Two new whitepapers show that quantum computers could crack vital elliptic-curve cryptography with far fewer resources than previously estimated. One study using neutral atoms suggests breaking 256-bit ECC in 10 days with under 30,000 physical qubits. Google researchers outlined a method to target bitcoin's secp256k1 curve in under 10 minutes using about 500,000 physical qubits.
Researchers have demonstrated that neutral atoms trapped in optical tweezers can serve as reconfigurable qubits, allowing all qubits to interact freely. This approach enables more efficient error correction compared to superconducting qubits limited to nearby neighbors. Their analysis, titled 'Shor’s algorithm is possible with as few as 10,000 reconfigurable atomic qubits,' concludes that fewer than 30,000 physical qubits could break 256-bit elliptic-curve cryptography (ECC) in 10 days—a 100-fold reduction in overhead from prior estimates. The team noted that arrays exceeding 6,000 qubits have already been built and urged a shift to post-quantum cryptography standards. “Appropriately designed neutral-atom architectures could support cryptographically relevant implementations of Shor’s algorithm,” the researchers wrote. Separately, Google researchers improved Shor’s algorithm to solve the elliptic-curve discrete logarithm problem over secp256k1, the curve securing bitcoin and other blockchains. They described two quantum circuits: one with fewer than 1,200 logical qubits and 90 million Toffoli gates, the other under 1,450 logical qubits and 70 million gates, requiring roughly 500,000 physical qubits—20 times fewer resources than 2003 estimates. Google withheld algorithmic details, releasing a zero-knowledge proof instead, citing risks of misuse by adversaries. The team consulted the US government and argued that progress now warrants limiting disclosures on quantum cryptanalysis. Brian LaMacchia, a cryptography expert formerly at Microsoft, said the papers show steady advances in qubits and algorithms toward practical cryptographically relevant quantum computing. However, Matt Green of Johns Hopkins University called Google's caution alarmist and more hype than substance. LaMacchia also questioned the focus on cryptocurrencies over broader public-key systems.