Elliptic Curve Algebra ⎯ to understand the material presented, please familiarize yourself with the basic operations.

Elliptic Curve Digital Signature Algorithm

ECDSA ⎯ implementation of the Digital Signature Algorithm on an Elliptic Curve.

Elliptic Curve parameters

Elliptic Curve Y2 = X3 + a × X + b (mod MEC)
Y2 = X3 + × X + ( mod )
Base point G(x,y)
x y GOrder

The initial values ​​correspond to the Elliptic Curve parameters for Bitcoin.

Keys

Alice's Secret key ⎯ Point coordinates Ap = As * G

Try entering the following numbers in sequence (as Alice's secret As) and compare the result with point G
1
2
115792089237316195423570985008687907852837564279074904382605163141518161494336
115792089237316195423570985008687907852837564279074904382605163141518161494337
115792089237316195423570985008687907852837564279074904382605163141518161494338
115792089237316195423570985008687907852837564279074904382605163141518161494339

Enter 123 and check the resulting coordinates in Google.

Signing a Message

⎯ Nonsense coordinates R = k * G ⎯ r = Rx (mod GOrder) Message ⎯ S = k-1 * ( Msg + As * r )

Signature Verification

⎯ W = S-1 = SOrd-2 (mod Ord) = Msg * W (mod Ord) = R * W (mod Ord) ⎯ H = U₁ * G + U₂ * Q, addition of a pair of points on an elliptic curve
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