Title: Verifying G on y² = x³ + 7 mod p Post by: Harald1970 on December 09, 2021, 08:12:50 PM 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? Title: Re: Verifying G on y² = x³ + 7 mod p Post by: BlackHatCoiner on December 09, 2021, 08:21:10 PM So what did i do wrong? In here, you're mod-ing 7 with p instead of (x3 + 7) with p:Quote (55066263022277343669578718895168534326250603453777594175500187360389116729240)³ + 7 mod 115792089237316195423570985008687907853269984665640564039457584007908834671663 If you mod (x3 + 7) with p, you will, indeed, get: Code: 32748224938747404814623910738487752935528512903530129802856995983256684603122 Title: Re: Verifying G on y² = x³ + 7 mod p Post by: garlonicon on December 09, 2021, 08:24:29 PM Quote 1669770616981538039777298102996166657201110805898885633627016627799942916593334 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.7716953447757272370428515427513339781177865265195629184436663606848320359309455 8427352525126936769086968791554813695916119291254705683450242657305024007 Edit: Quote you're mod-ing 7 with p You are right, using 7 modulo something bigger than 7 does not change anything.Title: Re: Verifying G on y² = x³ + 7 mod p Post by: Harald1970 on December 09, 2021, 09:18:42 PM Thank you guys! What harm a simple bracket at the wrong place can do! 8)
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