Verifying G on y² = x³ + 7 mod p

[Harald1970]

Hi guys,

About the elliptic curve y² = x³ + 7 mod p Bitcoin uses:

As i understood base point G should be on that curve where point G should have the following coordinates:

x = 79BE667EF9DCBBAC55A06295CE870B07029BFCDB2DCE28D959F2815B16F81798
y = 483ADA7726A3C4655DA4FBFC0E1108A8FD17B448A68554199C47D08FFB10D4B8

In decimal format:

x = 55066263022277343669578718895168534326250603453777594175500187360389116729240
y = 32670510020758816978083085130507043184471273380659243275938904335757337482424

and p should be:

2^256 – 2^32 – 977 = 115792089237316195423570985008687907853269984665640564039457584007908834671663

However, when I enter these values in the equation (y² = x³ + 7 mod p)

(32670510020758816978083085130507043184471273380659243275938904335757337482424)² mod 115792089237316195423570985008687907853269984665640564039457584007908834671663 = (55066263022277343669578718895168534326250603453777594175500187360389116729240)³ + 7 mod 115792089237316195423570985008687907853269984665640564039457584007908834671663

I come to a totally different conclusion.

Namely:

32748224938747404814623910738487752935528512903530129802856995983256684603122 =
1669770616981538039777298102996166657201110805898885633627016627799942916593334 7716953447757272370428515427513339781177865265195629184436663606848320359309455 8427352525126936769086968791554813695916119291254705683450242657305024007

So what did i do wrong?

[BlackHatCoiner]

So what did i do wrong?

In here, you're mod-ing 7 with p instead of (x³ + 7) with p:

(55066263022277343669578718895168534326250603453777594175500187360389116729240)³ + 7 mod 115792089237316195423570985008687907853269984665640564039457584007908834671663

If you mod (x³ + 7) with p, you will, indeed, get:

Code:

32748224938747404814623910738487752935528512903530129802856995983256684603122

[garlonicon]

1669770616981538039777298102996166657201110805898885633627016627799942916593334
7716953447757272370428515427513339781177865265195629184436663606848320359309455
8427352525126936769086968791554813695916119291254705683450242657305024007

Just use modulo on that number and it will be correct. You used modulo on x-value, but not on y-value, so they are obviously not equal.

Edit:

you're mod-ing 7 with p

You are right, using 7 modulo something bigger than 7 does not change anything.

[Harald1970]

Thank you guys! What harm a simple bracket at the wrong place can do!