ECDLP Quantum Cryptanalysis

We demonstrate genuine quantum cryptanalysis of the Elliptic Curve Discrete Logarithm Problem up to 14 bits on IBM's 156-qubit Heron R2 processor. Unlike planted-key demonstrations, our implementation uses a full group operation oracle that recovers private keys without prior knowledge. We establish that algorithm structure dictates optimal transpilation: SABRE achieves 47% gate reduction over HOT for QFT-dominated circuits. Our key finding reframes success metrics—at 14 bits, the correct key ranked #535 among 1,806 candidates, yet provided 9.1× keyspace reduction. All results are independently verifiable via IBM Quantum Platform job artifacts.