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## About GEECM  

GEECM (Grovers Algorithm on Edwards Curves for Elliptic Curve Factorization Method) is a hybrid quantum-classical factorization method designed to efficiently break elliptic curve cryptography using near-term quantum hardware. By applying Grover’s search algorithm to the classical ECM workflow on highly efficient Edwards curves, GEECM reduces quantum resource requirements while exposing vulnerabilities in widely deployed cryptosystems.  

**Innovation**:  

- 50% lower quantum gates vs. Shor’s for 1024-bit RSA.  

- Attack path for ECC keys using twisted Edwards curves.  

- Open-source Qiskit/PennyLane implementations.  

**Impact**: 

Informs post-quantum standardization (NIST PQC) and defends against quantum adversaries.