When Breaking Elliptic Curve Cryptography (ECC) is a Piece of Cake Linearizing secp256k1 through Midpoint Symmetry

Standard cryptographic security relies on the assumption that discrete points on an elliptic curve lack a visible causal connection, rendering brute-force attacks impossible. This paper challenges that paradigm treating the Generator not as a static point, but as a dual-coordinate gear defining rotation and descent. By establishing a "Sovereign Midpoint" as an absolute reference, the perceived complexity of the secp256k1 curve is reduced to a linear measurement. Using a stylized 11-unit model and empirical proof for secp256k1, the author demonstrates that every private key functions as a simple index number in a symmetric field. By mapping the "Minimum Pulse" of the Y-coordinate horizon, the search space is transformed into a "Double-Sided Ruler," where any public key can be identified as a specific offset from the center. This approach effectively converts the discrete logarithm problem into a straightforward task of surveying and counting, rendering traditional ECC encryption as simple as a "straight line."