptic curve, the order is needed (signatures like ecdsa, zk-proof, etc).

See https://github.com/xJonathanLEI/starknet-rs/blob/194631520a02ce0f0b7c7bd3784831047bc43eac/starknet-crypto/src/rfc6979.rs#L7 for example.

[LandauRaz]

Got it, thanks for the clarification, and thanks again for the contribution!

[starknet-bot]

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